CALIFORNIA PATH PROGRAM INSTITUTE OF TRANSPORTATION STUDIES UNIVERSITY OF CALIFORNIA, BERKELEY Micro-simulation Modeling Approach Applications of On-line Simulation and . 0 Ztftf^f" I to Data Fusion LianyuChu Will "?*e\ Recker California PATH Research R e p o r t UCB-ITS-PRR-2004-1 * * This work w a s performed as part of the California PATH Program of the ^O University of California, in cooperation with the State of California Business, Transportation, and Housing Agency, Department of Transportation; and the United States Department of Transportation, Federal H i g h w a y Administration. T h e contents of this report reflect the views of the authors w h o are responsible for the facts and the accuracy of the data presented herein. T h e contents do not necessarily reflect the official views or policies of the State of California. T h i s report does not constitute a standard, specification, o r regulation. Final Report for Task Order 4 1 4 3 January 2 0 0 4 ISSN 1055-1425 CALIFORNIA PARTNERS FOR ADVANCED TRANSIT AND HIGHWAYS V ^J&* ^ J^ (. -* Final R e p o r t for T04143 Micro-simulation M o d e l i n g A p p r o a c h to of On-line Simulation a n d D a t a Lianyu Chu and Will Fusion Recker California P A T H A T M S Institute of Transportation Center Studies U n i v e r s i t y o f California at Irvine Irvine, CA Applications ACKNOWLEDGEMENTS Scott Aitken and E w a n Speirs, from Quadstone in Scotland, provided invaluable technical supports in the process o f applying the P A R A M I C S model. Their continuous collaboratiori to the project greatly facilitated the work. 11 EXECUTIVE SUMMARY This r e p o r t s u m m a r i z e s research w o r k conducted under X0.4143 at the California P A T H A T ^ I S Center at the University^of California, Irvine. This project has two tasks: • Functionality enhancements of the P A & A M I C S simulation m o d e l through A P I -- programming for the on-line simulation application; Vf • On-line data fusion algorithm for a better section travel t i m e estimation based o n •point-detector, data and probe vehicle data. In order to cpntjuct these two tasks, w e complete the following two related studies, w h i c h are the basis of the two, tasks of this project: • .Development ofrthe capability-enhanced P A R A M I C S singulation environment through.API p r o g r a m m i n g ; • Calibration and validation of microscopic simulation m o d e l s . in Contents t i \ CONTENTS..: t s X 1 C H A P T E R 1. I N T R O D U C T I O N 3 C H A P T E R 2: D E V E L O P M E N T O F T H E C A P A B I L I T Y - E N H A N C E D PARAMICSSIMULATION ENVIRONMENT 5 2.1 n s r M o b u t r n o N 2.2 F R A M E W O R K O F C A P A B I L I T Y E N H A N C E M E N T S 2.2.1 Overview of PARAMICS . ' 2:2.2Hbw'APl works in PARAMICS 2.2.3 Aspects of PARAMICS need to be complemented and'enhanced 2.2.4 Framework...t...... 2.3 B A S I C M O D U L E S 2J.1 Basic control modules 2.3.2 Traffic Information Collection 2.3:3 Database connection 2.3.4 Performance measures 2.4. A D V A N C E D M O D U L E S 2.5 C O N C L U D I N G R E M A R K S 2.6 R E F E R E N C E S ^.~.T: C H A P T E R 3. C A L I B R A T I O N A N D V A L I D A T I O N O F M I C R O S C O P I C SIMULATION M O D E L ;..*. 3.1 I N T R O D U C T I O N 3.2 O V E R A L L C A L I B R A T I O N / V A L I D A T I O N P R O C E D U R E 3.2.1 Basic Data Input J NetworkVoding 3.2.2 Calibration of Driving Behavior Models 3.2.3 Calibration of the'Route Choice Behavior Model 3.2.4 OD Estimation 3.3 S T U D Y SITfe'AND C A L I B R A T I O N D A T A A C Q U I S I T I O N 3l.3.1 Study Site 3.3.2 Preparation of Calibration Data 3.3.3 Calibration Data Reduction 3.4. C A L I B R A T I O N 3.4.1 Basic Data Input /Network Coding 3.4.2 Calibration of Driving Behavior Models 3.4.3 Calibration of Route Choice Model 3.4.4 OD Estimation 3.4.5 Model Fine-tuning 3.5. O V E R A L L M O D E L V A L I D A T I O N 3.5.1 Determination of Number of Simulation Runs 3.5.2 Validation Results 3.6. C O N L U D I N G R E M A R K S 5 6 6 6 6 9 10 W 13 14 14 15 16 17 18 18 19 19 19 19 19 22 23 23 24 24 24 25 25 ,25 30 30 30 31 35 3.7 R E F E R E N C E S 35 CHAPTER 4 ON-LINE SIMULATION 4.1 F R A M E W O R K O F O N - L I N E S I M U L A T I O N I N P A R A M I C S 4.2 L O O P D E T E C T O R D A T A P R O C E S S I N G 4.3 T R A F F I C F L O W P R E D I C T I O N 4.3.1 Introduction .• * 4.3.2 Kalman Filtering basedprediction method..* 4.3.3 Solution Jo the Kalman filter based'prediction 4 ; 4 0 D ESTIMATION MODEL ...'. -.: .-. 4.4.1 Volume conservation J?„ 4.4.2 Model for distributing off-ramp traffic-to upstream zones 4.5 D E M A N D L O A D I N G / V E H I C L E R E L E A S I N G ' . < . 4.5.1 Random model' 4.5.2 Constant headway model 4.5.3-Composite model 4.5.4 Random number generator 4.6 R E F E R E N C E S . . / . -. 38 : 38 39 40 41 41 42 43 43 44 44 44 45 45 46 46 C H A P T E R 5. ftATA F U S I O N F O R B E T T E R T R A V E L T I M E E S T I M S t l O N . . . . 4 9 5.1 INTRODUCTION.,.,..., 5.2. M E T H O D O L O G Y * , 5.2.1 Kalman Filter 5.2.2 Application of Kalman Filter to the Section Travel Time Estimation 5.2.3 Adaptive Kalman Filter:, estimation of noise statistics 5.2.4 Summary of the AKFfusion algorithm 5.3. E V A L U A T I O N -. , 5.3.1 Study Site .,-. 5.3.2 Travel Time Estimation Methods 5.3.3 Performance Indices 5.3.4 Evaluation Scenarios 5.3.5 ^valuation Results v ; 5.4 C O N C L U D I N G R E M A R K S ; 5.5 R E F E R E N C E S 49 50 50 51 54 56 56 56 57 60 60 61 65 66 ' ' -UK J ,i H .1 C h a p t e r 1. I n t r o d u c t i o b u j. '.This; study focuses;ori>the/use i of'micr.oscppic simulation, i.e. P A R A M J C S , a s : a . t o o ^ f o r on-line,simulation a n d data-fusioa studies, undej: ^ t r a f f i c syste,m w i t h various. Intelligent Transportation* S y s t e m s ..(ITS) .components. -These IT^,qojnp,onents, 1 include^actuated- / <adaptive'signal control, ramp> metering, ftaffic suryeiltenee catneras, C h a n g e a b l e M e s s a g e Sign (CMS)/rtooprdetector data 1 collection,,and^tjie fl-S c o m m u n i c a t i o n system> ( A Traffic M a n a g e m e n t Center, can o b t a m traffic .data frpm m u l t i p l e sQurces. ano^control,/ m a n a g e traffic:.This k i n d ' o f traffic s y s t e m , h a s i b e e n - i m p l e m e n t e d in .the real w,orld. J n o r d e r t o emulate.this ITS^ready t r a f f i d s y s t e n v t b e capabilities o f c o m m e r c i a l P A R A M I Q S m o d e l needsSOJOQ e n h a n c e d through £ P I - p r o g r a m m i n g . A s e r i e s o f A P I p l u g i n s are d e v e l o p e d for this purpose. ;, .Aj simulation m o d e l o f ^the, t a r g e t . n e t w o r k , w h i c h c a n . b e established u n d e r this I T S capable. traffic simulation- model'*- n e e d s t o b e ftalibrated-fiisti Ojhe,rwise, it*cahnoJ-fee-used fociany .application., D u e ; t p t h e lack o f . s y s t e m a t i c rules/and guidelines, o f calibration and validation o f Jraffifc m o d e l s , A . g e n e r i c appxfiach^that is., suitable fQr a n y m i c r o s c o p i c simulation .-models is proposed. This m u l t i - s t a g e p r o c e d u r e -is d e m o n s t r a t e d gin a .caIihration.study w i t h . a corridor n e t w o r k o f t h e southern California in P A R A M I C S . ? '• * * B a s e d o n a calibrated n e t w o r k with v a r i o u s I T S c o m p o n e n t s , w e c a n i m p l e m e n t a n d evaluate a v a r i e t y o f A d v a n c e d T r a n s p o r t a t i o n and Information S y s t e m s ( A T M I S ) applications. T h i s project o n l y focuses o n s t u d i e s o n t h e o n - l i n e s i m u l a t i o n a n d d a t a fusion for a b e t t e r section travel t i m e estimation b a s e d o n p o i n t detector data a n d p r o b e vehicle data. Potentially, t h e o n - l i n e si m u l a t i o n c an b e u s e d t o p r o y i d e r eal-time t raffic i riformation and select t h e oest control and m a n a g e m e n t strategies a c c o r d i n g to t h e Jesting simulation r u n s o f candidate control strategies u s i n g predicted traffic d e m a n d s . T h e task o f this project is'to e n h a n c e the capabilities o f P A R A M I C S to enable its application for on-line simulation. W e establish t h e c o n n e c t i o n b e t w e e n r e a l - w o r l d l o o p detector d a t a and simulation. A- simple O D estimation m e t h o d is developed for t h e estimation o f d y n a m i c O D d e m a n d m a t r i c e s for a freeway n e t w o r k b a s e d o n real-world l o o p detector data. A K a l m a n filtering b a s e d traffic flow prediction algorithm is also developed. T h e predicted traffic flows"serve for t h e prediction o f future d e m a n d matrices. I n t e r m s o f t h e d e m a n d loading or vehicle releasing from a zone, P A R A M I C S releases v e h i c l e s b a s e d o n r a n d o m n u m b e r s . O u r d e m a n d loading m o d e l m a k e s is possible for P A R A M I C S to release vehicles based on a certain distribution, i.e. t h e h e a d w a y b e t w e e n t w o adjacent vehicles subject to a c o m p o s i t e m o d e l , w h i c h is a c o m b i n a t i o n o f shifted n e g a t i v e e x p o n e n t i a l distribution (under v e r y l o w traffic flow condition) and n o r m a l distribution with t h e m e a n o f a constant h e a d w a y (under congested or saturated traffic condition). T h e data fusion study o f this project is motivated b y the recent advances in surveillance technologies, such as Global Positioning Systems (GPS), Automatic Vehicle Identification ( A V I ) , a n d vehicle re-identification. These- technologies 'promise High accuracy traffic information; however, their performance in field is insufficient yet m o s t l y d u e to the lack of probe vehicles. Meantime, the m o s t prevailing traffic surveillance system in the world is t h e conventional inductive loop detector system although this s y s t e m often fails to p r o v i d e accurate measures:* W e discuss h o w ^ o . i m p r o v e travel t i m e estimates from loop J detectors b y incorporating data from advanced surveillance technology, 1 a n d p r o p o s e a data fusion m e t h o d based o n Adaptive "Kalman Filter ( A K F ) t e c h n i q u e that dynamically calculates data noise vaYiancesibyadapting-to the r e a l - t i m e data. T h e p r o p o s e d algorithm is t e s t e d ' a n d evaluated under b o t h recurrent a n d non-recurrent ^congestion rising the-enhanced P A R A M I C S simulation* model. In this study, a s a m o s t p l a u s i b l e case, w e use* two-different sources o f data: o n e from loop detectors and t h e other from a small sample *of probe*vehicles. T h e evaluation results sho*w that t h e p r o p o s e d fusion algorithm significantly i m p r o v e s section travel t i m e estimates c o m p a r e d to t h e cases w h e n single data source is used. T h i s report is" organized as follows^ Chapter 2 d e s c r i b e s " o u r development of the capability-*enhanced P A R A M I C S singulation environment through A P I programming. Cfiapter : 3 p r o p o s e s a general a p p r o a c h ' t o calibrate and* validate microscopic; "simulation m o d e l s a n d p r o v i d e s a n e x a m p l e calibration study under P A R A M I C S environment. C h a p t e r '4 e x p l a i n s ' h o w w e erihance the capabilities of P A R A M I C S in order to m a k e it fit to t h e n e e d s of on-line simulation. Chapter 5 presents 'our-efforts on the. development of data fusion algorithm that can provide a better estimation o f section travel time. I > 1 ••* ' i '' ' t t f 1 f -I I ,-)* 'f I a* 'Ut .u '•n C h a p t e r 2. Devfeldpment of t h e C a p a b H i ^ E n h a n c e d ^ARAIVIltS Simulation Environment $ i 1 ». ./ " 2.1 I N T R O D U C t i O N Microscopic traffic simulation is a software tool to model' the* real-world trdffic system, including the road, drivers, and vehicles, in fine details. In the micro-simulation process, includ m e sti oasea1* accejStanbe ^models *hxe the basic elements of a microscopic- tftCffic' simulator. "(Notable instances of* micro-simulators i n c l i n e * ' P A R A f a l C S ; COKLSIM; V l S S I M ; A I M S U N 2 , T R ^ N g B ^ / a n d ' I v l l f S I M (i]: With 1 " the 'advancements " o f c o m p u t e r technology,' micro-simulation "has b e c o m e a n increasingly popular and e'ffective'tool for marly 'applications'; which*- are n o t aniendable to study b r o t h e r ineahs. For the academic side1, one" application is to test new-traffic nio'dels. For t h ? practical' side, m o s t applications are m e ^evaluation "(and development) o f Intelligent T r a h s p o r t a t i o n ^ y s t e m s (ITS^becaiise theyaPe v difficult to-be evaluated in 1 t h e field operational tests and they need cost-benefit analyses before their implementation [2]. In general, ITS involves the introduction of a variety of advanced technologies, such as information'tecnnologies, to t h e transpbrtltion-systerh in order t o - m a k e ' t h e existing road network, o'e efficiently used. Typical I T S applications'"include adaptive 'signal control, r a m p metering, ! and"dynamic r6ute gUidarfce system; fetd. O n e of their c o m m o n "features is mat thev'need the real-time traffic information," generally collected b y detectors o r p r o b e vehicle's. For a complex' ITS'^strategy, 'such as Changeable M e s s a g e Sign ( C M S ) routing, n o ? only drivers' Behaviors a n d ' r o u t e s b u t also*!traific" control 'facilities need to b e controlled. Inbugh*current micro-simulators have enabled a lot of ITS features, it is still impossible to implement a complicated ITS strategy b y the micro-simulatdr itself. The'direct w a y t o ' e n h a n c e the capabilities of a1 micro-simulator is to w o r k ' o n the source codes. Another w a l l s ' to code cofhplerrientary' of E n h a n c e d c o m p o n e n t s through A p p l i c a t i o n ' P r o ^ a m m i r i g Interface (API)' p r o g r a m m i n g - a n d then interface t h e m to t h e simulator! Sirice t h e ' s o u r c e c o d e is p r o p r i e t a r y / A P I p r o g r a m m i n g is a practical w a y for users. API* p r o g r a m m i n g needs to u'se provided A P P library 'of 'a micro- simulator^ w h i c h includes a Iset of interface functions, through w h i c h users c a n access the b o r e m o d e l s o f t h e micro-simulator. M o s t current popular commercial micro-simulators,' 'including P A R A M I C S , VISSIM, and A I M S U N 2, provide a series of their A P I functions for users. This chapter will* describe our practices on developing a capability-enhanced P A R A M I C S simulation environment through A P I p r o g r a m m i n g . It is organized as follows. First, w e will give a b r i e f overview o f t h e micro-simulator, P A R A M I C S , u s e d for t h e c apability enhancements. W e e xplain h o w A P I w orks i n P A R A M I C S , i n w hat aspects w e enhance the capabilities of P A R A M I C S , and the framework o f the capabilitye n h a n c e d PARAMICS„simulation Environment-. Then, w e describe the basic enhancement m o d u l e s in m o r e details. T h e advanced modules, developed o n t o p o f b a s i a m o d u l e s , are further introduced. Finally, concluding r e m a r k s are presented. 2.2 F R A M E W O R K O F C A P A B I L I T Y ENHANCEMENTS i > 2.2.1 Overview o f P A R A M I C S i t P A R A M I C S ( P / t R A l l e l M I C r o s c o p i c Simulation) is a, s p i t e of microscx>pic t simulation tools used to m o d e l t h e moyenjenti and behavior o f i n d i v i d u a l yehiple.s on urban and h i g h w a y road n e t w o r k s [3]. It offers, v e r y plausibly detailed m o d e l i n g for . m a n y c o m p o n e n t s of the,traffic -system. Npt^only the characteristics o f drivers, vehicles, and t h e interactions between vehicles b u t also the network geometry can influence simulation results. P A R A M I C S is fit to ITS studies d u e to its high performance, scalability and the ability o f m o d e l i n g the e m e r g i n g ITS infrastructures, s u c h as loop detectors and V M S . In addition, P A R A M I C S proyides users w i t h A P I through w h i c h users can customize and extend m a n y features o f the underlying simulation m o d e l without h a v i n g ^ q deal with the u n d e r l y i n g proprietary code. T h o u g h P A R A M I C S can m o d e l s o m e simple ITS strategies, A P I p r o g r a m m i n g is eventually required to implement m o r e complicated ITS strategies., 2.2.2 H o w A P I w o r k s in P A R A M I C S P A R A M J C S provides users w i t h an A P I library that include a set of interface functions, w h i c h caiffce used to access its core,models. Basically, PARAMICJ3 provides two g r o u p s of interface functions ? callback functions and .control functions. The. callback functions are u s e d for p r o v i d i n g a n f o r m a t i o n about u i e attributes o f v e h i c l e s a n d their environment. There % are ,two types o f control, functions, override and overload functions. Override functions are used"to replace an internal function o f standard simulation loop„such as carfojjowing models.* p v e r j p a d j u n c t i o n s are used to add, a d d i t i o n a l functions to the P A R A M I C S simulation loop. . . r „ , , A s s h o w n in Figure 2-1, the simulation process is like this^afjer the start,of simulation, s o m e b a s i c elemente.of.the simulation, such.as the speed and, position of yetycles^traffic signals, etq., a r e - u p d a t e d a t every time,, step. I f an A P I m o d u l e . i $ r i n y o j v e d in the simulation, it m a y , w o r k at ev^ry time step", or be triggered aj a,specific simulation t i m e orj b y a .specific event. I n ..general, an. a\PI m o d u l e .gets necessary infprmatjon from the] simulation world through callback f u n c t i o n , a n d then a f f e c t s ' t h e - s i m u l a t i o n through] control functions. ~ -> ;o» « t 0 2.2.3 A s p e c t s o f P A R A M I C S nee$l-to b e complemented and enhanced^ r* Tach micro-simulator Has its'-own features to-simulate the r e a l - w o r l d traffic.-Specifically pop P A R A M I C S , m a n y - a s p e c t s £ f P A R A M I C S n e e d ' t o i b e r c o m p l e m e n t e d - a n d enhanced [through A P I p r o g r a m m i n g in o r d e r t d . b e t t e r m o d e M T S i O u r current efforts are limited to I the following basic aspects of the software. * U p d a t e vehicles and their environment at e v e r y time step: ' "S3 Callback << en i = 5> 6 "• i Override *~~ Overload I I •< X* **1 I I O t h e r applications e.g. database Figure 2.1 T h e P A R A M I C S simulation p r o c e s s w i t h A P I m o d u l e s 2.2.3.1 Routing P A R A M I C S is a lirik-based simulator. Vehicles being simulated do n o t carry their w h o l e routes b u t decide thejr-route based on the routing table stored at each node, along its route. These routing tables are prejcalculated based on the currently used traffic assignment method. A path-based routing m e c h a n i s m is required fo/ the applications qf traveler information related ITS strategies, such as d y n a m i c route guidance or C M S routing. 2.2.3.2 Real-time traffic information collection T h e c o m m o n feature o f ITS,is that ITS needs the real-time traffic information, generally collected b y detectors o r probe, vehicles, for decision-making. P A R A M I C S can m o d e l loop detectors, the m o s t frequently used sensors in the real world. H o w e v e r , aggregated loop data, which are generally provided by freeway systems and can be used for real-time traffic control, c a n n o t b e obtained d i r e c t l y from P A R A M I C S simulation. Also, the c o n c e p t o f p r o b e v e h i c l e s needs, P A R A M I C S to track a certain percentage o f p r o b e vehicles- and extract travel t i m e or travel speed information from them. This cannot b e d o n e without the i n v o l v e m e n t of A P I p r o g r a m m i n g . 2.2.3.3 Signal control P A R A M I C S can basically m o d e l the fixed-time signal control. Besides, P A R A M I C S also p r o v i d e a plan/phase l a n g u a g e (i.e. a kind o f script language) to simulate some simple actuated signal control logics. However, in the field,, the w i d e l y used actuated signal controller uses t h e c o m p l e x N E M A logic or t y p e - 1 7 0 l o g i c , O u r "experiences found this script language is difficult t o b e used to m o d e l these c o m p l e x control logics and to replicate these logics to multiple signalized intersections. 2.2.3.4 R a m p m e t e r i n g control i P A R A M I C S can m o d e l fixed-time ramp metering with multiple timing plans. H o w e v e r , a ramp-metering controller, developed^ in P A R A M I C S A P I , is required for the support of development of adaptive r a m p ' metering -algorithms, w h i c h h a v e m o r e complicated control logics. T h e r a m p - m e t e r i n g cbntroller should p r o v i d e interface functions that c a n b e used for querying t h e old metering rate and s e t t i n g ^ n e w metering rate based on the adaptive r a m p m e t e r i n g algorithms. W h e n the adaptive ramp-metering algorithm is not activated, the fixed-time m e t e r i n g will b e the default control. 2.2.3.5 Database connection P A R A M I C S does n o t h a v e the capability to connect with a database. T h e advantage o f t h e u s e o f database i s that database c a n b e c o m e t h e m e d i u m w h e r e A P I m o d u l e s c a n e x c h a n g e data w i t h outside p r o g r a m s or applications. 2.2.3.6 Performance m e a s u r e P A R A M I C S h a s s t r o n g abilities o n the collection o f statistics data. Except some general performance data, P A R A M I C S can output link-based, trip-based, intersection : based, and detector-based data. H o w e v e r , the current difficulties are 1. W i t h the increase o f the size o f the network, 'the n u m b e r ' o f l i n t s / trips, intersections, a n d detectors increases drastically*in P A R A M I C S . 2. Large a m o u n t o f data-are required to b e processed after, simulation runs in order-to f J obtain the expected" performance measures-. 3. Some'f5er'formance measures, such as on-ramp waiting time, c a n n o t be extracted from output m e a s u r e m e n t data. 4. P A R A M I C S h a s a restriction on the n u m b e r 6 f ou'tfrat'files t o b e opened-during simulation u n d e r W I N D O W S version. T h e u s e ' o f A P I t o collect performance m e a s u r e s can effectively-decrease the amount of data'post-proc'essing w o r k s ' a n d obtain m o r e performance m e a s u r e s directly. •J * . , r 2.2.4 Framework - - , The above capability^enhancements-are- focused o n the^ba^iC 1 aspects o f the microsimulator, P A R A M I C S . - E a c h of these basic m o d u l e s refers tb an important aspect o f simulation. T hese functionality-jenhanc'ements c ( an b e e lassified i nto the following f o u r categories: i ' .__ 1. Basic control-modules, including signal, ramp m e t e r i n g a n d routing 2. Traffic information collection 3. Database connection • t *r 4. Performance measures J x * Figure 2.2 s h o w s 'the-framework-*)f the .capability-enhanced* P A R A M I C S simulation environment. A n y an A P I m p d i i l e j n th'e_eiman,ced~PARAMICS environment exchanges dynamic data with thefcore P A R A M I C S imodel and-other advanced Af(l m o d u l e s through the Dynamic Linking L i b r a r y (DLL) m e c h a n i s m ! Besides these basjc r m^dujes, ttie capability-enhanced P A R A M I C S -environment also includes advanced modules. Examples o f advanced m o d u l e s include r a m p metering algorithms, adaptive signal control, and integrated control, w h i c h include^several I T S components. These advanced m o d u l e s are developed on top o f .basic enhancement modules. This hierarchical A P I development approach, demonstrated in Figure 2.3, can thus re-use the codes developed in the basic modules. Advanced Modules Figure 2.2 Framework o f the capability-enhanced P A R A M I C S simulation Signal Provided A P I Library Ramp -*• Control Modules -> 1 1 w Basic modules r > w Data Handling w ^-w fr V Advanced Modules — Routing Loop... CORBA Database XML... Adaptive Signal Control / i f ' •l • Rantp'trfetering alg6rithms Integrated Control F i g u r e 2.3 T h e hierarchical A P I development approach 2.3 B A S I C MODULES 2.3.1 Basic control m o d u l e s 2.3.1.1 Full-actuated Signal Control T h i s plug-in m o d u l e i m p l e m e n t s the eight-phase, dual-ring, concurrent controller logic. T h e d a t a input t o t h i s A P I is t h e signal t i m i n g plan, t h e geometry a n d detector informatiorjbof e a c h intersection. Interface functions h a v e b e e n provided b y this A P I for external, m o d u l e s to acquire and change the default tjming plan. This A P I provided a couple of interface functions for external A P I m o d u l e s to acquire- the current signal t i m i n g plan and set a n e w j i m i n g p l a n to a specific signal. A n - a d v a n c e d signal control algorithm A P I c a n be-further developed b a s e d on them. T h e prototypes o f these, interface functions are s h o w n b e l o w [4], ' u S i g n a l * s,ignaKgetj)aranieters(char * n o d e N a m e ) ; Function: Q u e r y i n g t h e current signal t i m i n g p l a n o f a specific'actuated signal R e t u r n V a l u e : J h e - c u r r e n t t i m i n g p l a n o f a n .actuated signal. 10 Parameters: n o d e N a m e a s the .name of the signal n o d e : fa - wu S i g n a l is t h a s t r u c t u r e of actuated signal data,;whose definition is: type Signal - •//intersectionname t ahd"lo'cafion char *node; char *controllerLbcation; ((H *I r / \ II signal parameters * int movements[8]V float m a x i m u m G r e e n [ 8 ] ; float-minimumGreen[8]; - float ex(eh'sjon[8];" ' ?' fioVsWe&teip]; ' float pha^eGreenTirfie[8];-' float m o v e m e n t G r e e n T i m e [ 8 ] ; l // current p h a s e information int currentPhase; i n t expiredTimeJ '* float redTimeLeft;' B o o l cycleEhdFlag;' • V o i d s i g n a l _ s e t _ p a r a m e t e r s ( S i g n a I *sig); Function: - Setting a ' n e w tiniirig p l a n id zfspecific signal/ Return Value: N o n e " '" Parameters*! 1 sig stores the n e w t i m u i g p l a h . 2.3.1.2 Rdrhp-Met'ering'Coritr6l ' This plug-in module is designed to m o d e l pre-timed r a m p m e t e r i n g control on either onecar-per-green basis o r n-cars-pef-gre'eh basis (with n >'l)V'It'alsb s(i{)pofts'mulfiple.'timihg plans, H O V bypass, a n d the Us'e o f r a m p detedtofs for m e t e r i n g ' control. T h e data ifiput o f this A P I is a time-of-day r a m p control plan'ancfthe detect'of'ififormation'ofeach meter. In addition,-this A P T provided £ c 6 u p i e ' ' o f interface-functions for external A P I m o d u l e s to acquire the current metering rate and set a n e w metering 'rate* to a specific r a m p meter. A n advanced ramp-metering algorithm A P I can b e further developed based on these interface functions. T h e prototypes of t h e m are shown below. R A M P * r a m p _ g e t _ p a r a m e t e r s ( c h a r *rampnodje) / Function: Querying the current metering p l a n o f a specific'jamp meter. Return Value: The current metering control plan of an o n - r a m p signal. 11 m Parameters: r a m p n o d e is t h e n a m e o f an o n - r a m p signal node. R A M P is the structure o f r a m p control data, w h o s e definition is: type R a m p { // o n - r a m p signal n o d e n a m e a n d its location char *rampNode; char *controllerLocation; // r a m p control types and parameters int ControlType; float meteringCycle; }; W h e r e c o n t r o l T y p e is t h e ' s t a t u s , ( o r t y p e X o f the r a m p metering control, w h i c h c a n be 0 (if R A M P _ C L O S U R E ) , ' l ( i f s H A M P _ O N with single-entry metering), 2 (if R A M P _ O N w i k i p l a t o o n metering) and 9 (if R A M P _ O F F ) . v o i d ramp_set__parameters (RAlVtP * r a m p , B o o l staus) Function: Setting a n e w m e t e r i n g rate, to a specific r a m p meter. R e t u r n Value: N o n e Parameters: r a m p stores the n e w metering control-data o f a specific on-ramp; status is a Boolean value. s t a t u s = r T R U $ m e a n s to set a n e w metering rate b a s e d on an external algorithm; status = ; F A L S E m e a n s to restore the default time-of-day timing plans. 2.3.1.3 Path-based routing T h e path-based routing plug-in .module establishes tlje- m e c h a n i s m for vehicles to follow. a g i v e n p a u \ w h i c h is an essential requirement for the simulation o f ^ r i y e r responses to the informatiorTsupply and the resulting route choice. O n l y those vehicles tha,t need to follow specific p a t h s will guided b y this A P I and other vehicles will select route based on the internal routing m e t h o d o f P A R A M I C S . O n e interface ^function of this-plugin, -which is u s e d to set a path for a vehicle to follow, is shown as follows: v o i d u c i _ v e h i c I e _ r o u t e _ s e t ( v p i d * Y p , V ^ O U T E route), > ,4 fj ( Parameters^ Y p : t h e pointer o f p. v e h i c l e r e q u i v a l e n t t q vehicle I p f 3 , / w j rou^e is«the initial address of the w h o l e patfw . , ,# w , t, V R O y T E is a link r Iist storing, w h o l e patli Jhe, vehicle, should follow, w h i c h is defined-as: .. , typeVROUTE d { ' // link n a m e along the route r char • l i n k N a m e ? ' ** VROUTE*next;'M' ! '-:* r ^c 1 c 12 • n-w*i* i w 2.3.2 Traffic rnformatioh Collection J .tt„ 2.3.2.1 Lodp-detector.data n i tf .>o In the real world, loop dejectors are .placed »qn freeways' and artdrials for collecting aggregated d a t a . a t ascertain time-interval ( t y p i c a l l y ^ O seconds) ,for the purposes o f traffic a n a l y s i s a n d traffic control. T h e s e a g g r e g a t e d l o o p d a t a a r e s t o r e d e i t h e r i n t h e database or shared m e m o r y . Other traffic operation.c&mponents canigetf-access ; to these data through data communication networks and u s e t h e m for generating real-time control J strategies, .-i - ^ ^ Ja > >' T h e l o o p ' t a t a aggregator A P I works.as the,traffic data c o l l e c t i o n andrprovisior^ server in -the enhancedvPARAMICS environment. Itemulates.thejreaL-world data collection from inductive loop detectors and broadcasts the latest aggregated loop data,t o. the d y n a m i c m e m o r y during simulation. Other A P I m o d u l e s c a n obtain t h e s e data in real t i m e t h r o u g h the interface function provided by this A P I . In addition, this^API- c a n report the aggregated loop data to text files or the M Y S Q L database as performance m e a s u r e s for -data analysis and performance comparison. O n e interface function o f thfsrAPI c a n - b e u s e d f o r q u e r y i n g t h e # g g r e g a t e d loop d a t a at a detector station at a certain time interval.' T h e aggregated loop data includes, grouped volume, average o c c u p a n c y a n d average speed, a s well as lane-based v o l u m e , average occupancy and'average speed. - L O O B A G G l o o p ^ a g g ( c h a r *dete.ctorName)' Return Value: T h e aggregated detector data o f a loop detector Parameters: d e t e c t o r N a m e : loop detector n a m e L O O P A G G is a structure that h a s t h e following definition: typeXOO?AGG, i U i. int i detectorlndex; float AggregationTime; lane; int int g_vol; float g occ; float g_spd; *vol; int float *occ; float *spd; J: where d e t e c t o r l n d e x is the network-wide index for the detector; 13 waprrt * tt-r, A g g r e g a t i o n t i m e is the time o f the latest aggregation, determined b y the loop data collection interval; g_vol is the total traffic counts passing all lanes o f a detector station; g_occ is t h e average o c c u p a n c y o f all lanes at a detector station; g _ s p d is the average speed o f all vehicles passing ja detector station; lane is the total n u m b e r o f lanes at the detector station; *vol; *occ, and ^spd are-pointers for recording value&of,volume, o c c u p a n c y and average, speed at each lane of a detector station. ! 1 2.3.2.2 Point-to-point travel t i m e data collection Similarly, w e d e v e l o p a p r o b e vehicle A P I to simulate point-to-point travel t i m e data collection through G P S equipped vehicles. T h e sample rate, w h i c h is equivalent to the percentage o f G P S - e q u i p p e d vehicles, c a n b e specified through control,interface. Pointto-point 'travel t i m e data can b e output to the 'dynamic m e m o r y and text files or .the M Y S Q L database: 2.3.3 Database connection t M Y S Q L d atabase i s c urrently r egarded a s t h e m ost p opular a n d h ighly e fficient O p e n Source S Q L (Sequential Q u e r y Language) database in the world. W e developed the interface functions, including a s e t o f simple C r b u t i n e s ' p r o g r a m m e d 'in*MYSQL A P I , in order to c o n n e c t r P A R A M I C S w i t h M Y S Q L database: .r > . r M Y S Q L database can thus b e used for storing intermediate simulation data o r final simulation r esults if 1 arge a m o u n t s o f d ata a re g enerated. In a ddition, A P I m odules o f P A R A M I C S can also get access the database duringrthe simulation to pbtain^'outside data. *j' •i 2.3.4 Performance m e a s u r e s '•• * i » * i A n important aspect of the evaluation studies -is to use -some overall performance m e a s u r e s to evaluate h o w the, implementation of an 'ITS strategy benefit the whole traffic system, including the freeway and arterial part of the network. T o b e m o r e efficient to evaluation studies, w e developed a M O E A P I for Computing, gathering and reporting a n u m b e r of user-preferred overall performance" measures, each of which corresponds to a specific aspect of interest. i 2.3.4.1 Overall performance M O E # 1 sy stem e fficiency m easure: a verage sy stern* t ravel t ime ( A S T T ) o f t he w hole simulation period. A S T T is calculated a s the weighted m e a n o f the average travel times of all O D pairs . '* (2.1) vi.y /• v/.V ."U 'U 14 where Ntf is t h e total h u m b e j o£v.ehicles that'actuall>aravele'd*from. t origin'i to.destination jl-Tfi is t h e . a v e r a g e £ ) D travel t i m e ^ r o m origin"/ urdestinationy';<• t M O E # 2 s y s t e m - r e l i a b i l i t y m e a s u r e : a v e r a g e staridard, deviation q f > O D t r a v e M i m e s ( S t d e v X T ) o f the e n t i r e - s i m u l a t i o n p e r i o d . . S t d e v ^ T T * i s : calculated as.-the w e i g h t e d .standarddeviation f ofthe;av'erage*travel t i m e s ,ofallJQD pairs for t h e w h d l e studyiperiod: StdevJT w h e r e Std(T{J destination^". = ^(Std(TiJ)*NiJ) fiTNu (2.2) > , f is the standard deviation o f t h e average p D travel t i m e from origin / to 2.3.4.2 F r e e w a y P e r f o r m a n c e M O E # 3 freeway efflciency'measure t fi (1) average m a i n l i n e travel speed o f the" entire simulatiorrpprjod%AMTS) (2) average m a i n l i n e travel speed during ithe congestion period (peak__AMTS). T h e congestion p e r i o d is defined a s t h e c o n g e s t i o n p e r i o d o f t h e baseline-scenario. •a r M O E # 4 o n - r a m p efficiency m e a s u r e (1) total o n - r a m p d e l a y ( T O D ) (2) t i m e p e r c e n t a g e o f the o n - r a m p q u e u e spillback to t h e local streets ( P O Q S ) 2.3.4.3 Arterial P e r f o r m a n c e M O E # 5 arterial efficiency m e a s u r e (1) average travel t i m e from t h e u p s t r e a m e n d to the1 d o w n s t r e a m e n d o f an arterial (ATT) (2) th&stahdard d e v i a t i o n o f A T T ( s t d ^ A T T ) 2.4. A D V A N C E D MODULES A n advanced m o d u l e , such as a signal coordination strategy, adaptive r a m p m e t e r i n g algorithm, or ah 1 '"integrated 'control strategy, generally i n v o l v e s ' t h e control 6 f o n e or several'control c o m p o n e n t s , 1 including signals, r a m p s , V M S , a n d rbufirig vehicles,' b a s e d on traffic information. A s intfbSuced m Section 2 ' 4 7 l h e c a p a b i l i t y - e n h a n C e d ' P A R A M l C S environment u s e s a hierarchical' a p p r o a c h t o cleVelop a d v a n c e d mo'dufes. In o t h e r w o r d s , advanced m o d u l e s are developed based oh several basic m o d u l e s , 'which c a n b e accessed b y interface functions provided b y b a s i c m o d u l e s . A s an example, Figure* 2.4 describes h o w an a d v a n c e d r a m p - m e t e r i n g algorithm is developed. T h e a d v a n c e d A P I is built on t o p *of t w o b a s i c p l u g - i n m o d u l e s , i.e., r a m p metering controller and loop data aggregator. T h e entrance r a m p signals in the simulation n e t w o r k a r e controlled b y t h e r a m p m e t e r i n g A P I , t h r o u g h w h i c h m e t e r i n g rates c a n b e 15 queried and set b y other A P I m o d u l e s . T h e loop data-aggregator API-emulates the realw o r l d loop data collection, typically with a thirty-second interval, a n d broadcast :the latest loop data to the d y n a m i c m e m o r y . T h e advanced A P I can access the d y n a m i c m e m o r y and obtains the required loop d a t a through interface functions provided b y the loop data aggregation A P I . T h e n t h e m e t e r i n g rate for t h e n e x t control interyal is. calculated* based o n 'the advanced r a m p - m e t e r i n g algorithm.' T h e n e w metering rate is sent back to the r a m p controller A P I for implementation [5]. PARAMICS simulation New rate nA Provided API R a m p metering Controller New rate' 1 Loop Data Aggregator Old metering rate Loop data Advanced ramp-metering algorithms Efasic API modules i Advanced API modules Figure 2.4 T h e hierarchical approach to develop advanced r a m p metering m o d u l e 2.5 C Q i y C U J B I N Q JUEJMARKS T h i s chapter presents our practices on the> d e v e l o p m e n t , of a capability-enhanced P A R A M I C S simulation environment through integrating s o m e plug-in modules implemented in P A R A M I C S A P I . T h e s e plug-in modules c o m p l e m e n t and enhance the functionalities o f t h e commercial P A R A M I C S m o d e l ^ A s a - r e s u l t , the capabilitye n h a n c e d P A R A M I C S simulation can better m o d e l and evaluate ITS. Our.,experiences s h o w that AJ*I ,can be, used to access .thg core m o d e l s r o f f a - m i c r o sirnulator and potentially, researchers.can u s e ' c o m m e r c i a l micro-simulatprs^as a shell for testing their o w n njQdels gnh algorithms. Since other commercial micro.-s^mulators. such as VTSSIM and A u M S y N t 2 , £lso .provide users with their owji A P I functipns, .users can replicate o u r m e t h o d s jto e n h a n c e their capabilities., O u r current capability enhancements o f P A R A M I C S only cover s o m e aspects of the micrq-sjmulator, m o r e efforts a r e .expected in order to m a k e the enhanced P A R A M I C S better fit to ITS-related studies. ••> ,, 'i • ~* * 16 ifcitiig-m 2.6 R E F E R E N C E S J ' C f t > * K i P * 1'* - \ * j V . / sa,» #* «• » , K 1. Jayakrishnan, R., Oh, J., and Sahraoui A. (2001) Calibration^ and Path D y n a m i c s Issues in Microscopic simulation For Advanced Traffic M a n a g e m e n t and Information Systems, 80th Transportation Research Board Annual Meeting, Washington D.C. 2. Algers, S., Bernauer, E., Boero, M., Breheret, L., di T a r a n t p , £ . , Dougherty, M-, Fox, K., and J. Gabard (1998) Smartest Project deliverable D 3 . University o f K kee4?- h . ,. mL , \ \ Srnith, M . , \ S. Druitt, G. £ a m e r o i j and D . MacArthur, Paramics final R e p o r t , Technical Report E P C C - P A I ^ A M I C S - F r i ^ A L / ' U n i v p r s i t ^ of" Edinburgh, July, . W , " ' . ' " .„ \ i ',. " r v " , . • ,4. Liu, X., C h u , L . , and Reqke?;, W . ,(2001) P A R A M I C S . A P I R e s i g n p o c u n i e n t for .r.„Actuated ;SignaI^ -Signal ,Coprdinatipn .and (Karnp QontrpI, California P A T H WorkingjPaper, U g B - I T S , : P \ ^ P - 2 0 c ( l r l i , University o f California at Berkeley, 200 L > > * . * ' 5. Chu, L., Liu X., Recker, W., Zhang, H . M . (2002) P e r f o r m a n c e Evaluating of , Adaptive f J^amp^ .Metering Algorithms, .accepted,, ,by A S C E _ J o u r n a l of Transpqrtationingjneering. t ,, t 17 C h a p t e r 3. Calibration a n d Validation of Simulation 3.1 Microscopic Model INTRODUCTION Simulation m o d e l i n g is a n increasingly p o p u l a r and effective tool for analyzing transportation p r o b l e m s that are n o t amendable 1 *to s t u d y b y other rrieans'. In the transportation simulation field, there is g e n e r a l agreement that microscopic-simulation, i.e., a computational resolution d o w n to the level of individual travelers, is n o w a viable alternative and m ^ y b e t h e only answer to questions arising from a w i d e variety of problems 1 . 1 Recent a d v a n c e m e n t s in computer 1 technology h a v e led to*th6 development of h i g h fidelity m i c r b s c o p i c simulation models: E x a m p l e s -of w i d e l y u s e d microscopic traffic simulation m o d e l s are AEVISUN2, M I T S I M , P A R A M I C S , a n d VISSBvI. A microscopic traffic simulation model' generally includes physical components, s u c h as the r o a d w a y n e t w o r k , traffic control systems, and drive'f'-vehicle units, etc., and associated behavioral m o d e l s , such as driving behavior m o d e l s and route choice models. T h e s e components and m o d e l s h a v e complex data requirements and numerous m o d e l parameters. Although m o s t simulators provide data input guidelines and default m o d e l parameters, these m o d e l s nevertheless n e e d to b e calibrated for the specific study network a n d t h e intended applications [1]. I n t h e traditional p r o c e s s o f m o d e l calibration, m o d e l p a r a m e t e r s are adjusted until reasonable (qualitative and quantitative) correspondence b e t w e e n the m o d e l and fieldobserved data is achieved. S u c h adjustments with multiple parameters are a timec o n s u m i n g ^ a n 4 tedious process. T h e trial-and-error m e t h o d based on engineering j u d g m e n t or experience is usually employed for m o d e l calibration. M o r e systematic approaches include t h e gradient approach a n d Genetic A l g o r i t h m s ( G A ) [2, 3]. T h e s e approaches regard t h e m o d e l calibration procedure as a n optimization problem in w h i c h a combination o f p a r a m e t e r v a l u e s that b e s t satisfies an objective function is searched. M o s t calibration efforts reported in the literatures have focused on either the calibration of driving behavior m o d e l s [3, 4, 5, 6], or the calibration of a simple linear freeway n e t w o r k [2, 7, 8, 9]. H o w e v e r , these studies represent only an incomplete process of m o d e l calibration a n d validation. In order to analyze network-wide transportation problems, it is necessary to include n o t only driving behavior m o d e l calibration b u t also d y n a m i c O D estimation and route choice in t h e calibration process. T h e purpose of this p a p e r is to p r o v i d e a systematic, network-level calibration and validation framework for microscopic traffic simulation models. Along with the framework, w e p r o v i d e a case study to demonstrate h o w w e calibrate a corridor network consisting o f b o t h a freeway a n d its adjacent parallel streets using the P A R A M I C S microscopic simulation model. This-chapter j s i o r g a n i z e d as^follows: an joverall-calibration a"nd validation procedure j s proposed irtSection 2. The'third'section brieflydescriaes\the study, n e t w o r k "and data used i n ' t h e ' c a l i b r a t i o n study. "Sectjoni 4 explains the. details* o f hosv* the study n e t w o r k , is c a l i b r a t e d ' u s i n g ' the proposed procedure*; The> m o d e l validation results are* given in Section 5. Discussion a n d conclusions are presented in t h e last section. 3.2 O V E R A L L C A L I B R A T J O N A ^ A L I D A T I O N I P R O C E D U R E t Model calibration involves checking t h e - m o d e l results against observed data and adjusting parameters until the, model results "fall Within "an'acceptable r a n g e o f error. Various components in microscopic simulation 'models 1 are calibrated according to the following procedure, as s h o w n iiTFfgure T.l. 3.2.1 Basic D a t a Input / N e t w o r k Coding T h e first step is to input basic dataj including-network- geometry,, travel d e m a n d , drivers, vehicle characteristics, and'traffic c o n t r o l s y s t e m s . T h e ' a c c u r a c y and/or availability o f these data are very important-because-these-inputs-directly-affect 1 the performance o f the micro-simulation m o d e l s , , and the accuracy of such inputs n e e d s to b e taken into consideration during the "model calibration and" validation procedures. F o r most cases, demand data are not a v a i l a b l e ? T h e proposed procedure includes the O D estimation as a part of calibration in step four. 3.2.2 Calibration of Driving Behavior M o d e l s T h e second step involves the calibration o f d r i v i n g b e h a v i o r m o d e l s using either disaggregated data Or aggregated data. T h e driving b e h a v i o r m o d e l s include carfollowing (or acceleration) and Jane-changing modejs, w h i c h govern vehicular traffic m o v e m e n t and need to b e calibrated,for the specific region. Global parameters o f these models are calibrated w i t h i n t h e sub-network level. 3.2.3 Calibration of the R o u t e Choice Behavior M o d e l T h e third step is to calibrate the route choice b e h a v i o r m o d e l , w h i c h m u s t b e conducted o n a network-wide level. T h e route ^choice behavior m o d e l c a n be calibrated using either aggregated data or b y aggregating individual data obtained from driver surveys. 3.2.4 O D Estimation T h e next step is OD^estimation and/or model adjustment. T h i s step involves several tasks if applicable. 3.2.4.1 Acquisition o f O D demand^pattem 19 TB-- - rg,-'*^yrw !•- •»' A simulation m o d e l n e e d s to h a v e a n O D d e m a n d pattern a s a starting point o f t h e calibration. A g o o d s o u r c e of-this is from the p l a n n i n g m o d e l s , such as Transplan and T r a n s C A D b a s e d o n t h e social-economic data of the target network. Q f course, this O D d e m a n d pattern c a n also b e obtained from the. traditional four-step m o d e l calculation u s i n g t h o s e s o c i a l - e c o h o m i c data. Calibration data preparation I Basic data input / Network coding I Calibration of driving behavior models I Calibration of routing-behavior model Reference O D from planning model Route choice adjustment ( Total O D estimation Reconstruction of timedependent O D demands j : : : : = i ^ g : : : : - Fine-tuning parameters .«»i / Overall m o d e l ' validation / Evaluation Figure 3.1 Flow chart o f calibration procedure 20 ' 3.2:4.2'Modification .of rouje choices * ,!'• • • " u This-task-irivolvesvthe. modification of *the "route/link^ specific, c o s t ' i n r o r d e r to reflect r e a s o n a b l e , r o u t e x h o i c e s ^ I n t h e . O D e s t i m a t i o n , p r o c e ' s s , all m o d e l ' p a r a m e t e r s a n d route choice -behayjrorsftneed -to .be fixed ifirst .since, .this [ p r o c e s s is. ;based on .JheMraffic assignment matrix that is affected by* any c h a n g e in simulation inpufcor parameters. 3.2.4.3 F i n e - t u n i n g t h e total O D matrix • *- « T h e O D (Jemand matrix from the planning m o d e l is not accurate enough" and thus this matrix can**become a starting point of the calculation o f ' a better 6 D matrix. T h i s O D matrix can be called the total O D d e m a n d matrix that needs to cover the w h o l e simulation period. Th£-estimation of the total O D matrix is an iterative process t o m a t c h simulation results with the aggregated traffic v o l u m e observations at s o m e specific m e a s u r e m e n t locations. T h e objective of this process is: .jnin' \^{VOh^[n)-VOLsimin))2 (3.1) where N is the total n u m b e r of ( measurement locations. I s * A * f , This O D estimation process can b e conducted outside of t h e microscopic simulation m o d e l . ( There, are some, software tools, such as T r a n s C A D , Q u e e n s O D that c a n hejp the estimation of a static OD.. However, this m a y .cause, some, O D estimation r errors if different traffic assignment m e t h o d s are used in the 6 p estimation .process and the microscopic simulation. The microscopic simulation models h a v e started to develop their o w n O D estimation tool in order to avoid this problem. F o r example; I N T E G R A T I O N provides Q u e e n s O D as its O D estimation tool and P A R A M I C S provides an O D estimator tool in i t s n e w , version. 3' 3.2.4.4 D y n a r n i c O D estimation I n order, to obtain a m p r e accurate simulation model, t h e - d y n a m i c .(or time-dependent) O D estimation is required. Theoretically, it is a dynamic O D d e m a n d estimation p r o b l e m , which m a y not need a total O D as basis. So far, there is not an effective m e t h o d that c a n solve tljis prpblern .[15,16], except that the F R E Q m o d e l can b e used for the estimation of time-dependent O D o f freeway,network for,micro-simulation [7]. This estimation is generally based on the total O D d e m a n d matrix,, estimated in a previous step. This dynamic O D estimation process can be regarded as a process that assign the total O D to'detailed time slices. T h o u g h some existing O D estimation tools, i.e. QueenOD i a n d Estimator of P A R A M I C S , h a y e . a certain potential to handle the dynamic O D estimation, their capabilities are not recognized. 3.2.5 Model Fine-tuning 21 T h e last step o f calibration is m o d e l fine-tuning using aggregated traffic data in order to reflect network-level congestion effects. T h e driving behavior m o d e l s need to b e further validated locally (intersection-by-intersection or junction-by-junction) and adjusted to reflect the local characteristics. T h e local characteristics .can- b e b a s i c a l l y examined t h r o u g h the c o m p a r i s o n o f v o l u m e - o c c u p a n c y curves drawn based o n aggregated point detector data from b o t h simulation and the real world. T h i s step o f calibration is performed as a two-objective optimization process: min T N ££(row«.0-raw«.'))2 r min (3.2) N ZS(7T^("*')_7T^(n»'))2 /-I n-1 (3.3) T h e t w o objectives c a n b e called v o l u m e m a t c h and travel t i m e m a t c h . S o m e previous calibration efforts actually started from this point [2, 8]. This is the reason that w e think that t h e c u r r e n t s t u d i e s represent o n l y an i n c o m p l e t e p r o c e s s o f m o d e l calibration a n d validation process. U n d e r the following situations, there is no p r o b l e m to start calibrating a n e t w o r k from this step: (1) T h e network h a s been coded and roughly'calibrated. (2) T h e driving b e h a v i o r m o d e l s h a v e b e e n calibrated a n d validated based o n previous studies on the s a m e network. (3) There is no* data that'can support the calibration of route choice model 1 , or o n e of ' the route c h o i c e m o d e l s in the m i 6 r o s c o p i c s i m u l a t o r can b e accepted. (4) T h e ' O D d e m a n d matrices h a v e b e e n given. ' 3.2.6 M o d e l Validation M o d e l validation is typically an iterative process linked to each model- 6alibration. T h e m o d e l validation is generally conducted with a different data set o f larger area within the m o d e l i n g n e t w o r k in order to check if the calibrated m o d e l 'parameters -are 1 suitable. M o d e l validation is regarded as a final stage to investigate if each c o m p o n e n t adequately reproduces observed travel characteristics and the overall performance o f the m o d e l is . 10 reasonable. I.J. T h e following'sections o f this ^chapter'will'focus o n ' a case-study tha^ follows the above procedure o f m o d e l calibration "and valiaatiorf to calibrate a" network*'in a P A R A M I C S (version 3.0 Build 7), a widely used microscopic simulation m o d e l developed b y •i * Q u a d s t o n e in Scotland. ' 3 . 3 S T U D Y S I T E A N D C A L I B R A T I O N bjiTA ACQUISITION ! T h e data are an important issue in the calibration of a microscopic simulation moflel. T h e m o r e data and the better data w e have, the better the calibration result can be achieved. In 22 this section,* w e talked about dataussues, b a s e d .on our practices jri the calibration o f the case study network-in P A R A M I C S . i 3.3.1 Study Site Vl The^shidy'network is a h i g h l y x o n g e s t e d ^ O r r i d o r network i r r t h e c i t y ' o f Irvine,/Orange County, X a l i f d r h i a ; ; a & « h a w n ' i n Figure 3.2.,The»network includes a 6-mile.section of freeway J - 4 0 5 , a 3-mile section .-of freeway'I^^'Si-mjle section o f freeway SR-l j 33-*and the adjacent surface streets:* T h i s n e t w o r k u s calibrated torinvestigate.the effectiveness o f various Intelligent Transportation Systems (ITS) strategies on relieving traffic congestion happened along the n o r t h b o u n d 1-405 in the m o r n i n g peak periods. »" ' *J * ~"i * J. ' , . 6, ' .fl I ;*r> 1-405 i a i » Culver .*" t* ',. '* "•/* a "V i t ) . » r y / V j •Bar " U'"'" -^L A / ^ ^ f : 3 > X j#, ^ S ^ / ^ v " " ^ ^'M^V'^V M •JeBery^ ' ^ ^ r % Q T a T j N 7 ^i\fcj^fifl_'' i ' i, *~~.-~.1— ^ n ^ j K i C. rt^V jAflon i-lt J "• / * «• . V . \ ? ^-'f J.S * - , / tR-133 ?£b Jl? 'i ,5 IrvfeW CenterDr* i . i.. 1-5 Figure 3.2 Overview o f the study n e t w o r k 3.3.2 Preparation of Calibration D a t a Microscopic simulatidn ' m o d e l s h a v e very c o m p l e x data requirements and n u m e r o u s model'parameters. T h e niofe'data that'can-be collected and used for Calibration, the better the calibration'Can'be. T h e following data, including basic input data of the simulation and observed data for calibration / validation p u r p o s e are prepared. 1) Vehicle characteristics and performance data These data include vehicle length, m a x i m u m speed, m a x i m u m acceleration and deceleration rates, etc., w h i c h are obtained from California D e p a r t m e n t of Transportation (Caltrans). 2) Vehicle mix b y type 23 V e h i c l e composition b y type is determined b y the statistical analysis of traffic flow data observed from surveillance videos at two freeway locations in t h e n e t w o r k / 3) Arterial v o l u m e d a t a W e obtained 15-minute interval traffic counts at all important cordon points of the network. S o m e of t h e s e data w e r e from the City o f J r v i n e , collected in January 2002 and J u n e 2 0 0 1 . O t h e r s w e r e derived based- on t h e s u r v e i l l a n c e video - data, .video-taped b e t w e e n M a r c h 27, 2 0 0 2 and April 19, 2002. T h e d a t a .from the City of-Irvine also includes traffic count d a t a at/important links inside t h e network. 4 ) Travel t i m e data W e obtained floating car data of northbound and southbound freeway 1-405 collected at Oct. 17 and Oct. 18 o f 2 0 0 1 from Caltrans. 5) F r e e w a y loop detector data W e directly access mainline, on-ramp and off-ramp l o o p detector data from an on-line database at the University of California, Irvine. **" 3.3.3 Calibration D a t a R e d u c t i o n B e c a u s e field observatioris\vary from day to d a y due, to the stochastic nature o f traffic, o u r calibration objective is "to' re-construct the typical real-world traffic variation in simulation. W e selected o n e d a y ' s data for the calibration process. t. T h e m ethod w e e m p l o y e d i n t h i s s election i s t o c o m p a r e t h e p eak-hour (i.e. 7 -8 A M ) v o l u m e of a candidate day at any selected loop station w i t h the average p e a k - h o u r v o l u m e of all candidate days u s i n g the G E H statistic, used b y British engineers [10]: GEH = (Vol(0~ave_Vol)2 *(Vol(i) + ave_Vol)/2 (3.4) In o u r study, if the G E H values for m o r e than 8 5 % of the selected loop stations are less than 5, the demand, pattern-,of the ^candidate day is typical. There are 3 5 selected,. loop stations, placed at the.npstre.am end of each freeway, all o n - r a m p s ano! all pff-ramps. This study showed that the d e m a n d pattern at Oct. 17, 2001 is typical based on t all w e e k d a y s ' data in October. Therefore, the travel time and loop data of Oct. 17 were chose for the calibration study, t ft 3.4. C A L I B R A T I O N 3.4.1 Basic D a t a I n p u t / N e t w o r k Coding (• W e built the study n e t w o r k in P A R A M I C S based on aerial p h o t o s and road geometry and infrastructure m a p s obtained from Caltrans and the city of Irvine. The. simulated .network h a s the same configuration of loop detector stations as those in the real world and the 24 same traffic. controL operations* including actuated .signal control and t i m e - b a s e d - r a m p metering, m o d e l e d b y full-actuated signal and r a m p m e t e r i n g plugins-, respectively [11]. T h e zone structure o f t h e network is based on data from the O C T A M model. , •* * ' ' T h e basic input data also include vehicle m i x b y type, vehicle characteristics and performance .data? a n d some;driving restrictions. S i n c c . P A R A M I C S regards,each* vehicle -in ther^simulatidn as tsc Driver -Vehicle i .Unit (DVU),- 'driver" jdata, r e p r e s e n t e d b y aggressiveness*iand. awareness" factors^ are Jalso inputs o £ simulation. For this 1 study, w e u s e d thendefault'distributionsjof these t w o factors.,) if 3.4.2 Calibration o f Driving'Behavior M o d e l s * ' *» x T h e driving behavior m o d e l s of P A R A M I C S have*been extensively studied.[4,-5, 6]i Lee et al. [5] conducted a calibration study based on a sub-network of this s t u d y network, -which shows calibrated v a l u e s , o f i h e two^major parameters*6f driving.behavior m o d e l s , i.e. the m e a n target h e a d w a y and driver reaction time, are 0.625 and 0.415 respectively. •These two v a l u e s m a y be'£hanged in the-parameter fine-tuning step, in order t o ' m a t c h the •observed congestion patterns'. , "> 6 . 4 . S C a l i b r a t i o n of R o u t e Ghoice'Model; © u e ' f o . the-existence o f freeways and parallel streets 'in\the s t u d y network, *the routing algorithm adopted i n the simulation is -important.; W e . calibrated .the n e t w o r k under s t o c h a s t i c ' a s s i g n m e n t . 'Stochastic 'assignment i n - P A R A M I C S ' ^ a s s u m e s , that different drivers perceive different costs from -a', decision n o d e to the destination. T h e perceived cost is calculated based on the given perturbation factor w i t h a r a n d o m n u m b e r assigned to the.vehicle, .and the'shortest perceived route is-cnosen a t the decision node. Since-we- h a v c . n o data to calibrate.perturbatibn factors,- w e take a value o f 5 % for all driVers'based on the-assumption that most drivers in t h e m o r n i n g . p e a k are familiar drivers who-have^a good k n o w l e d g e , of the road n e t w o r k , and traffic condition. In addition, the "familiarity" attribute 'affects t h e route ehoic6, behaviors -in P A R A M I C S . Since w e calibrated the n e t w o r k using the morning p e a k d e m a n d , when- m o s t travelers are commuters, w e assumed that 9 5 % of drivers are familiar drivers, w h o c a n choose from among both'arterials and secondary streets. 3.4.4 O D E s t i m a t i o n 3.4.4.1 Reference.OD matrix A static origin and 'destination (OD) d e m a n d matrix is sub-extracted from the O r a n g e County Transportation Authority Model ( O C T A M ) 2 0 0 0 model. It is used as the reference O D matrix o f this study. T h e reference O D matrix is evenly loaded for the w h o l e simulation.perjod (subject to .a flat demand "profile"). T h e vehicles are observed as vehicles m o v e through tne network. 25 A b n o r m a l behaviors always correspond to n e t w o r k coding errors, w h i c h need to b e identified and solved. 3.4.4.2 Modification o f route choices Based on- the calibrated route choice m o d e l (i.e. stochastic assignment), w e need to further fine-tune s o m e local parameters, such as link costs*-in order to^have a reasonable resulting routing, w h i c h c a n b'e based on. survey data. Since travel .delays caused b y intersection signals and freeway ramp control are not considered for traffic; assignment in P A R A M I C S , w e a d d e d tolls to o n - r a m p links to reflect o n - r a m p control, and decreased speed limit values o f arterial links in order to 'reflect ssignal control. t 3.4.4.3 Fine-tuning the total O D matrix T h e reference O D matrix obtained from the O G T A M m o d e l needs to b e adjusted for t w o reasons: > t • (1) It is for the m o r n i n g p e a k hours from J6 J o 9. H o w e v e r , the congestion.in the study network cannot b e totally cleared at 9 o ' c l o c k . Consequently^ the O D d e m a n d matrix needs to b e further expanded to 4 hours, i.e. from 6 to 10; (2) It is not accurate because the data sets of O C T A M n i d d e l are generally limited to t h e nearest decennial c e n s u s year a n d t h e sub-extracted O D matrix is based o n t h e four-step m o d e l o f T R A N P L A N . A s a r e s u l t , w e n eed t o adjust t h e w h o l e O D matrix based o n the-reference O D , tfxe'assumed-traffic a s s i g n m e n t - m e t h o d a u d i t s resulting route choice. T i u V i s a static OD-estimation problem,-which h a s . m a n y solution m e t h o d s . T h e least square m e t h o d i s mo'st-frequently used [12,1-3]. . J -if'' i >r Since w e h a v e 15-minute interval traffic c o u n t s ' a t all cordon points of. the network, the total traffic attractions and generations o f each z o n e are k n o w n . W e assumed the same trip distribution as that t>f the reference O D m a t r i x e s applied to all z o n e s i n the adjusted O D matrix. T h e F l J R N E S S technique is=then-used for balancing the adjusted O D table. If the total ^attractions are n o t equal to-the .total generations, the-total generations are used! as t h e total: For Ihe-'following steps o f ' O D modification, the-total origin and destination d e m a n d s will b e basic constraints. " i i t *' \ , i W e evenly load the adjusted O D matrix for the w h o l e simulation period (subject Jo-a flat d e m a n d '^profile"). B a s e d on the simulation results, w e can c o m p a r e the observed a n d simulated total traffic counts at selected measurement locationsrrwith the 'objective function s h o w n in Equation 3.1. In this study network, there are 52 selected measurement locations, including 13 mainline loop stations, 29 on-ramp loop'stations, 1 a n d 10 arterial links. T h e measure o f t h e overall quality o f the O D estimation is the G E H statistic: I, i. ' f . U T ^ I f t h e G E H values for m o r e than 85%"of the measurement locations are-less than 5, the l adjusted O D is acceptable. ' i J' J ' • 1 '' 26 A n iteration p r o c e s s is required in order to obtain a satisfactory total O D matrix. B a s e d on a simulation run and its resulting GEH'values'at^measurement'Ib'c.atioris, w e can further adjust the complete O D matrix according to assumption of the proportional assignment [14], w h i c h assumes t h a t the link volumes are proportional to the O D flows. T h e modifications t td Vehicle routes ' m a y also n e e d ' ' t o be^ i n v o l v e ^ to generate an a d V e p t a b l e ^ h o l e O D matrix. ' * " * "• " ' »t i B a s e d ' o n multiple Iterations, a good and acceptable total O D ' c a n , b e obtained. Table 1 3.1 .(left side) shows the calibration results at this step. It shows tKat; except* for a single onr a m p Ideation anil o n e arterial' link location, "k\\ o t h e r m e a s i i r e m e n t locations h a v e a G E H value" lower than 5; which'satisfies the calibration acceptance criteria o f this step. 3.4.4.4 Reconstruction o f time-dependent O D d e m a n d s T h e objective o f this step is to assign the total O D to a series o f consecutive t i m e slices. Otir Tne'thod tries* 'to simplify I the'"c6mplex' tunfe-dependent O D estimation problem through reconstructing & e d y n a m i c ' O D ' d e m a n d s - ' b a i e d ' o n ' a ' s e t o f * d e m a n d profiles. P A R A M I C S has an enhanced feature o f d e m a n d loading, i.e. the^ ability to specify *different"*demand profiles'for e a b n O D pair. : Thre-ugn t h e ' u s e o f " m a u H x " and "profile" files* "a'profile c & r b e gpecifiiid f o r a specific OD'pair. Since the 16-mmute interval*traffic counts at all cordon points of the network are known, the pro'flle o f Vehicle generation from any origin z o n e and that of vehicle attraction to any destination zones are thus known. W e further assume a n u m b e r o f i nitial d e m a n d profiles f o r a 11 O D p airs b ased o n t h e fonowing>criteria: i(l),T)ie f jdemand profile from a n arterial origin z o n e to a n y arterial destination z o n e has.Jhe.same profile, .which is the s a m e as the vehicle generation profile from this origin zone; (2) T h e d e m a n d profiles fro;n a . freeway ..origin, zone to a freeway d e s t i n a t i o n zone, from,a freeway origin z q n e to an arterial destination,zone, fromran arterial .origin z o n e e t o . a freeway destination z o n e will ,be bajsed^n the v tra/fic count profile at corresponding, loop, stations placed at freeway mainline, off-ramp, and bn-ramp, jTespectiyely. Based ori.these criteria, w e will furjher. find the d e m a n d profile for e a c h O D pair. A s wp know, trie O D estimation process is related tp, the other calibration process. Without me,paIibration.of other c o m p o n e n t s of the simulation m o 4 e l , [the d y n a m i c O D d e m a n d s are almosl i m p o s s i b l e to b e obtained because the traffic during p e a k h o u r s involves the capacity o f the network, w h i c h is what the calibration needs to find out. A s a result, this step has two calibration objective ^functions. The,first o n e is an easy one, which is to m i n i m i z e ,the deviation b e t w e e n the observed <and corresponding simulated traffic counts at selected measurement- locations, for .tjie peak h o u r o f the simulation period: 27 ^(VOLobs(n,peak_T)-VOLsim(«,peak_T)): min (3.6) rt-O. w h e r e A^ is t h e total n u m b e r o f m e a s u r e m e n t locations; VOLobs(i, peak T) and VOLsim(i, peak_f) are total o b s e r v e d and simulated traffic counts for the p e a k Jiour at measurement location i9 respectively. T h e selected m e a s u r e m e n t points are the s a m e as those in last step. T h e p e a k h o u r is defined as from 7 to 8 A M . T h e following criteria are required to b e satisfied for this objective: • ThQ-modeled p e a k h o u r v o l u m e s at measurement locations m u s t be within l S percent o f the observed vofumes for flows greater tfcan 700 vphpl, o r within 100 v p h for flows less than 700 v p h . These targets m u s t b e satisfied for 85 percent of the cases; • Total screenline flows (normally > 5 links) to be within five percent for nearly all screenlines; T h e G £ H statistic to be .less than five for -individual flows f o t . 8 5 percent of the cases, and less, t h a n four for screenline totals for nearly all screenlines; • T h e second objective function is to m i n i m i z e the deviation, betwpen the observed and corresponding simulated traffic counts at' selected measurement locations at five-minute interval. It c a n b e formulate as: T N m™ YYiVOLeln{n,t)-VOLalm(n,Qy (3.7) M n=\ w h e r e N and T are t h e n u m b e r o f measurement locations and t i m e periods, respectively; VOLobs(h, tXand VOLsim(n, t) are observed a n d simufated trafficcounts of time period 1 t at m e a s u r e m e n t location I, respectively. T h e length o f each p e r i o d i s 5^minutes m this study. T h i s step l of calibration is an iterative process. W e m a i n l y modify t h e d e m a n d profiles from'a* freeway origin z o n e ' t o a freeway clestina'tibh zone, frorrr^a freeway origin z o n e to an arterial 'destination zone, and from afi arterial'ori^in'zorieto a-freeway destination zone in order to m a t c h the traffic counts-at selected measurement locations. T h e trial-and-error m e t h o d is used t for the modification of d e m a n d profiles based on t h e following criteria: (1) T h e pr6file~rrbm a freeway origin zone to an arterial 'destination zone can b e estimated, b a s e d o n the 15-minute loop data at a corresponding off-ramp location. (2) T h e profile from an arterial origin zone t o a' freeway destination z o n e -can b e 'estimated b a s e d on the 15-mihute 1 loop data at a'corresponding on-famp location. ( 3 ) ' T h e profiles from freewa^'origiri zones to' freeway1 "destination z o n e s ' a r e decided J last!' ' ' '* "*•>J' • Traffic count .calibration h e r e ' i s ' a n initial m a t c h o f v o l u m e ' d a t a ; v o l u m e calibraHorf will b e fine-tuned 1 'in next s t e p / T h e calibration results o f this step a r e - s h o w n in Table 3.1 (right side), w h i c h s h o w s t h e comparison of traffic counts of p e a k h o u r at those selected m e a s u r e m e n t locations. 28 Table 3.1 Traffic counts calibration results o f the total A M peak-period and*the peak^hour Peak Hour (7-8 AM) AM Peak Period (6-10 AM) Simulated. ,% diff GEH Observed Simulated %,diff .GEH Mainline detectors *- ««% J * -Observed 24505 0% 0% {f.06 24428 0.49 405n0.93ml 6^0,3. , ,. 6808 v J -1%' \%f ' 33274 ° 32646 -2% 9127'" 1 9006 3.46 405n3.31ml " ( w 8^22- '' -2% 29890 4.02 495^3:86™^ 'PJ 8248~'<jI * - w ,-o:8i ' ^30589" :-2% ' -U3 34277- j 33475 -2% 9545? i 0 937Z, i 4.36 405n5.74mli * i ' ' 8 5 7960 on . 28255 279,04 -1% 2.09 405s6.21ml 1? *b >W* 8098 . « • 8 0 1 0 r -1% t 0.98 28501 27795 -2% 4.21 40qs3.31pl 1 ' 5514 ( 405s6.77ml 5583' 19638 -2% 2.97 -1% ' tf.93 "2d057 j 2% &75 ' '26830 26614 -1% 1.32 7686 5ri22.2mF' ' ' - 7&P 6499 „ + , 6974 '7% i 5.79-' •24464 -2% 2.82 5s22.14ml f * 24025 4 133n9.37ml -8%, 1.76 - 1496 1498 -i T,0% 0.05 7t ' Slfllj' 133n10.05ml , 804 817 2% 0.46 2534 2607 3% 1.44 '*-3% ** 1.50 11 §557 0%* 2752 2674 85571 0.00 133s10.05mf ,, *' J -6% 2.61 52331' 5429 4% 133s9.37rnf' ' *v r "1760*"" 1652 ^ 2.68 v Rsmi^ Defectors 1 1% 0.16 546 56^4 3% .0.76 4Q5i]0i93fr_ . ( ,160 M162, 405n0.93orb » . 512 507 ,-1% 0.22 1815 1760 -3% 1.30 ,f ' 'Hio '35% 3.43 445 0% 0.09 149* 447 ' 405nffilort> l ! 54 M% o.2r '213 197 -8%' 56 1.12 405nf.73ffs *' 2227 2166 -3% .1.30 6887 *~-~6987 1% 1.20 405M.93ft *!* 165 196 19% 2.31 726 705 0.79 405n2.99fr (-3% 405n2.99orb 436 442 1% 0.29 1418 1358 '-4% 1.61 3% 0.82 2737 2704 0.63 405n3.86fr 709 731 -1% 4% 0.73 *931* 3% 405n3.86orb * " ' 307320 963' 1.04 816 ^1% 0.25 2889 2686 -7% 3.84 405n4.03orb 809 460 426 -7% 1.62 1626 1659 2% 0.81 405n5.55fr -2% 0.46' 2161 2134 -1% 0.58 405n5.55orb 682 670 405n5.74orb 1026 1075 5% 1.51 3567 3576 0% 0.15 12% '•3.52 1 3182' 3139 -1% 0.76 40*5s5.69fr 853' 959 -13> 2.32 , 983 921 -6% 2.01 4*05s5.69orb' 316 276 4p5s5.5orb 241 , 281 , .t „<17% 2.48 9,40 914 -3% 0.85 405s4.03fr 409 392 -4% 0.85 1602 1554 -3% 1.21 16% 2:06 ' 647 3% 664 0.66 405s4.03orb 183 212 -10% :4.64 624 567 -9W 2.34 0 2112' 1904 405s3.84farb 864 - 817 -5% 1.62- 2937 2743 -7% 3.64 405s2.88fr 405s2.88orb 152 159 5% 0.56 468 505 8% 1.68 592 573 -3% 0.79 1881 1953 4% 1.64 405s 1.58ff 70 117 67% 4.86 315 319 1% 0.22 405s1.57ff -3% 1.28 4906 4907 0% 0.01 405s0.96fr * 1546 1496 405s0.96drb '20 65% 2.53 58 123 112% 6.83 33 11 22% 0.63 43 43 0% 0.00 405s0.77ort) 9 742 802 8% 2.16 2443 2600 6% 3.13 5n22.1fr 84 94 12% 1.06 289 339 17% 2.82 5n22.1orb 199 232 > .17% , 2.25 752 735" -2% 0.62 5n22.2orb Arterial Detectors 6563 2119 -7% 3.45 6317 -4% 3.07 Jeffery 405-Alton 1963 1 882 1057 20% 5.62 ' 3520 3505 0% 0.25 Alton E of Jeffery ** 758 604 -20% 5.90 1987 2038 3% 1.14 439 446 2% 0.33 1470 %1386 -6% 2.22 624 -29% 7.84 1675 1480 -12% 4.91 Alton E of Sand 443 729 777 7% 1.75 2443 2469 1% 0.52 804 619 -23% 6.94 2102 2382 13% 5.91 Alton E of Laguna 491 606 23% 4.91 1714 1921 12% 4.86 -2% 0.39 1287 -4% Barranca SR133-ICD 428 420 1240 1.32 959 962 0% 0.10 3235 3161 -2% 1.31 29 3.4-5 M o d e l Fine-tuning T h i s step fine-tunes v a r i o u s p a r a m e t e r s "in order to- re-construct traffic variations and m a t c h the congestion pattern o f the study network. These, parameters include: * (1) Link specific parameters, including the signposting setting or the target h e a d w a y o f those links at critical bottleneck locations w h e r e a very_ m i n o r change in capacity can h a v e a<major effect on congestion. (2) Global p a r a m e t e r s for ^he car-following and lane-changing models, i.e., the m e a n target h e a d w a y and driver reaction time. T h e y are two k e y user-specified parameters in< t h e car-following and lane-charrging m o d e l s that can drastically influence overall driver behaviors o f the simulation*. (3) D e m a n d profiles from freeway o r i ^ r i zones to freeway destination zones m a y need to b e further modified, in order to adapt traffic congestion along freeways. T h e objective function o f this step is to m i n i m i z e the deviation between the observed arid t h e corresponding simulated 5 m i n v o l u m e and point-to-point travel time measurements. It is a two-objective o p t i m i z a t i o n process, w h o s e formulations are shown in Equation 3.2 and 3. B a s e d ' o n travel t i m e matching, the 5-min traffic counts at measurement points*are further matched. In o u r study, the point-to-point travel time matching w a s performed only for the northbound and s o u t h b o u n d freeway 1-405 between the interchanges at Irvine "Center D r i v e and Culver D r i v e d u e to the lack of data for other trips. ' B e c a u s e of the high traffic d e m a n d s during the p e a k hour, and recurrent congestion along the northbound 1-405, s o m e network coding p r o b l e m s ' ' m a y show up and need td^tfe corrected. Congestion a n d queuing p h e n o m e n a o n the northbound 1-405 m a y take extra effort to modify d e m a n d profiles of s o m e specific OD' pairs. This step m a y involve multiple simulation* r u n s in order to determine a g o o d combination o f rthese aforementioned p a r a m e t e r s . T h e trial-and-error m e t h o d is used for parameter modification. T h e final calibrated m e a n ' target h e a d w a y and driver reaction time are 0.78 and 0.66, respectively. Figure 3.3 s h o w s the calibrated-demand profiles for several major O D pairs. 3.5. O V E R A L L M O D E L V A L I D A T I O N . * T h e final m o d e l validation requires^ multiple simulation runs because of the stochastic nature of microscopic simulations; T h e m e t h o d to determine the number- o f runs^is described in Section 3.5.1. , r j 3.5.1 Determination of N u m b e r of Simulation R u n s 30 -Microscopic* simulation* is' a-Jgenerally stochastic sprocess, w h i c h rely u p o n r a n d o m numbers to-release Vehicles, select 'vehicle type* select* theiF destination and their> route, and to determine t h q h x ' b e h a v i o r as they m o v e through -the network. Therefore, the -average results o £ several 1 simulation runs-'Using: different seed n u m b e r c a n reflect the traffic condition o f a specific"scenario. 12% •o c « £ o •o « 9% Z o 6% <D o> a c 3% -! a> a 0% 6:00 6:30 7:00 7:30 8:00 8:30 9:00 9:3"0" - a freeway zone to a freeway zone —•— an arterial zone to an industrial zone • a freeway zone to an arterial zone —X— a/i artertial zone to a freeway zone Figure 3.3 Demand-profiles for m a j o r O D pairs is In order to determine the n u m b e r of simulation m o d e l runs, w e need to k n o w the variance of a n u m b e r of performance measures from simulation results, w h i c h are u n k n o w n before simulations T h e flow chart to determine the n u m b e r of simulation runs is s h o w n in F i g u r e 3.4. W e execute nine simulation runs first and then calculate the n u m b e r o f runs needed according to the m e a n and standard deviation of a performance m e a s u r e o f these nine runs: N = {tan -)• ft • £ (3.8) where n and 5 are t h e m e a n and standard deviation of the performance m e a s u r e based on the already conducted simulation runs; £ is the allowable error specified as a'fraction of the rnean p.; t ^ is the critical value of the't-distribution'at'the confidence interval of a . This calculation n e e d s to be done for all performance m e a s u r e s of interest. T h e highest value f r o m v ariances i s the required n u m b e r o f runs. If,the' current n u m b e r o f r u n s j s already'larger than this valufe, the simulation of this scenario is ended. Otherwise, o n e additional run is performed and then the required n u m b e r of runs needs to be recalculated. 3.5.2 Validation Results 31 F o r o u r case, the p e r f o r m a n c e m e a s u r e s w e u s e are.the total vehicle hour traveled and the northbound point-to-point travel' time (i.e. from I C D to Culver). T h e total n u m b e r of simulation runs is 3 1 in order to achieve statistically meaningful performance measures. T h e m e a s u r e o f g o o d n e s s of fit w e used for evaluating t h e calibrated simulation m o d e l is t h e m e a n abstract p e r c e n t a g e error ( M A P E ) , w h i c h can b e calculated by: «• (3.9) MAPE = 1 £ W*> (0 " Msim (0) / Mobs (/)) 1 r=t Start Original nine runs 1' Calculating the mean^and its std o f each performance m e a s u r e V. ' Calculating t h e required # o f runs for each performance m e a s u r e Additional o n e simulation run j Is curreait # o f runs enough? N Y Figure 3.4 F l o w chart o f the determination of n u m b e r o f simulation runs W e compared the simulation results w i t h the loop data and'the floating car data o f Oct. 17, 2001. Figure 3.5 shows,.the comparison o f observed arid simulated 5-mihute traffic'counts .at eight major freeway m e a s u r e m e n t locations. T h e M A P E error of traffic'counts at these m e a s u r e m e n t locations r a n g e frpm 5^8% to 8.7%. T h e travel, t i m e calibration results are s h o w n in Table 3.2. Figure 3.6 and 3.7 s h o w the comparison o f observed and simulated point-to-point travel,time for the.northboupd and -the sou'tnbound 1-405", w h i c h have the M A P E errors o f 8 . 5 % and 3.1%, respectively. 32 In summary, simulated traffic counts and point-to-point travel t i m e data correspond well to the observed measurements. T h e calibrated simulation, m o d e l accurately captures the congestion natterns of t h e target netwo'fk s h o w n oh Oct. 1 7 , 2 0 0 1 7 J± 900 700* j c 300 6:00 ^ W 7:00' * ^ 8:00* 9:00 10:0C 6:00 •*-=-405N0.93rhl-sim — 405N0.93ml-obs 7:00 8:00 9:00 10:0C •405N1.93ff-sim —— 405N1.93ff-real 900 300 6:00- -1 T 7:00 8:00 • N3.04ml-sim 300 4 6:00 ** 7:00 7:06 10:00! •N3.04ml-obs 8:00 9:00 10:0C -6:00 8:00 • 5n22.2ml-sim 9:00 10:0C •5n22.2ml-real 7:00 8:00 9:00 10:0C •405N3.86ml-sim —— 405N3.86ml-obs 6:00 •405N5.55ml-obs •405N5.55ml-sim 6:00 9:00 7;00 8:00 -405s3.31-sim 6:00 7:00 •133s9.37ml-sim 9:00 10:0C -405s3.31-obs 9:00 10:OC •133s9.37ml-real Figure 3.5 Traffic counts calibration (5-minute volume) at major freeway m e a s u r e m e n t locations 33 Table 3.2 Travel time calibrations v **; t, tV;* ;?j % «fl. *ur ^ ? ^ .•***•• Arrival Arrival Mainline Trip Analysis Start time Time Observed Start time time Southbound 1405fromCulver to ICD 6:00:22 6:04:38 256 6:00:00 6:15:00 6:25:14 6:29:36 262 6:25:00 6:30:00 6:47:01 6:51:17 6:45:00 6:50:00 256 7:06:34 7:10:56 262 7:05:00 7:10:00 7:24:45 7:28:54 249, 7:25:00 7:30:00 7:45:00 7:50:00 7:46:23 7:50:48 265 8:05:14 8:09:41 267 8:05:00 8:10:00 8:24:23 8:28:44 261 8:25:00 8:30;00 8:43:42 8:47:47 245 8:45:00 8:50:00 9:04:27 9:08:34 9:05:00 9:10:00 247 MAPE Northbound 1405fromICD to Culver 6:00:58 6:04:45 227 6:00:00 6:05:00 6:19:32 6:23:40 6:20:00 6:25:00 248 6:40:51 6:44:50 239 6:40:00 6:45:00 7:00:58 7:05:05 247 7:00:0/) 7;05:00 7:23:06 7:27:57 291 7:25:00 7:30:00 7:40:53 7:49:29 514 7:45:00 7:50:00 7:57:57 8:05:58 481 8:00:00 8:05:00 8:22:06 8:27:59 353 8:25:00- 8:30:00 8:40:27 8:44:25 238 8:40:00 8:45:00 8:59:57 9:04:03 246 9:00:00 9:05:00 MAPE Travel time *c •*. t •* - simulated % diff 264.5 7.0% 257.8 3.3% 255.7 , 5.4% 259.6 1.7% 263.1 5.9% 278.9 1.1% 326.8 .- 0.3% 262.6 0.6% 259.5 2.1% 246.4 3.2% 3.1% 247.7 248.3 252.2 294.2 325.1 504.4 505.1 390.4' 281.6 256.0 9.1% 0.1% 5.5% 19.1% 11.7% 1.9% 5.0% 10.6% 18.3% 4.1% 8.5% T \ "S-400 o M a> • > 200 L. I- 6 00 - 6:30 7:00 7:30 8:00 8:30 . 9:00 *$:30 * v —— simulatioo -^observation 10: DC i Figure 3.6 O b s e r v e d and"simulated travel time of northbound 1-405 34 ;< ~r~~i ; * r • ' n<* *fii /" TTT*^ i .» • v i , / f ,0 . ,' "J? rt ,6:00 r - 1 li)l 6:30, 7:00 •* * 0 7~J" '.' 7.-30„ 8:00 ,,8:30 9:00 Un 9:30 10:00 - ^ sirhulatibrt-^-*-*-' observation .c i )y r ~» F i g u r ^ 3 . 7 Observeci and simulate^,travel time p f southI?pund J-405 ** 3-J6.. COmV&WQ REMARKS / " - r * This chapter proposes a calibration a n d validation p r o c e d u r e for microscopic, simulation ' m o d e l s . ' I f t ^ e j j r e x z o u s studies-focused mostly ojijdriyjng .behavior m o d e l calibration t o study a-sectipn g f freeway,. Jhis study p r o v i d e s a general s c h e m e of,mqdel. calibration and validation for network-level simulation^ -responding tp^the extended u s e - o f microscopic s i m u l a t i o n , mgdels, Such extension, -requires, m o r e systematic *apprpach in m o d e l calibration since various, model-,cornppnents^ are i n c l u d e d * in- -the *proc,es,s. JJie* p r o p o s e d procedure r is demonstrated via>a c a s e n e t w o r k s that,- involves / n u l t i p l e s t a g e s a n d t h e calibrated-, model s h ^ w s reasonable * performance in replicating ;the .observed .flow condition, J/ tr i- i In this^cjiapter^vanptis" c o m p o n e n t s p/mq^ej&-were, addressed in-the m o d e l ^calibration process; however, w e u s e d t h e default route choice m o d e l in P A R A M I C S b e c a u s e o f t h e interaction .^etween v #ied:pute choice m o d e l a n d , O D estimation p r o b l e m . In the, n e t w o r k Jevpl<"mpdel calibratjfin/yalidatiqn (process, the i ; ipter-rejationship- f between route choice and O D estimation m a k e t h e p r o b l e m complicatechunlessf o n e o f 4hem is, externally determined. This -wi]l ; b e o n e o f topics t& b e further studied in micros-simulation calibration/validation process: 'Another further topic w o r t h y of study is-the-development ojf an, automated and systematic topi *for microscopic simulation mode,l calibration/validation b y incorporating optimization-based _model calibration m e t h o d s within t h e proposed multiple stage approach. 3.7 R E F E R E N C E S 35 1. M . G. M c N a l l y , J - S . O h , "Technical M e m o r a n d u m on Calibration / Validation o f Traffic M i c r o s i m u l a t i o n M o d e l s , " Research Report for Orange C o u n t y Transportation Authority.(OCTA), D e c e m b e r 20Q2. + 2. J. Hourdakis, P. G . Michalopoulos, J. Kottommannil, " A practical procedure for calibrating m i c r o s c o p i c traffic simulation m o d e l s , " 8 2 n d Annual Meeting Preprint C D - R O M , Transportation Research Board, J a n u a r y 12-16, 2002^ Washington, D.C. 3. R. L. C h e u , X . Jin, K. C. N g , Y . L. N g , and D . Srinivasan, "Calibration o f F R E S I M for Singapore expressway using Genetic Algorithm*, Journal o f Transportation Engineering, Vol. 124, N o . 6, 1998, pp. 526-535. 4. T . M a a n d B . A b d u l h a i , " G E N O S I M : A G e n e t i c A I g o r i t h m - b a s e d o p t i m i z a t i o n approach and generic tool for the calibration o f traffic microscopic simulation parameters^" 81st A n n u a l M e e t i n g Preprint'"(JD-RbM, Transportation Research Board, J a n u a r y 13-17,- 2Q02, W e l l i n g t o n , D . C . 5. D - H Lee, X . Y a n g , and P. Chandrasekar, "Parameter calibration for P A R A M I C S using Cjenetic Algorithm^'' 80uV ' A n n u a l - M e e t i n g 'Preprint CD-ROM, Transportation Research Board, January 7-11, 2001, Washington, D.C. 6. B. Abdulhai, J - B Sheu, a n d W . Recker, "Simulation o f I T S on the I r v i n e F O T area using ' P a r a m i c s 1.5' scalable microscbpictrafiic*simulator:- Phase* I: m o d e l calibration and validation," California P A T H Research Report, U C B - I T S - P R R 99-12, T999. 7. L. Chu, H . ' X . Liu, W . Recker, and H . M . Z h a n g / " P e r f o r m a f i c e Evaluating 'of Adaptive R a m p M e t e r i n g Algorithms U s i n g 'Microscopic Traffic' Simulation M o d e l , " accepted b y Journal o f Transportation Engineering. 8. Y. Gardes, A . D . M a y , J. Dahlgren, A. Skabardonis, " F r e e w a y Calibration and Application o f t h e P A R A M I C S Model,"" 81st'Annual M e e t i n g Preprint C D - R O M , Transportation R e s e a r c h ' F o a r d , J a n u a r y 1 3 - 1 7 , 2 0 0 2 , Washington, D.'C. 9. M : B e n - A k i v a / ' A . -Davol, T. Toledo, H . N . Kbustopoulos, ''-'Calibration arid evaluation o f M I T S I M L a b in Stockolm", 82nd A n n u a l Meeting Preprint C D R O M , Transportation Research Board, January 12-16, 2002, Washington, D . C . 101 U K H i g h w a y s A g e n c y , " t J K design rnanu'al fbr roads and bridge's," London, U K , 1996. - . .)J-I I • , 11. H.X. Liu, L. Chii, W : Recker, "Paramics A P I -Development- Ddcument for Actuated S i g n a l , H S i g n a l Coordination arid".Ramp-Control", California P A T H workingpaper,UeB-ITS-TWP-2b01-ll. ' * 1 1 12. E. Cascetta, "Estimation of trip matrices 'from traffic counts and survey"'data: A generalized least squares estimator," Transportation "ResV-B. Vol. 18 (4/5),' 1984, p p 289-299. ' 1 3 . M . G . H . Bell, *The : e'stimation o f origin-destination rhatrices b y constrained generalized 1 east square*s,'*Transportatibh R'esearCfi B . V of.25", N b . 1, 1*991[ p p 13-22-. r "> • * *• , 'Li. r . * 14. P. Robillard, "Estimating the O - D matrix from observed link volumes," Trans. Res. 9 s p p . l 2 3 - 1 2 8 , 1975. 15. E. C a s c e t t a , D . Inaudi, G. M a r q u i s , " D y n a m i c estimators o f Origin-Destination matrices u s i n g traffic counts," Transportation Science,"' 'VdWSJ, *No.4°, 1994, pp363-373. 36 16. K. Ashok, M . E . Ben-Akiva, "Alternative approaches for real-time estimation and prediction o f time-dependent origin-destination*flows," Transportation 6 Science, Vol. 34, N o . l , February, 2000. '^ii a, K ! * w *i . ^0" p -r i'i - i 1i t »r* jl K il l •* iV ** J. I * o . *•* i i t i « f' U J r r ' i m ? ) '1 I J ' i J 37 Chapter 4 On-line simulation 4.1 F R A M E W O R K O F O N - L I N E S I M U L A T I O N I N P A R A M I C S T h e goal o f this sub-task of the project is to enhance the capabilities £>f the P A R A M I C S simulation m o d e l t h r o u g h A P I p r o g r a m m i n g for t h e on-line simulation application. T h e framework o f the on-line system to b e implemented can be illustrated in Figure 4.1. T h e real-world loop detector data are inputs o f t h e system. D a t a o f those loop detectors located at cordon points of the n e t w o r k are queried from the database. T h e s e r a w d a t a are processed in o r d e r to obtain lane-based speed estimation and aggregated volume, o c c u p a n c y data at the detector station. T h e m i n i m u m aggregation c y c l e is equal to t h e t i m e interval o f l o o p detector data from the field, w h i c h is 3 0 s e c o n d s in California. A typical aggregation cycles is 5 minutes or 15 minutes. Reference O D pattern Dynamic O D estimation Forecast lead t i m e Historical Data Traffic flow prediction D e m a n d loading Paramics simulation l * D a t a aggregation Consistency check 2 Traffic data at cordon points L o o p data at measurement points L o o p data from Oracle database at A T M S Testbed Figure 4.1 F r a m e w o r k o f the implemented on-line system in P A R A M I C S I f t h e s ystem i s w o r k i n g u n d e r p rediction m ode, t h e future t raffic c ondition a t e ordon points o f the n e t w o r k will be predicted u s i n g the aggregated loop data of last several time intervals. T h e K a l m a n filtering based traffic prediction is applied. A forecast lead time c a n b e specified as a n input o f the prediction, w h i c h represent h o w long in the future the traffic condition is predicted. If the system is working under the responsive mode, this prediction process is ignored. T h e traffic flow data at cordon p o i n t s o f the n e t w o r k are then output to the d y n a m i c O D estimation module, that performs the estimation of an O D matrix based on the d a t a of the current time interval. T h e current d y n a m i c O D estimation 38 m o d u l e is a.'^imple method that e a r s o n l y .handle, a.freetvay network*. A n advanced dynamic O D •estimation: method, iwhich may. n e e d s a reference d e m a n d pattern as its input, can" be-inserted here for-the capability e n h a n c e m e n t s , o f the on-line simulation system. Currently, there are. s o m e on-going projects focusingrori.this.study.r } . •' « '1 A f t e r t h e acquisition o f the O D matrix, t h e - d e m a n d l o a d i n g ' m o d u l e remploya releasing vehicles j r o m its original' zone to* the network.„A composite m o d e l is' implemented in order to release vehicles with a certain h e a d w a y distribution, i.e. shifted negative exponential distribution u n d e r v e r y l o w traffic flow condition, n o r m a l distribution w i t h the>mean;of a:xohstant h e a d w a y under xongested'traffic condition,, a n d the, combination o f two distributions u n d e r o t h e r conditions. > A s a result, P A R A M I C S is connected w i t h the real-world J o o p datatdirectly a n d ' e a n j h u s on-line simulate traffic. S o m e d e m a n d errors m a y cause m o r e c o n g e s t e d q £ l e s s congested traffic •condition in.t&e simulation. A consistency checking m o d u l e ^s-.used, to .keep the simulation as similar as that in the real world. T h e real-world loop detector data at m e a s u r e m e n t points q f i h e n e t w o r k a r e . i n y o l v e d ' i n this p r o c e s s to-detect .the difference between the real w o r l d and the simulation. D u e to the current theoretical l i m i t a t i o n on consistency checking, t h e current project leaves this topic for t h e future."' - ' ' " u T h e following s e c t i o n s o f this ; chapter will-talk about the details h o w w e implement this on-line simulation system. 4.2 L O O P D E T E C T O R D A T A PROCESSING T h e objectives o f t h e p r o c e s s i n g o f r a w l o o p d e t e c t o r d a t a a r e t o o b t a i n : ( 1 ) t h e l a n e based speed estimation; (2) the aggregation o f v o l u m e and o c c u p a n c y data o f last several t i m e intervals. These data will further b e u s e d to O D estimation and d e m a n d loading. The; loop detector data ; sJor,ed a t t h e A T M S testbed,datal?ase : are obtained from the, F r o n t End Processor (FEP) of d i s t r i c t 12 qf Caltrans. These data are.raw data an,d not processed b y the A T M S system o f Caltrans.-A script language is used to p r o c e s s these data in order to store them to the Oracle database. T h e s e data can b e queried for t h e research u s e inside our local network. A n example of the data w e query from a typical mainline loop detector station is: 05/22/2001 06:00:00, 1201203, 5, 5, 1, 10, 0, 1, 9,-0, 2, 13, 0, 1, 7, 0, 0, 0, 0 w h i c h corresponds to the format: D A T E T I M E , V D S J D , # o f L A N E S , # of L O O P S , L A f l E _ l _ V O L , L A N E _ l _ O C C , LANE_1_STATUS, LANE_2_VOL, LANE_2_OCC, LANE_2JSTATUS, ...., LANE_n_VOL, LANE_n_OCC, LANE_n_STATUS 39 'tVDS__ID" represents vehicle detector station index. A-detector station c a n h a v e several loop" detectors', each o f w h i c h covers o n e lane. "# o f L A N E S " representS'the<total n u m b e r o f -lanes at the loop detector station. " # o f L O O P S " represents the total n u m b e r of installed loop detectors at the station*. " L A N E _ 1 " represents the leftmost lane. T h e actual o c c u p a n c y value o f a lane is equal to the L A N E I O C C / 9 0 0 because the scan rate of loop- detectors is 3 0 ' H z and the time, interval o f these data is 30 second. " L A N E _ 1 _ S T A T U S " represents the status of the data, w h i c h shows* " 0 " for good data a n d " 1 " f o r b a d data. * T h e l o o p d etector data* f r o m t h e field m a y suffer f r o m . a l o t o f p r o b l e m s . T h e r e a s o n s m i g h t b e the c o m m u n i c a t i o n , noises, and sensitivity o f loopsi T h e quality o f t h e data cannot b e detected. T h e data processing m o d u l e has the following features: (1) Analyzing the existence o f l o o p data (2) Filtering.those d a t a w i t h p o o r quality (3) Aggregating v o l u m e and o c c u p a n c y data-at a certain aggregation cycle, .typically, 5 -minutes or 15 m i n u t e s ^ (4) Estimating -the average lane-hased speed based o n aggregated .volume and o c c u p a n c y data T h e estimation of speed is based on the assumption o f an effective vehicle length. For lane*i o f l o o p detector station k, the average^speed o f time interval t is defined as (4.1) v,u(0 = — - r *Skj OkAO where, qk,i = traffic count Okj = occupancy* gkj = average "effective vehicle length * T h e ' a v e r a g e effective^ v e h i c l e ' l e n g t h "needs-to*be estimated'before the r o p e r a t i o n ' o f the algorithfri. W e take" t h e default values of effective vehicle length's from the A T M S "system of District 7 and'12 in durialgorithrnl T h e s e default'values^are: < ' *" l (1) Leftmost laneV ^ f e e t " -» • '' * (2) Middle lanes: 2 2 feet (3) Rightmost lane: 2 5 feet 4.3 T R A F F I C F L O W PREDICTION If t h e system is w o r k i n g under prediction mode, data of those l o o p detectors" located' at cordon points of the n e t w o r k are outputted to the traffic flow prediction m o d u l e for the prediction b f the future, traffic condition based "on the aggregated loop data of last several t i m e intervals! If the s y s t e m is w o r k i n g , under the" responsive, m o d e , this'prediction J f process is bypassed. * ' 40 A typical O D O D together (Ashok et-al? cordon points traffic flows. estimation & prediction method combines.the estimation and prediction o f using K a l m a n filtering and Generalized Least Square ( G L S ) approach 1996). T h e proposed m e t h o d h e r e i s - t o predict the future traffic flows at o f n e t w o r k first and then estimate the O D matrix b*ased on these predicted The'traffic "flow-'prediction involves the stations of upstream o f m a i n l i n e freeway, •previous time penods^of the-same-day. '< -/ . h "-prediction o f traffic counts at loop detector on-ramps and off-ramps based on loop data o f *J •« ' • 4.3.1 Introduction A c c o r d i n g ' t o l o o p data, w e c a n only k n o w the traffic counts o f last several time intervals. In order to reflect traffic counts of the current running t i m e interval (or, next t i m e ^interval), w e have to use^traffic flow.#rediction.,techniques. *A n u m b e r of traffic? fl6w predictive models h a v e b e e n developed and proposed, including ,historic .profile approaches (Shbaklo, S., B h a t , et al 1992, Kreer, J. B., 1975, Hoffmann, G. and J. Janko, ;1990, Jeffrey,'D. £F.,d987),-non-parametric r e g r e s s i o n (SeungjaeXe.eKeUaly 1998y D a v i s , G. Av and/Nihan,,N>iL.,U991), time-series (Mobrthy, G. K . -and RatcIffieT-B. G v 19&8), ^leurabnetworks (BaherA-bdulhai, e t a i ; 1998,-Jinsoo Y o u a n d - J s c h a n g h o ^ l 9 9 8 ) ^ K a I m a n filtering jtYoung^-Ihn Lee,t C h a n Y o u n g -Choi* 1995), t r a f f i c simulation, a n d D y n a m i c Traffic1 Assignment m o d e l s . 4.3.2 Kalman Filtering b a s e d prediction-method * The;Kalman filter, p r o p o s e d b y K a l m a n in. I 9 6 0 , provides an.efficient least square b a s e d solution to the estimate p £ t h e state, vector x o f a discrete t i m e controlled process.^ K a l m a n filtering has shown g o o d p e r f o r m a n c e in a lot o f real-time f applications. T h e K a l m a n filtering based prediction m e t h o d is applied in this study. T h e traffic flow at a detection station is the state variable for the K a l m a n filtering process. W e can establish the state equation as follows: xk = xk_{ + uk + wA_, (4.2) where x* is the traffic flow at time interval k. Wk is the state nois"6, which" has a n o r m a l distribution with zero m e a n and a variance of Qk. Uk is the predicted traffic flow increment based on the last several traffic flow data (Xk-n, Xk-i) using the linear regression approach, which h a s the objective to fit a linear relationship: xt-a + b-i ' (4.3)' where i varies from 1 to n. a is the intercept o f the o f the line with the vertical axis and b is the slope of the line. T h e least square solution for this regression problem is 41 n n »-£(^*M)-<LO-.<5>*-,) M (=1 (4.4) »-(Z«2)-(Z**-i): /-I i=l T h e value of b is actually the predicted c h a n g e o f traffic flow at the detector station UkLet Zk denotes the observation o f traffic flow at time interval k, w h i c h is obtained) from t h e real-world loop detector. T h e m e a s u r e m e n t equation associated with the state variable Xk is given by: (4.5) 2* = *k + vk w h e r e v*. denotes t h e m e a s u r e m e n t error, w h i c h has a n o r m a l distribution with zero m e a n a n d a variance o f Rk' i. In m a n y applications, the state^noise c o v a r i a n c e Q and m e a s u r e m e n t noise c o v a r i a n c e R are often a s s u m e d t o b e constants, which-are usually jdetermin&l.prior t o t h e operation o f t h e filter. R is generally determined b a s e d ' o n off-line^sample measurements. H o w e v e r , Q i s m o r e ^difficult to b e determined bedause t h e p r o c e s s state* is typically n o t bbservable. T h e m e t h o d s described in Section 5.2.3 are used to the online estimation*o£R-and Q.. L 4.3.3 Solution to the K a l m a n filter based prediction) Let xk and Pk denote a priori state estimation-'and its estimation variance a t time step k, xk a n d , ^ d e n o t e t h e ^p'dsteriori'state e s t i m a t e a n d ' its' estimation covariance at t i m e step k, arid Kk denotes ' K a l m a n gain. T h e solution* Jo th'e'above K a l m a n filter problem, is s h o w n a s follows: S t e p 1: Initialization x0 = E[xQl pQ =E[(x0-x0)2] (4.6) Step 2: State propagation t xk = xk_x + uk (4-7) (4-8) Step 3: K a l m a n gain calculation: Kk=Pk[Pk+Rkyl (4.9) Step 4: State estimation *k =Xk+Kk[z*-*k] (4.10) 42 Pk=Pk-KkPk . i (4.11) Step 5: State prediction If there is only one-step ahead prediction, the predicted traffic flow is: 'Jt '-5fti-= * * + " * + i * ' (4-12) • where Uk+i is calculated based on Equation 4.4. T h e prediction variance is: Jt t ?»Mt.ft ^ (4-13) If the prediction is for several time intervals ahead, t h e predicted traffic flow will b e used as the observation for a re-iteration prediction p r o c e s s (i.e. Step 5, Step 3, and Step 4). 4.4 O D E S T I M A T I O N MODEL Traffic xounts-.at.alLcordoncpbints, of the^ s t u d y n e t w o r k are n e e d e d for-(3D estimation. Thesetcordon points-include the-upstream end of freeway, d o w n s t r e a m end of freeway, all on-ramps and all off-ramps. 4.4.1 Volume conservation T h e freeway system h a s the following input flows: i (1) traffic flow at the upstream end o f freeway (2) traffic flow at eacji r a m p Since there are correspondent loops located at o n - r a m p s and the upstream end of the sum of entrance traffic counts is: In_Flow,(t) = Up_Flow(t) + > #amp_,Flow(i,t) freeway, (4.13) where i is ;the index o f r a m p s , In_Flqw(t) is the traffic count o f t i m e interval / at the upstream end of freeway, Ramp_Flow(i, t) is the traffic count of t i m e interval t on r a m p /. If there is no congestion at the freeway origin locations, In_flow(t) is the d e m a n d entering the freeway section. T h e system has the following outflows: (1) traffic flow at each,off-ramp (2), traffic flow.at the downstream end of freeway Since there are correspondent l o o p s located at off-ramps a n d the d o w n s t r e a m end of freeway, the sum of exit traffic counts is: Out_Flow(t) = Down_Flow(t) + ^Offramp _Flow(i,t) (4.14) 43 rrr T h e principle o f the t e c h n i q u e o f O D estimation is: fn_FIow(t) = Out_Flow(t) (4.15) A s s u m i n g the error caused b y loop detector detection can be ignored, this formula is true if the traffic is stable. U n d e r this condition, w e can further estimate each element in the O D table through distributing off-ramp traffic t o upstream origins/zones. 4.4.2 M o d e l for distributing off-ramp traffic to upstream zones T h i s m o d e l is originally proportionality s c h e m e . from FREQ model, w h i c h is based O, ODtj=Dj. on the intuitive (4.16) 2>ieA where A upstream freeway); freeway); is a set that includes all upstream z o n e s o f zone j (i.e., all on-ramps and the end o f freeway);. Dj is the total off-ramp traffic flow (or, exit traffic; flow from Oj is the-total flow from z o n e i to freeway mainline (or, entrance trafficiflowto O D y is t h e d e m a n d from origin i to j . 4.5 D E M A N D L O A D I N G / V E H I C L E RELEASING P A R A M I C S release vehicles to the links w h o s e ' m i d p o i n t lies within origin zones. T h e location that vehicles m a y b e released can be a n y point on the" link: T h i s Simulates the p a r k e d vehicles m o v i n g a w a y from t h e kerb, out o f driveways and emerging from l u n m o d e l l e d side-^streets. " H o w e v e r , for a n e t w o r k with freeways and arterials, there are some internal zones and s o m e cordon points, located at the b o u n d a r y o f freeways and arterials. The-vehicle release pattern o f P A R A M I C S can only simulate the vehicle release pattern from internal zones. H o w to release" vehicles from a cordon point o f a' network is *6ur inferest; T h e study on s t i m e h e a d w a ^ distribution w a s related to t h i s t o p i c . * ;r 4.5.1 R a n d o m m o d e l W h e n the traffic is not congested, or h a s a low density, Poisson'count'distribution cari'be u s e d to describe the distribution o f the n u m b e r of time periods, w h i c h ' c o n t a i n different flow level. T h e negative e x p o n e n t i a l distribution can b e further Serived from t h c P o i s s o n count distribution for m e ' d e s c r i p t i o n o f t h e ' n u m b e r of*'individual t i m e - h e a d w a y s in various time h e a d w a y intervals. Its probability distribution furictidh i s : ° ' P(kzt) = l-e P(h £ t) = e~% -^or (4.17) 44 ""BBli HLJ.-T3" vvnere t is a t i m e h e a d w a ^ Valued t is the avefag£-time'headway or-the reciprocal o f t h e departure rate"tuhit? veh/sec). Since Q'<P(hzt)<lks w e . f a n a s s u m e P(h>t) is a r a n d o m nurrioer rarigihg 'from 0 to J f'."Theii the" cofresporidiri| 'time h e a d w a y of the r a n d o m n u m b e r is: ( 4 -18) t$MK)*~t w h e r e x = P(h>t), w h i c h is a r a n d o m n u m b e r uniformly distributed between 0 and 1. Therefore, the intern-departure time from drrofigin zone is: tM-tt = -ln{X)*~t ' ( (4.19) w h e r e tj+i and ti are the departure t i m e o f two vehicles. T h e negative exponential ffis*rnDutfon''has t h e ' inhefeht M a t u r e Hhat the S m a l l e s t "headways- are m o s t likely occur. However, r if-is 1 impossible to h a v ^ s u c h a'low"time h e a d w a y u n d e r the^ow-densityfrafficT h e shifted negative exponential distribution is thus -employed. Its probability distribution function is: P(h>t) = e-I=a -" (4.20) where a is £he m i n i m u m time headway under the low 7 density .traffic. T h e inter-departure time is: „ .i tM-t,=a-I„{X)*(t-a) (4.21) 4.5.2 Constant h e a d w a y m o d e l If the traffic is congested, vehicles are traveling under car-following regime, T Vehicles departing from an origin z o n e can be thought to have a constant h e a d w a y . T h e interdeparture time between two consecutive vehicles is the reciprocal o f the departure rate, i.e., 'W-</=)£ (4-22) T h e normal distribution is used to describe the condition that drivers attempt to drive at a constant time h e a d w a y but the actual h e a d w a y varies around the expected h e a d w a y because of drivers* perception error. 4.5.3 Composite m o d e l T h e random model is suitable for the very low traffic flow conditions and the constant h e a d w a y model is suitable for the very high traffic flow conditions. It is h a r d to identify if the traffic condition is under r a n d o m state or constant h e a d w a y state. W e can thus integrate above two m o d e l s to a n e w m o d e l via the use o f a distribution factor, w h i c h h a s 45 a value b e t w e e n 0 a n d 1. T h e distribution factor determines the m o d e l selected for t h e departure o f vehicles., F o r example, 0.3 o f the distribution factor indicates that 3 0 % o f vehicles departs according to constant h e a d w a y model a n d other 7 0 % according to die r a n d o m model. tM-tt* MX if <b>df a-la(X)*(t-a) if <b<df (4.23) w h e r e O is a r a n d o m n u m b e r uniformly distributed between 0 and 1, df is the distribution factor, w h i c h can b e determined based on the following equation: df = \.S/t (4.24) w h e r e 1.5 second is r e g a r d e d as the, m e a n t i m e h e a d w a y w h e n ( all vehicles are under v e r y h i g h traffic, flow conditions, r c a n be obtained if w e k n o w - t h e total n u m b e r of-vehicles that will b e released from an origin zone. ( 4.5.4 R a n d o m n u m b e r generator P A R A M I C S uses t h e Marsaglia r a n d o m n u m b e r generator. However, 1 w e take the modified version of t h e r a n d o m n u m b e r generator proposed b y P a r k & Miller to generate r a n d o m number' for vehicle releasing. J o h n Burton of G & A "Technical Software, I n d is the author of this modified version of r a n d o m n u m b e r generator, which is also the r a n d o m n u m b e r generator o f M i t s i m . T h e advantage o f this generator is that it can run on any m a c h i n e with a 32-bit integer, without overflow. ' T h e source code for this r a n d o m n u m b e r generator is s h o w n below, in w h i c h " s e e d " is a global parameter. d o u b l e p p _ u r a n d o m (void) { // Constants for linear congruential r a n d o m n u m b e r generator. const long int M = 2 1 4 7 4 8 3 6 4 7 ; // M = m o d u l u s (2 A 31) const long int A = 4 8 2 7 1 ; const long int Q = M / A ; const long int R = M % A;, J "'< seed = A * (seed % Q ) - R * (seed / Q); seed = (seed > 0) ? (seed) : (seed + M ) ; return (double) seed / (double) M ; 4.6 R E F E R E N C E S 46 •B& Ashok, -K. (499'6) Estimation' a n d 'Prediction ofi'Time-Dependent Origin-Destination Flows, P h D ' t h e s i s , D e p a r t m e n t o f - C i y i l a n d Environmental. Engineering, .Massachusetts Institute of Technology, Cambridge, M A . Baher Abdulhai, H i m a n s h u Porwal, Wilfred W . Recker, Short''TerrrTFreeway »Traffic Flow Prediction U s i n g Genetically-Optimized Time-Delay-Based Neural N e t w o r k s , U C I - I T S - W P . 9 8 4 4 , 'July, 1998 ^ , , " * , . B a h e r Abdulhai, J i u h B i i n g Sheu, Will Recker, Simulation o f I T S on t h e l f v i n e F O T A r e a U s i n g ' P A R A M I C S 1.5' Scalable Microscopic Traffic Simulator: Phase I: M o d e l Calibration and-Validation, California PATH.ResearcRTlepoft,UCB-JTS-PRR-99 f -12. i* , .• i A I i t i. Brian L.Smith and Michael J.Demetsky Short-term Traffic F l o w Prediction: N e u r a l N e t w o r k Approach, Transportation Research R e c o r d 1453, P P 9 8 - 1 0 4 Davis, G.'A..and.Nilian, N . L.-1991. NonparametritrRegression^tnd Short-Term F r e e w a y Traffic Forecasting, Journal o f Transportation Engineering, P P 1 7 8 - 1 8 8 D e r - h o r n g Lee, X u Y a n g , P. Chandrasekar, P a r a m e t e r Calibration for P A R A M I C S U s i n g Genetic Algorithm, T R B 2001. H e n r y Liu, Lianyu C h u , Will Recker, P A R A M I C S A P I D e v e l o p m e n t D o c u m e n t for Actuated Signal, Signal Coordination and R a m p Control, P A T H w o r k i n g p a p e r U C B ITS-PWP-2001-11 Jeffrey, D. J., R u s s a m , K . , and Robertson, D . L, Electronic R o u t e Guidance b y A U T O G U I D E : the Research Background., Traffic Engineering and Control, 1987, PP525-529 Kreer, J. B., A C o m p a r i s o n of Predictor Algorithms for Computerized Control, Traffic Engineering, vol.45, N o . 4 , 1 9 7 5 , P P 51-56 Hoffmann, G. and J. Janko, Travel T i m e as a B a s i c part o f t h e L I S B Guidance Strategy, paper presented at the I E E E R o a d Traffic Control Conference, L o n d o n , M a y , 1990 Moorthy, C. K. and Ratcliffe, B. G., Short Term Traffic Forecasting U s i n g T i m e Series Methods, Transportation P l a n n i n g Technology, v o l . 1 2 , 1 9 8 8 , P P 4 5 - 5 6 Seungjae Lee, D a e h y o n K i m , J u y o u n g Kim, B u m c h u l Cho, Comparison o f M o d e l s for Predict in Short-term T r a v e l Speeds, Proceedings o f 5 t h W o r l d Congress o n ITS, Korea, 1998 Shbaklo, S., Bhat, C , K o p p e l m a n , F., Li, J., Thakuriah, P., Sen, A., and Rouphail, N . , Short-term Travel T i m e Prediction, A D V A N C E Project Report, T R F - T T - 0 1 , 1992, Illinois University Transportation Research Consortium 47 Smith, B. L. and D e m e t s k y , M . J . , Traffic F l o w Forecasting: C o m p a r i s o n o f M o d e l i n g A p p r o a c h e s , Journal o f Transportation Engineering, vol.123, N o . 4, 1997, PP261-266 Park, S. K . and Miller, K . W . (1988), R a n d o m n u m b e r generators: Good ones are hard to find,-Comm. A C M , . V o l . 31, N o . 10; R. Jayakrishnan, J u n - S e o k Oh, A b d - E l - K a d e r Sahraoui, Calibration and,Path D y n a m i c s Issues in M i c r o s c o p i c simulation For A d v a n c e d Traffic M a n a g e m e n t and Information Systems, T R B 2 0 0 1 , 2 0 0 1 . i Y a n g , Q. and H.-Koutsopoulos,(1996): A microscopic traffic simulation'for evaluation of d y n a m i c traffic m a n a g e m e n t systems, Transportation Research 4C, p p l 13-129. i v * ^ i / Y o u n g - I h n Lee, C h a n Y o u n g Choi, D e v e l o p m e n t o f L i n k Travel T i m e Prediction A l g o r i t h m , for U r b a n E x p r e s s w a y , Proceedings o f 5 t h ' W o r l d - C o n g r e s s : on ITS? Korea; 1998. IT -1 r 1 i in 1 » i ' •* ). ' i f y i. 'i t .3 1 1. tc * . n **. * * r ' '- M i '-U'Ji l , i. 48 **-»- C h a p t e r 5. D a t a Fusion-for B e t t e r T r a v e l TiirteEstimation 5.1 I N T R O D U C T I O N tin current traffic surveillance systems,; point detection systems, .such .as, inductance, loops, -microwave detectors, aridiultrasonic'detectors; have„be.en v±se4 for trafficjp'ata-collection. -Among ! these detection tech#ologies,jnost';agenc.ies,,rely p n jnductange-loop,detectors, .mostly j i n g l e - l o o p s . S o m e double, Joppdfctepjors- haye? bjeen installed b e c a u s e d o u b l e J o d p s x a n provided-accurate*point speed estimation besides the traditional traffic count and 'occupancyoutputs. Although_most;of the-purxent traffic "control a n d m a n a g e n i e n t s y s t e m s , suchuas r a r n r u m e t e r i n g - a n d incident deteption>.-p'e.pend on -mege, point-based, data, for t operation, these point d e t e e t i o n s y s t e n x s l i a y e limitaJiQn-in.prpyiding-se^cJipn travel-times that are preferable for other Advanced Transportation M a n a g e n i e n ^ and Information Systems ( A T M I S ) applications, such as the traffic information and route guidance systems'. T h e ?mqthods.;estimating, section^ teavel *tirne( from,, sjngle'.,loop,,dete i ctpr 4ata -involve t h e conversion .of point volume .and o c c u p a n c y data £o fraveitfa&Hjasea! on .traffic flow theory [,l]rThis estimation is i n a c c u r a t e n o t ^ n l y because o f the conversion error but also! because o f t h e points detection* system-*s l i m i t a t i o n in capturing ar-ea-wide traffic dynamics. *. . Recent advances injsensing technologies, s u c h a s Automatic- Global Positioning Systems (GPS) [2], Vehicle Identification (AVI) [3], pejlular phone*.positioning [4], and vehicle re-identification technology based on advanced loop detectors [5] o r v i d e o i m a g i n g technologies [6], provide information on timestamps w h e n vehicles p a s s predefined locations. In such circumstances, the travel t i m e during a t i m e interval can^be calculated b y averaging individual vehicles' travel times from upstream to downstream. Currently, the GPS-based on-board navigation systems h a v e b e e n m o r e and m o r e installed to passenger cars, w h i c h will b e c o m e potential p r o b e s if a suitable c o m m u n i c a t i o n ' m e t h o d Even though these systems'arq expected to p r o v i d e high fidelity traffic '.information y/hen there are enough p r o b e vehicles, these systems'are insufficient yet to p l a y a major r o l e as m a i n detection systems due to the lack o f p r o b e rates. It seems inevitable to h a v e multiple data sources for A T M I S applications. T h e y will b e either point detection data or probe vehicle data. In terms o f the 'acquisition of section travel time from these data sources, the p r o b e - b a s e d detection systems m a y suffer from the low frequency'of p r o b e s or the situation that the probe vehicle travel t i m e cannot reflect the travel times of all vehicles that traversed the section while the point detectors suffer from the inability iri obtaining travel t i m e 'data directly. I n other w o r d s , e a c h d a t a source provides traffic information with "different -characteristics, but h a s its »own limitation. H o w e v e r , these different sources of data could be complementary each other, and it will b e possible to achieve better measures w h e n t h e y are considered 49 simultaneously. T h e m a i n interest of this p a p e r is h o w to u s e both probe-based data s o u r c e a n d p o i n t s b a s e d d a t a source for b e t t e r section travel, time estimation. D a t a fusion is a t e c h n i q u e t o c o m b i n e data from several sources in order to provide c o m p r e h e n s i v e and accurate information. Several data fusion techniques h a v e b e e n d e v e l o p e d and m o s t o f t h e m are derived from physical models, feature-b£sed (inference m o d e l s , and cognitive-based m o d e l s [7]. Physical models estimate the classification and identity o f an object b y m a t c n i n g m o d e l e d or pre-stored object signatures to the observed data/ A n e x a m p l e o f physical m o d e l s is Kalman'filtering, Which is- m o s t often used to positional 'estimatioh^aricl target tracking 'applications '[8*,f 9].< Feature^based .inference m o d e l s classify or idbntify objects b y m a p p i n g data,-such as-statistical k n o w l e d g e about an object or recognition of its features. TheYe are m a n y feature-based'algorithms, such as B a y e s i a n , Dempster-Shafer, artificial n e u r a l network, entropy' iriethodj woting m e t h o d , figure o f Merit, etc. Cognitive-based m o d e l s emulate a n d automatevthe decision-making p r o c e s s e s used b y h u m a n analysts. E x a m p l e s t>f this* T y p e o f m o d e l s a r e knowledge-based expert s y s t e m ' a h d "fuzzy logic m e t h o d . f T h i s chapter proposes a -data fusion algorithm for section travel t i m e estimation that fuses b o t h ' p o i n t detectOf data and a r e a - w i d e ' p r o b e - d a t a ' u s i n g - t h e ' A d a p t i v e K a l m a n Filtering ( A K F ) technique.' T h i s paper" is* organized^ as follows: Section "2,'describes t h e m e t h o d 6 1 o g y o f the' p r o p o s e d A K F baSea" section -travel' t i m e fusion algorithm, w h i c h h a s the capability to dynamically estimate the variances o f state noise and measurement noi'se. I n Section 3, the p r o p o s e d algorithm is implemented in a microscopic simulation environment and t h e -'algorithm is evaluated u n d e r ' both recurrent and noh-recurreht scenarios: Finally t h e c o n c l u d i n g r e m a r k s a r e ^ v e n . 5.2. M E T H O D O L O G Y 5.2.1 K a l m a n Miter ' ' T h e K a u n a n filter, p r d p o s e d ' b y K a l m a n in,1960, provides^an^fficient.least square based solution to the estimate o f tne"stafe Vector x o f a disorete'tinle controlled process t h a r c a n b e described b y tije linear stochastic difference equation*[ 10j: * * Xk =®k.k-\xk-y +Uk+Wk_} '(5.1) i w i t h a m e a s u r e m e n t vqc^or y that is, yk = Hkxk+ Y* it* • . , v ., ** j ) i$t& , wfc a n d v i a re t he s tate a n d m easurement n pises, r espectively. (J-ljey a r e a ssurned J o b e uncorrelated white noises.with,normal distributions;i * ** -, .~-f/. piw)~(0,Q) . •* -r .($••?> i 50 j*v)~$<U) i n , (5.4) In m a n y applications, t h e state n o i s e covariance Q and m e a s u r e m e n t n o i s e covariance R are often assumed to b e constants, w h i c h are usually determined prior to the operation of t h e filter. R is generally determined b a s e d on off-line s a m p l e m e a s u r e m e n t s . H o w e v e r , Q is m o r e difficult to b e determined because the process state is typically not' observable. In Equation 5.1, O is a transition matrix that connects the state at the previous time step k - 1 with the current time step k. u is an optional control input to the state x. In Equation 5.2, matrix H relates t h e sfatfe t o t h e m e a s u r e m e n t y. In p r a c t i c e , '3>, u* Etrid H m i g h t ' b e time-variant. If Q and R are^exactly k n o w n , the solution to t h e K a l m a n filter p r o b l e m is: xk=<S>k,k-\Xk^+uk * , ^ = 7^1mkMl^kTl xki=Sk +Kk[yir-Hkxk] (5.5) . J h=rk-'KkHkPk> (5.7) (5,8) ^__<5-9) w h e r e xk' and Pk are defined as a priori state estimation and its estimation covariance at t i m e step k. xk and Pk are defined as the a posteriori state estimate a n d its estimation covariance at t i m e step k. K* is defined as K a l m a n gain. Equations 5.5 a n d 5.6 propagate t h e current state and error c o v a r i a n c e estimates to obtain a priori state estimation for the next t i m e step. Equations 5.8 and 5.9 are used to incorporate t h e rneasurement into t h e a priori state estimation i n order to obtain a n i m p r o v e ^ a posteriori estimate. 5.2.2 Application o f K a l m a n Filter to the Seciion Travel Time.Estiniatioh K a l m a n fitering has b e e n used to solve sorne r traffic p r o b l e m s , such as the d y n a m i c estimatidn of traffip density [ 1 1 , 1 2 ] , freeway O D dernand m a t r i c e s [13], the prediction o f traffic v o l u m e a n d travel t i m e [ 1 4 , 1 5 , 1 6 1 . l l i i s p a p e r uses K a l m a n filter.to associate t w o data sources^ point detector daja and probe vehicle, data. W h i l e b o t h traffic count and p c c u p a n c v data, ,are provided frorn the point* detectors, t h e section travel t i m e c a n b e directly sampled from probe vehicles. H i e objective is to obtain a better estimation of section travel time. This section provides an overall description o f t h e model. 5.2.2.1 Travel T i m e from Section Density T h e m o d e l w e are proposing 1 here is based 'on the conservation o r continuity equation. T h i s equation s h o w s t h e s a m e form as in fluid flow, and t h e solution o f t h e conservation equation in traffic flow w a s first proposed b y Lighthill and W h i t h a m [ 1 7 ] and R i c h a r d s [18]. T h e fluid conservation equation characterizes compressible 1 flow, that is, 51 —£. + = o (or traffic generation rate) d x ax (5.10) where, q - flow (vehicles/hour) k = density (vehicles/mile) x = location t = time If the speed of such traffic fluids is v, w e h a v e the following basic identity: q = k-v (5.11) F r o m this equation, travel t i m e can b e derived as a function o f section density and traffic flow rate. For a section w i t h detector stations at its boundaries, the traffic flow passing this section (i.e., q) c a n b e estimated as a linear function 6f the tiafficsfiow'passing the upstream detector station q u and d o w n s t r e a m detector station qa- A s s u m i n g that the traffic inside the section is h o m o g e n e o u s , a n intuitive estimate of the section travel t i m e is: A * ^ ^ v q ^ * _ _ oc-qu+{l~a)-qd ( M 2 ) where, ttSD = section-density-based travel t i m e Ax = length of the section a = a smooth'parameter E q u a t i o n 5.12 actually establishes the relationship among t i e section travel'time, section density, and passing flow of section m e a s u r e d b y t w o point detectors at boundaries ( of the section. A s in E q u a t i o n 5.12, the section travel time can b e estimated as long as accurate m e a s u r e s of section density. ' J Figure 5.1 shows a typical section of urban freeway, \sjhich includes, oiie ofi-rarrip and'one b f P r a m p . Let l^J(t) d e n o t e 'the n u m b e r o f vehicles*within a section a H i i n e ' t and'let* N u ' ^ Na(t), represent trie n u m b e r o f vehicles passing the* upstream and downstream de^ectpr stations during time (t-1., t). *^<m(t) and No«(t)' are the' traffic cdunts' entering and exiting the freeway section from on-ramps and" off-ramps, "respectively/If the count information l is precise, then "the s e q u e n c e Nft) can b e represented" b ^ : " ' *' ° N{t)^N(t-l) + {Nll(t)+N0„(t)-[Nd(t) + Nojr(t)]}=:N{t-l) + ^N(t) ^,(£.13), Let k ( t ) denote the .section 4 e n g i t y ,at t i m e t. k(t) c a n b e estimated based, o p the relationship be,twe,en N ( t ) and-)t(t): , f ^ * j •*. y L*Ax where, 52 L = n u m b e r of lanes on'mainlinel freeway At = time interval o f detector data aggregation Nu i** 'Hi Nc -Figure 5.1 A typical section pf-freeway T h e section density is a non-observable state variable. A s a deterministic equation, the section density sequence-mayoiot.be correctly,or-jpbustly. estimated using/Equation 5.14 rif £here v are a n y inpufcdata errors. T h e worst. situation^ is that this .equation cannqt? c o n v e r g e and thus";losathe ability.to-estiniate;the section d e n s i t y . ^ solutionjtofthisjs tp. introduce a feedback control m e c h a n i s m , s u c h as K a l m a n filtering, t o this estimation process. 5.2.2.2 Travel T i m e from Probe Vehicles 'When, pfobe vehicje d a t a are available, J h e travel- t i m e during a> time, interval .can be .calculated b y averaging- individuali vehicles.' JraveijtiniQS from'upstream, to dQwnstreani. "That is, the average travel time (ttA\ is calculated based on-the .vehicles tfjat arrived at the vdownstream station during.a given time-step v[-l 9]. £ « - « ) ,! tt. = M=l N (5.15) where, * '* '* N =Aiumbet o f s a m p l e vehicles arriving the d o w n s t r e a m station ~ ty- time w h e n vehicle n passes the downstream station d t" = time when vehicle n passes the upstream station u 5.2.2.3,Design o f K a l m a n Filter ' W e apply K a l m a n filtering to this travel t i m e estimation process. W e u s e b o t h d a t a sources: one from point detectors and the other from probe vehicles. Based o n E q u a t i o n 5.14 and Equation 5.12, the state and m e a s u r e m e n t equations o f t h e K a l m a n filter are: State equation: k(t) = k(t -1) + u(t).+ w(t -1) (5.16) Measurement equation: tt(t) = H(t)*k(t) + v(t) (5.17) where w(t) is the system noise, w h i c h is a zero-mean Gaussian white noise with the variance of Q. v(t) is the measurement noise, i.e., the n o i s e of section travel t i m e 53 estimates from p r o b e vehicles. v(t) is a w h i t e n o i s e w i t h t h e variance o f R. In addition, according to E q u a t i o n 5.14, w e have: u{t) = -^-*W(t) L*Ax (5.18) Based on Equation 5.12, w e set a = 0.5 in this study. T h e n w e have: //(,) = *Z <?*(0 + * r f (0)/2 (5.19) N o t e in this p r o p o s e d m o d e l , the •transition'matrix, O, is^a constant of 1. In addition, w e u s e k instead o f x and tt instead of y. T h e solution of this Kalman'filter is s h o w n in Equation 5.5 to-Equation;5.9: At each t i m e step, the K a l m a n filter w i l t output a posteriori-state estimate o f the section density, w h i c h -can b e further used to calculate the estimated section travelrfme using E q u a t i o a 5 . 1 2 . 5.2.3 Adaptive K a l m a n Filter: estimation of n o i s e statistics i A w e l l - k n o w n limitation o f the application of K a l m a n filter is that it is hard to obtain the estimates o f state n o i s e covariance Q"and m e a s u r e m e n t n o i s e covariance *R,'which'might c h a n g e with each t i m e step or m e a s u r e m e n t in a real-world .system.-If R and Q- cannot reasonably represent the-features of the state and m e a s u r e m e n t noises, the performance^of K a l m a n filtering will degrade. T h e inappropriate values of covariance matrices *R and Q can cause the divergence of the optimal estimator o f K a l m a n filter. A c c u r a t e k n o w l e d g e o f n o i s e covariance R and Q is critical for the successful application o f K a l m a n filter to t h o s e processes, such as the section travel time estimation process, with time-varrant-*noise statistics. Several researchers h a v e studied on the sorcalled A d a p t i v e K a l m a n F i l t e r ( A K f ) , w h i c h . i n c o r p o r a t e s ^ h e o n l i n e estimation o f R t l a n d Q w i t h the K a l m a n Filter process. The.methop's of A K F w e r e class4fied;jntp four categories, Bayesian, m a x i m u m likelihood, correlation, and covariance m a t c h i n g [20]. y T h i s paper uses a covariance matching m e t h o d based on the research work d o n e b y M y e r s K.A. and T a p l e y B.D. [21]. T h e basic concept of this method is to -niatch "trie estimated covariance w i t h theoretical covariance. 5.2.3.1 Estimation o / R Based on Equation 5.17, the measurement noise v(t) cannot b e determined because the true state vector k(t) is u n k n o w n . A n intuitive' approximation o'f the'measuremeht noise at t i m e step j is given by: ' • . u rj = ttj-Hjkj •* (5.20), 54 where'-rj is r f e f i n e d ^ t h e m e a s u r e m e n t n o i s e sample-, it is also k n o w n as the innovation or ' t h e m e a s u r e m e n t residual. T h e innovation s e q u e n c e is>.a zero meant Gaussian, w h i t e n o i s e sequence. This is a necessaity and sufficient-condition for the optimality o f - a K a l m a n filter [22]. A s s u m i n g "that t h e n o i s e sample s e q u e n c e r / can" b e representative ,of t h e true measurement noise sequence Vj, rj and v, should b e independent and h a v e the s a m e distribution. T h e n t h e actual covariance o f Vj can, b e approximated b y t h e u n b i a s e d estimate of its sample covariance: •n N > ~ Cr=—Yrrf • > (5.21) where :N" is the number, of measurement noise* s a m p l e s , , w h i c h is selected empirically in order to provide a reasonable noise statistics'based o n the latest^lata. < Based on Equations 5.20 and 5.21, the expected value* of Cr is: E(Cy) = j-^HjPjHj+R (5.22) T h e unbiased estimation of R-will be: k =jhit>lrjr> y=" ~^ w > ] (5 -23) 5.2.3.2 Estimation o f Q B a s e d on'Equ'ation 5.16, the-state h o i s e w(t).cannot be"determined b e c a u s e the t r u e state vectors k(t) a n d k(t^l) are unknown". T h e intuitive approximation o f the state noise at t i m e step j is given by: qj^kj-QjjJj^ (5.24) w h e r e q; is defined as t h e state noise sample. It is a zero m e a n w h i t e noise. A s s u m i n g that the no'is^ sample sequence oj can b e representative of the true state noise sequence Wj, qj and wj should b e i n d e p e n d e n t and h a v e t h e s a m e distribution. T h e n t h e actual covariance o f Wj can be approximated b y the unbiased estimate of its sample covariance: *.-7fei>"> (5 -25) 55 w h e r e N is the n u m b e r o f m e a s u r e m e n t noise samples, w h i c h is selected empirically in order to provide a reasonable noise statistics based on the -latest data. Following the s a m e p r o c e d u r e in estimating R,<the unbiased estimation o f Q will be: 5.2.4 S u m m a r y o f t h e A K F fusion algorithm T h e p r o p o s e d A K F b a s e d fusion algorithm can b e s u m m a r i z e d as follows. A t each time step, (1) Calculating u (t) a n d H ( t ) b a s e d o n t h e d a t a o f l a s t t i m e interval f r o m p o i n t detector u s i n g Equations 5.18 and 5.19. (2) State propagation: calculating a priori estimate o f k(t) and estimation covariance.using Equations 5.5 and 5.6. (3) Estimating R using Equation 5.23 based on last N measurement noise samples (4) U p d a t i n g K a l m a n gain using-Equation 5.7. (5) State estimation: calculating a posteriori estimate o f k(t) and estimation covariance using Equations 5.8 and 5.9. (6) Estimating Q using Equation 5.26 based on last N state noise samples. (7) Calculating the section travel time based on Equation 5.12. T h e p r o p o s e d fusion algorithm can b e executed without specifying initial estimates of R and Q, although good initial values o f t h e m can m a k e the algorithm perform better at the b e g i n n i n g o f its operation. 5.3. E V A L U A T I O N T h i s study evaluates the proposed algorithms b y comparing various travel time estimation m e t h o d s . T h e e v a l u a t i o n ' s p e r f o r m e d in a strptch of freeway .using, a microscopic •traffic simulation model; P A R A M I C S (Version 4 Build 10) -based on teal w<?£ld data. W e consider detection errors as well as non-recurrent traffic congestion for more, realistic evaluation. 5.3.1 S t u d y Site .?t The, study site is a six-mile stretch o f northbound freeway 1-40S, b e t w e e n junctions of freeway 1-5 and Culver Drive, in O r a n g e County, California. I ' h e schematic representation of the, study site is illustrated in Figure 5 ^ . T h e ' l i n e across the freeway lanes represents mainline detector, w h o s e l o c a t i o n is shown o n the bottom b y its postmile. A s a major freeway linking O r a n g e County to Los Angeles, this stretch of freeway experiences h e a v y traffic congestion during the morning p e a k hours, w h i c h is Caused b y h e a v y traffic flows from freeway S R - 1 3 3 and leffery Dr. In th\s study, w e only considered the section from S a n d C a n y o n D r to Jeffery Dr, w h i c h includes o n e o n - r a m p 56 and off-ramp. This section features a _ l o t p f Shockwaves durjng.the m o r n i n g peak-hours because o f the strong bottleneck point at Jeffery,Dr. Los Angeles <- Irvine • • Jeffery Dr Culver Dr © © © Sand canyon Dr SR-133 Irvine Central Dr © © © © & 6.21 5.74 5.55 5.01 4.03 3.86 3,31 '3.04 2.35 1.93 1.57 1.11 0.93 0.6 A .Study section Figure 5.2 Schematic figure of the study site This network used in P A R A M I C -simulation has_been calibrated b a s e d on previous simulation studies [23]. T h e time-dependent O D demands, estimated based o n the real world traffic data of M a y 22, 2001, w e r e used for this simulation study. T h e simulation period is frorheboto 9V00 A M . _ _ 5.3.2 Travel T i m e Estimation M e t h o d s In the previous section, w e described three w a y s o f estimating section travel time: travel time estimation from section density, travel t i m e estimation from p r o b e vehicles, and travel time estimation fusing two data sources. In addition to these three methods, -a b e n c h m a r k travel t i m e a n d a simple travel t i m e estimation m e t h o d from point detection ,data are considered for the comparison purpose. 5.3.2.1 B e n c h m a r k Travel T i m e Within a discrete t i m e and space domain, the representative travel t i m e can b e defined a^ a m e a n travel t i m e within the closed area defined b y the t i m e (t-1 and t) and space (x u and Xd), as shown in Figure 5.3. f The. true, space-mean speed for vehicles within the closed area is equal to, the total travel •distance, divided, b y .the totaj-travel t i m e ,of all vehicles in t h e closed area [24]. A n unbiased estimate of the space-mean speed is: ^ ^ n ^ . x j - m a x ^ x j v=-2=L Z W n»i (5.27) + U;)-max^:)} where, N = n u m b e r of vehicles traversing the section during the time interval x" = position of vehicle n at time t 57 xu — position o f the u p s t r e a m loop detector station u xd = position of the d o w n s t r e a m loop detector station d tnd — t i m e w h e n vehicle n p a s s e s the d o w n s t r e a m station d tl = time w h e n vehicle n p a s s e s the upstream station u Space t+1 time Figure 5.3 A temporal and spatial illustration o f section travel.time T h e average section travel t i m e can t h e n b e estimated. Ax «s = v where, ttg = average section travel t i m e Ax = length of thVsectiori, i.e.'x<j - x u i (5.28) J' i > v S u c h an average section travel t i m e can b e considered as a-"true" mean* travel t i m e that represents the section. In this study, this section travel time is used as a benchmark travel time. *" ' 5.3.2.2 1 Section Travel T i m e frorii'Pbint Detector D a t a T h e general m e t h o d to estimate section travel t i m e from loop detector data' is based on average speed estimates at the b o u n d a r y detector stations. T h e average speed b y lane can b e obtained'direptly from d o u b l e ldpps or estimated from s i n g l e loops [25^*26*]. Based dn these lane-based speeds, tne station speed is generally defiried'as the weighteo^ayerage'oT lane speeds. ^ v* o = X ( 9kAt)*vu(t) J 'I ) *(5.29) ;=i where, L = n u m b e r of lanes at loop detector station k q ki i(t) = traffic count at lane i o f upstream detector station k *V ,}i ; ! ' 58 'Vk,i(t) =4raffic count"at lane i dfidowhstream detector station-k. f iisi . '• •* • c <s a ^i T h e n l h e section t r a v e L t i m e l c a n b e . e s t i m a t e d [27] s: u / ' <'-« Ii ! * .. v (l . ^ J'_-jjAx, Ax 2 * „ <j - Ji X' 2 v„- -vd: * >:> * r»r t (5.30), where, vH = speed at upstream detector vd = speed atcjownstream detector In this study, w e only consider the double loop case in order to avoid handling the speed estimation from single l o o p data. * t' '' 5.3.2.3 Implementation o f Travel T i m e Estimation M e t h o d s W e implement the p r o p o s e d A K F fusion algorithm and other above-mentioned travel t i m e estimation m e t h o d s from double* l o o p s p e e d data, -section density.? alculation,, and probe*-vehicle data ih."a microscopic .traffic s i m u l a t i 6 r r m o d e l , . P A R A M I C S . T h e s e "travel time estimates are c o m p a r e d with the b e n c h m a r k travel- time described .above. T h e s e travel time estimation m e t h o d s are summarized in Table 5.1. Table 5.1 S u m m a r y of Travel T i m e Estimation M e t h o d s , Implementation M e t h o d Method D a t a source * B e n c h m a r k Travel T i m e Individual v e h i c l e ' s trajectory from simulation Speed data from double loop E q u a t i o n 5.29, 5.30 D o u b l e Loop Speeddetectors based M e t h o d Probe-based M e t h o d Travel time from, projpe Equation-5.15 vehicles, *t t t Traffic counts from loop Density-based M e t h o d E q u a t i o n £.14, 5.12 detectors (1) Traffic counts from loop AKF-based D a t a F u s i o n E q u a t i o n 5 . 1 5 , 5.16, detectors 5.17,5.12 Algorithm (2) Travel time from p r o b e vehicles I n the probe-based m e t h o d , w e do*not consider indrvip^ua^ vehicjes' t r a v e l . t i m e errors (introduced by sensing technologies) bu^jtheir sarnpling errors. The, performance p f this probe-based m e t h o d varies b y sampling rates o f p r o b e vehicles. In this method, there m a y not, havp a, -probe within, a, t i m e interval when; the s a m p l i n g rate is, low. I n ,such circumstances, the,-current t i m e step's travel time is assumed to b e s a m e as previous, t i m e step's travel time. 59 In this study, w e considered detection errors • o f point detectors. According to an evaluation report c o n d u c t e d b y T e x a s Transportation Institute [28], single loop detectors can p r o v i d e a typical 9 8 % accuracy on loop c o u n t data and .double loop*detectors can p r o v i d e a typical 9 6 % accuracy on speed data. W e understand this accuracy, 6, as the average abstract relative error o f 1- 8. D u e t o the lack o f t h e knowledge* about this error distribution, w e a s s u m e d it as a uniform distribution varying frorq - 4 % to 4 % with the abstract error m e a n o f 2 % and zero mean. It h a s the following,properties o f the probability density function: [0 f(X) ~\/(l-S)*2 ,/ if x<-(l-<5)*2,x>(l-<?)*2 'W'31) -0-^*2<x<(l-<5)*2 where, 5 = accuracy o f l o o p count, w h i c h is 9 8 % in this study 5.3.3 Performance Indices T w o error indices, R o o t M e a n Square Error ( R M S E ) and-Mean Abstract Percentage Error ( M A P E ) , are employed" forithe-performance evaluation o f section travel t i m e ' m e t h o d s . T h e s e t w o indices are defined as: A, -' • ^SE^ljf^t-'if (5-32) T MAPE = - y ^ ^ where ' Zj = the true valulTbf variable z at s a m p l i n g point i • >' z,= the estimated v a l u e o f variable z„at s a m p l i n g point i » N = total n u m b e r o f s a m p l e s d f variable' z 5 . 3 . 4 E v a l u a t i o n Scenarios ' -(5.33) *. ' * l ' fl ) W e considered t h e following four scenarios: * (1) Recurrent congestion: without loop error (2) Incident: w i t h o u t loop error (3) Recurrent 1 congestion: wiuY98% accuracy o f loop'couht (4) Incident: with 9%% accuracy of foop count " > J « ' , ) In the two incident scenarios^ari incident w a s injected to the m i d d l e o f ihe'study-section, as shown in'FiguYe 5.3 (the location is close t o ' t h e off-rarrip a t ' J e f f e r ^ D r ) . T h e incident w a s assumed to block a lane for 10 m i n u t e s from 8:20 to 8:30 A M . °~ 60 5.3.5 Evaluation Results ^ ;<l i All simulations-started t o r n 6 : 3 0 A M ' a n d tended-at 9:00 AM:. The-first T 5 m i n u t e s o f each "simulation r u n i » regarded a s . t h e w a r m i n g u p p eriod. S i n c e i h e fu'sion a l g o r i t h m needs s'ome t i m e - t o initialize a n d fine-tune p arameters,'its p erformance w a s c o m p a r e d with other-algorithms between the time period from 7:00ito 9:00 A M . T h e section travel time w a s estimated based on a 30-sec interval for all m e t h o d s under all scenarios. T h e estimated travel times w e r e compared with the b e n c h m a r k section travel time in order to obtain the two performance measures, including M A P E a n d R M S E . Table 5.2 and 5.3 s h o w s the performance o f all evaluated algorithms undex four scenarios in terms of M A P E and R M S E , respectively. B a s e d these performance m e a s u r e s , w e .find that the fusion algorithm can generate a better section travel t i m e estimate compared to all other evaluated estimation algorithms u n d e r all scenarios. Table 5.2 M A P E o f various estima tion algorithms under different scenarios 1 i Scenario 3 Scenario 1 Scenario 2 Scenario 4 D o u b l e L o o p Speedbased Method Probe-based M e t h o d ( 5 % probe rate) 24.3% 24.4% 22.0%—• 20.0% 15.3% 16.1% 15.3% 116.1% Density-based M e t h o d r t 10.9% 7.6% 18.8% 16.3% A K F Fusion Algorithm- 7.2% 7.8% 7.9%- 8.2% Table 5.3 R M S E o f various estima tion algorithms under different scenarios Scenario 1 Scenario 2 Scenario 3 Scenario 4 34.1 43.7 32.2 33.1 25.0 34.1 25.0 34.1 Density-based M e t h o d 12.5 * "* 28.4 19.8 35.9 A K F Fusion Algorithm 11.5 20.8 10.7 18.6 Double Loop Speedbased Method Probe-based Method ( 5 % probe rate) T h e density-based m e t h o d shows better performance compared to probe-based double loop detector based m e t h o d s u n d e r ideal detection conditions, i.e. Scenario 1 Scenario 2. D u e to the, involvement of- detection errors in Scenario 3 and 4, performance o f t h e density-based m e t h o d - b e c o m e s worse, as illustrated i n ' T a b l e 5.2 5.3. B u t it still h a s a c o m p a r a b l e performance with the probe-based m e t h o d . and and the and 61 M B a s e d o n the description of the p r o p o s e d fusion algorithm, t h e density-based concept is used in formulating the state equation and the p r o b e based section travel time estimate is used as the m e a s u r e m e n t . T h e fusion algorithm improves the: estimation of 4he section d e n s i t y i ( a n d ' t h u s t h e estimation.of t h e section travel time) t h r o u g h the .incorporation o f p r o b e - b a s e d travel t i m e data w i t h , p o i n t ^detector data. C o m p a r e d - t o the probe-based and density-based algorithms, the 'fusion- algorithm improves section travel time estimate significantly in t e r m s o f both M A P E and R M S E , as s h o w n in T a b l e 5.? and 5.3. 350 300 * 't » '•* . J_I * - ;_: * ± 8» 250 •j,*jh ««t* i.»ift-j.j! lu^U'-i^ ' *i J !*' V J 200 I 150 c so 100 CO 7f«...',"'•*'JI * •V- - 7:15 7:30 7:00 7:45 * 8:00 _-£- J t* 8:15 8:30 • Benchmark travel time —-*— AKF fusion algorithm * i.m ; 8:45 Probe-based method Figure 5.4 C o m p a r i s o n o f section travel t i m e estimation u s i n g t h e probe-based-method ( 5 % s a m p l i n g rate) and the A K F fusion algorithm u n d e r Scenario 3 J^i, 350 300 r"iT~ni J" fjtfff 2 250to .1 200 150 i T. ,.' 'n *!;,„.,.,,**>„. I 100 50 7:00 7:15 7:30 7:45 8:00 8:15 8:30 8:45 1 ,—u • |*i.,—'-* '—( p r : «—Benchmark travel time —.—AKF fusion algorithm * Probe^based method _LT ! I 1 ' i -'* L±i* £_ Figure 5.5 C o m p a r i s o n o f section travel i i m e estimation using*the probe-based m e t h o d , « (5%-skmplirig rate) and t h e A K F fusion algorithm u n d e r Scenario 4n> '• »*i K ^'. 1 ' Figures 5.4 and 5.5 further c o m p a r e the section travel time estimation using the probebased m e t h o d and the fusion algorithm under Scenarios 3 and 4, respectively. Regardless 62 of the obvious incorrect section travel t i m e estimates from t h e p r o b e - b a s e d algorithm during t h e congestion period, t h e fusion algorithm c a n p r o v i d e a better section travel t i m e estimate "for"the w h o l e study period. Therefore, t h e fusion algorithm effectively captures t h e variation o f section travel t i m e d u e to t h e integration o f b o t h l o o p count d a t a from single loops and p r o b e vehicle data. C T h e proposed A K F fusion algorithm -worlds in a w a y like this: t h e state variable, i.e. section density, is-estimated b y the state equation 1 , and t h e n t h e state variable-is further corrected based on ttie^measurement data from p r o b e r ' a r i d j i h e K a l m a n gain, estimated based "bn noise variances and the current system estimation variance. T h e k e y point o f t h e proposed fusion "algorithm is its on-line estimation o f state -noise variance R a n d measurement n o i s e variance Q. T h e estimated R a n d Q u n d e r Scenario 4 are s h o w n in Figure 5.6. Since R is the variance o f travel t i m e estimation error from p r o b e s a n d h a s a high value, w e u s e d ln(R) instead o f R in order to s h o w it together w i t h Q in a figure. This figure s h o w s t h a f t h e s y s t e m m o d e l ( i . e . s t a t e e q u a t i o n ) b e c o m e s - m o r e a n d m o r e accurate with the progression* o f the fusion process. D u r i n g t h e incident period, the measurement noise v a r i a n c e Q keeps ( a^small v.ajue, w h i c h represents that the system m o d e l is pretty accurate. H o w e v e r , the variance of the m e a s u r e m e n t n o i s e b e c o m e s larger because the* probe-basedJ algorithm cannot 1 provide a g o o d .sectionntravel time estimate right after the o c c u r r e n c c o f the incident, as illustrated in Figure 5.5. Figure 5.6 T h e on-line estimation o f noise variances of R and Q u s i n g the A K F fusion algorithm under scenario 4 T h e adaptive filtering m e c h a n i s m o f t h e proposed fusion algorithm provides a n appropriate feedback t o t h e e ^ i m a t i p n o f t h e section,-density at e v e r y t i m e step, w h i c h .causes an^optimized section density estjmate. Figure 5.7 . c o m p a r e s t h e section density estimation, using uje proposed,, fjusion algorithm and the section density £>ased .algorithm .under, S c e n a r i o 4 . T l i e s e c t i o n d e n s i t y es£imated,by t h e f u s i o n a l g o r i t h m h a s a M A P E error o f 5.3%. It is m u c h better than the density estimate, from the, section density based algorithm that h a s a M A ^ E error as high as 16.9%. F r o m this point of view, the proposed fusion algorithm has an accurate .estimation of the section density and thus leads to the accurate section travel time estimation. 63 7:00 7:15 7:30 7:45 8:00 -TR0E —m— Fusion 8:15 8:30 8:45 - Density Figure 5.7 C o m p a r i s o n o f the estimation o f section density using ,the j AKF fusion algorithm and the density-based m e t h o d u n d e r .Scenario 4 Figure 5.8 Section travel t i m e estimation using the double loop speed-based m e t h o d under Scenario 3 A s a comparison, t h i s ' s t u d y compared^the fusion algdfithm w i t h ' t h e double 'loop based section travel time estimatibh algorithm. B a s e d - o n v T a b l e 5 . 2 ' a n d 5.3, this double- loop based algorithm p e r f o r m ^ % e worst ainoftg W ^ g o r i t h m s l A s "shown in Figufe *5f.8,' the section travel tifnens underestimated by-double-lo#p d a t a . ' T h i s result is "consistent with the c u r r e n t : k n b w l e d | e about t h e point 1 detector,"*whicrT provides a ' h i g h e r average point speed'than'the / avera*ge [29], a n d ' t h u s causes a'lower travel time estimate'uslng r Eqifation 5.30. Therefore; the- estimation of section* travel time-using polht detector data-is not 64 robust and-the* estimation a c c u r a c y cannot be guaranteed b e c a u s e of various ^location specific issues, such as vehicle weaving, curve link, etc. T h i s explains that pointidetectors cannot capture the actual traffic condition. It also implies that an accurate estimation o f pointfspeed using point detector data cannot.be used to i m p r o v e the provision o f accurate area-wide traffic condition. ' < As" shown in Figure 5.9, a larger sample size X>f p r o b e s i m p r o v e s the accuracy o f the travel* time estimate-, a l t h o u g h this accuracy i m p r o v e m e n t is n o t obvious after-the s a m p l e rate^is h i g h e r "than 2 0 % . H o w e v e r , this travel t i m e , calculated, u s i n g the.&rrival-based methodj'does not r e p r e s e n t m e b e n c h m a r k ' t r a v e f t i m e well. H o w e v e r , the p r o p o s e d fusion algorithm- can significantly improve the estimate o f section travel" time through' the integration o f t w o data sources. It performs "well'with-even a small s a m p l e size o f p r o b e s . F o r example, 1% p r o b e s can provide a 11.8% M A P E error, w h i c h decreases to 8 . 4 % w i t h 3%-probes. Figure *5.9 also s h o w s ihat the-fusion of loop data w i t h a 10% sample size o f probes-can provide.a highly .stable-accuracyjof'the,section travel time estimate..A h i g h e r sample- size -cannot 5 provide a m o r e laccufate travel time/ estimate. This implies that the proposed fusion algorithm has reached itSjmaximal performance. It is because any m o d e l , including; the m e a s u r e m e n t ^equation of the ' p r o p o s e d A K F fusion, algorithm, cannot perfeitly capture the r a n d o m n e s s o f the traffic system. — __ J *' t^ hi „ J * % :><< .. r. ^--XJ->.:-1 „1 »£ j '••: \ t^!( ,* "i!i fP !l faff *• > ft '1 J*Jt . ? * £,<**•"**' .* K**M* •v ,w*' o% 10 20 30 . #1^ ¥*» E 40 50 60 Probe sampling-rate'(%) _VJL". 70 80 90 •AKF fusion algorithm —Br Probe-based method Figure 5.9 Comparison o f section travel t i m e estimation using the A K F fusion algorithm and the probed based method with respect to the s a m p l i n g rate o f probes 514 C O N C L U D I N G REMARKS This travel time data fusion problem is essentially a traffic Congestion recognition and trayel time estimation p r o b l e m plus the traditional data fusion 1 problem. A c c o r d i n g to the feature of available data s6urces, me^ectiori'travel t i m e ' c a n b e estimated based 6 n either limited samples o f a probe-based data source or statistical data from a point detector data source. Each data source h a s different features on its data collection method and t h u s 65 s h o w s different condition. a c c u r a c y o f section travel t i m e estimation under different traffic T h e p r o p o s e d fusion algorithm is established based on traditional flow theory and K a l m a n filtering theory. It appropriately fuses t h e single l o o p detector data (i.e. traffic count data only) with p r o b e vehicle data (i.e. s a m p l e section travel time data) in order to obtain a m o r e accurate section travel t i m e estimate. T h e state noise variance R and m e a s u r e m e n t n o i s e variance Q o f the K a l m a n filter are estimated dynamically b y adapting to the real-time data. T h e p r o p o s e d fusion algorithm was-evaluated through the c o m p a r i s o n with- other algorithms, including the probe-based ^method, the density-based m e t h o d and the d o u b l e - l o o p - s p e e d based 1 m e t h o d , under b o t h recurrent .and incident scenarios. T h e fusion algorithm s h o w e d m u c h better performance. T h e detectors in t h e field a r e n o t perfect a n d e a c h detector h a s its o w n e r r o r features. There is currently n o e n o u g h k n o w l e d g e ' t o s h o w w h a t thej^etection errors are..This paper a s s u m e s l o o p detector errors are.uniform distributed with certain accuracy..It,may not be t h e c a s e ' i n the real w o r l d . The. future w o r k will' be-io test the p r o p o s e d fusion algorithm using the data from real wbrld. h v a d d i t i o n , s i n c e ' t h e p r o p o s e d ' a l g o r i t h m .can self start without parameter inputs and adapt to the real data for n o i s e measurement, it-is eligible for on-line applications. T h e proposed data fusion algorithm is a generic algorithm. It can also handle different combinations o f d ata s ources, s u c h a s t h e f u s i o n o f s ingle 1 o o p d ata w ith d o u b l e 1 oop speed data. It m a y b e possible to use the single loop data only b e c a u s e w e did not u s e the o c c u p a n c y data o f single loop detector outputs yet. This m a y n e e d s o m e investigations on the p ossibilities b ased o n b oth s imulated d ata a n d r eal w orid d ata. A Iso, t he p roposed fusion algorithm can o n l y w o r k with two data sources. Potentially, if can b e applied to the multiple data sources. 5.5 R E F E R E N C E S 1. 2. 3. 4. >t Petty, K.F., Bickel P., Ostland r -M., R i c e , J., Schoenberg, F., Jiang, J., and Ritov, Y. (1998) A c c u r a t e Estimation o f Travel Times from Single Loop Detectors, Transportation Research*A, Vol. 32, N o . l*,.pp. 1-17: G u o P., and Poling, A.Z>-, (1?95) g e o g r a p h i c f o r m a t i o n Systems/Qlobal Positioning Systernsr Design, for, N e t w p r k Travel / H m e , Study, Transportation Research Record 1497, Transportation Research Board, Washington, D C , pp. 135-139. D i o n F . a nd R a k h a H . ( 2 0 0 3 ) E stimating.S patial 7 ravel T i m e u-smg A utornatic Vehicle Identification Data, 8 2 n d A n n u a l ^Meeting Preprint CE>-ROM, Transportation Research,Board, J a n u a r y 12-16, .Washington, D.C. Yim, Y,B.Y., anc},R. Cayfbrd. (200)1) Inyesti^atiori o f Vehicles ( as £ro]?es U s i n g Globa] Ppsitioning System ano^Cellular P h o n e Tracking: Fie\d"Operatibnaf ^ e s t . California P A T p R e p o r t . UCB-ITS-P^VP-2001-9. University o f California, Berkeley, C A . ' , '., " . , ,, 66 5. ,' Sun, C-, Ritchie, S „ Tsai, K., and Jayakrishnan,- R.i (1-999) U s e o f Vehicle Signature Analysis and Lexicographic Optimization for Yehicle Reidentification on Freeways, Transportation Research Part C. Vol. 7, No.4, pp. J 67-18$. o V M a c Q a r l e y - A . (-1999) Advanced I m a g e .Sensing M e t h o d s i b r TraffiCjSurveillance " a r i d ^ D e t e c t i o n , California P A T H :Research . R e p o r t U C B - I T S - P R R - 9 9 - 1 1 , University: o f California, Berkeley. .- ^ 7. *Klein,X.A.'(l 993) Sensor and Data.Fusibn Concepts and Applications-, V o l . T T 1 4 , SPIE Press, Bellingham, Washington, U S A . 8. 'Sarma, V..SJ and S. Raju (1991) Multisensor D a t a ' F u s i o n and P e c i s i o n ; § u p p o r t for A i r - b o m e Target Identification, I E E E Transactions o n Systems;. M a n and fl* 1 Cybernetics. -Vol. 21, f)p. 1224-1230. •> { H > 9. Qi, H . a n d ' M o o r e j - J . B. -(2002) D i r e c t Kalar*'filtering A p p r o a c h i b r Q P S / I N S , V -i Integration, I E E E Transactions o n A e r o s p a c e and Electronic Systems, YQI. 3 8 , N o . 2, pp. 6 8 8 . 6 9 3 . ' j lO^Kalman, R.E. (1960) ( A N e w * ' A p p r o a c h to Linear, Filtering a n d . Prediction Problem's, Transaction o f t h e ^ A S M E ' ^ J o u r n a l of Basic* Engineering, Vol. 82 -(Series-D),pp. 35-45. ' . ' 11. Gazis,D^C- a n d K n a p p QJ3£<(1971) O n - l i n e Estimation: o f T r a f f i c D e n s i t i e s from Time-series of F l o w and Speed Data, Transportation Science* V o l . 5„ N o . 3, pp. 283-301. -> -—12. Szeto M . W . and Gazis D. C. ( 1 9 7 2 ) Application o f K a l m a n , f i l t e r i n g to the Surveillance and Control o f Traffic Systems, Transportation Science, V o l . 6, N o . 4, pp. 419-439. 13. H u , S. R., M a d a n a t S. M., Krogmeier, J. V., and Prrta S. (2001) Estimation o f D y n a m i c A s s i g n m e n t Matrix and O D D e m a n d s using A d a p t i v e K a l m a n Filtering, Intelligent Transportation Systems Journal, Vol. 6, pp. 281-300. 14. Okutani I. and Stephanedes Y. J. (1984) D y n a m i c Prediction o f Traffic V o l u m e through K a l m a n Filtering Theory, Transportation Research, Vol. 18B, N o . 1, pp. 1-11. 15. Gazis, D . C . and Liu, C. (2003) K a l m a n Filtering Estimation o f Traffic C o u n t s for T w o N e t w o r k Links in Tandem, Transportation Research Vol. 37B, N o . 8 , pp. 737-745. 16. Chen, M . and Chien S. I. J. (2001) D y n a m i c F r e e w a y Travel T i m e Prediction Using P r o b e Vehicle Data; Link-based vs. Path-based, 81st A n n u a l M e e t i n g Preprint C D - R O M , Transportation Research Board, January 7-11, 2001, Washington, D . C . 17. Lighthill, M . J., and G. B. W h i t h a m (1957) O n kinematic w a v e s , II: A theory o f traffic flow o n l o n g crowded r o a d s . P r o c e e d i n g s o f t h e R o y a l S o c i e t y , L o n d o n Series A 229, pp. 317-345. 18. Richards, P. I. (1956) S h o c k w a v e s on the Highway. Operation Research, Vol. 4, pp. 42-51. 19. Dion, F . ' a n d Rakha, H . (2003) Estimating Spatial Travel T i m e s u s i n g A u t o m a t i c Vehicle Identification Data, 82nd Annual M e e t i n g Preprint CD-ROM, Transportation Research Board, J a n u a r y 1 2 - 1 6 , 2 0 0 3 , W a s h i n g t o n , D . C . 20. Mehra, R . K . (1972) Approaches to Adaptive Filtering, I E E E Transactions on Automatic Control, Vol. 17, pp. 693-698 67 21. M y e r s K . A . and T a p l e y B.D. (1976) Adaptive Sequential Estimation with U n k n o w n N o i s e Statistics, I E E E Transactions on A u t o m a t i c Control, Vol. 21, N o . 4,pp.520-523. 22. M e h r a R. K . (1970) O n the i d e n t i f i c a t i o n - o f Variances and Adaptive K a l m a n Filtering, I E E E Transactions on Automatic Control, Vol. 15, N o . 2, pp. 175-184. 23. Chu, L., Liu X . , Recker, W., Zhang, H . M . ( 2 0 0 3 ) P e r f o r m a n c e Evaluating of A d a p t i v e R a m p M e t e r i n g Algorithms; accepted, b y A S C E Journal o f Transportation Engineering 24. Gerlough, D . and M . Huber. Traffic F l o w Theory: A M o n o g r a p h , Special Report 165, T R B , 1975. 25. W a n g , Y . and N a n c y L. N . (2000) F r e e w a y Speed-Estimation U s i n g Single L o o p Outputs. Transportation Research Record, N o . 1727,pp* 120-126. 26. Hellinga, B . ' R . (2002) I m p r o v i n g - F r e e w a y Speed .Estimates from Single-Loop Detectors, Journal o f Transportation Engineering, Vol. 128, N o . 1, pp. 58-67. 27. Chen, C. (2003) F r e e w a y Performance M e a s u r e m e n t . System (PeMS),.California P A T H R e p o r t UCB-ITS-PRR-&003-22, University o f California, Berkeley, C A . 28. Middleton, D . R., Jasek, D . L., and Parker R. T. ( 1 9 9 9 ) Evaluation o f S o m e Existing Technologies for 1 Vehicle Detection, T e x a s Transportation Institute Research R e p o r t 1715-S: 2 9 . H a i g h t , F. A . (1963). M a t h e m a t i c a l Theories o f Traffic Flow. N e w York: A c a d e m i c Press. i ! T f r t 68