Update and Validation of the M-NCPPC TRAVEL/2 Model by Thomas K. Harrington, AICP Maryland-National Capital Park and Planning Commission Silver Spring, Maryland and Luc Deneault INRO Solutions* Montréal, Québec *Currently working with Groupe Conseil LOCTRANS INC. For Presentation at the 14th Annual International EMME/2 User’s Conference Chicago, Illinois October 20 –22, 1999 1 Update and Validation of the M-NCPPC TRAVEL/2 Model ABSTRACT The Maryland-National Capital Park and Planning Commission (M-NCPPC) in Montgomery County, MD has been a long-time user of EMME/2 in the development and application of the county’s travel demand model, called TRAVEL/2. Some of the innovative features of this model include: estimation of P.M. peak period travel (generation, distribution, and mode choice) rather than daily travel, modeling of non-motorized trips, modeling of intersection delay, and extensive use of feedback loops. Two recent projects have significantly improved the performance and usability of the TRAVEL/2 model. The first project involved the refinement of the TRAVEL/2 procedures to take full advantage of EMME/2 macros and software enhancements. Application of the model was converted from UNIX script language to EMME/2 macro language. Model improvements included use of multiclass assignment procedures to model HOV trips, revisions to volume-delay functions, modeling bimodal (park-and-ride) trips using matrix convolutions, and use of the successive average method for convergence of congested auto times in the feedback loop. After completing the model refinement project, the second major effort involved the validation of the model for a new base year. The validation study showed that the revised TRAVEL/2 model matches observed data reasonably well for individual model components as well as for overall measures such as screenline crossings. These recent model improvements will be of interest to agencies that need to update their models without the resources to perform a full-scale model development and re-calibration effort. ACKNOWLEDGEMENTS The authors wish to acknowledge the efforts of the project teams that completed the work described in this report. The Model Update Study was conducted by INRO Solutions Inc. including Luc Denault and Alain Audette, with special assistance from Dr. Michael Florian. The Model Validation Study was conducted by BMI Inc. including Phil Shapiro, Donald Stephens, and Daniel Goldfarb. The M-NCPPC staff involved in these studies include Eric Graye, Donald Ostrander, Yetta McDaniel, and Richard Hawthorne. Contact Information: Thomas K. Harrington Transportation Planner Maryland-National Capital Park & Planning Commission 8787 Georgia Avenue Silver Spring, MD 20910, U.S.A. (301) 495-4519 harringtont@mncppc.state.md.us 2 Introduction The Montgomery County Department of Park & Planning has used travel demand models since the mid-1970’s for administering the county’s Adequate Public Facilities Ordinance, developing area master plans, and supporting transportation planning studies. An EMME/2 license was obtained in 1986. The current travel demand model, called TRAVEL/2 was developed from 1991 to 1994. Transportation planning agencies rarely have the resources to perform a full-scale model development and re-calibration effort. Instead, often an incremental approach is used to refine and update procedures that take advantage of advances in computer software and hardware and the latest state-of-the-art modeling procedures. Model improvements have been undertaken to respond to the evolving analytical needs brought on by changes in federal (TEA-21), state (Smart Growth Initiative), and local legislation (County Ridesharing Goals). Two recent projects have significantly improved the performance and usability of the TRAVEL/2 model: (1) Model Update Study was conducted to streamline and improve the application of TRAVEL/2 procedures. The improvements took advantage of the latest EMME/2 features and macro language (2) Model Validation Study was conducted to compare travel model results with observed data to verify model performance. While the model components were not fully re-calibrated, some adjustment of model parameters was performed based on validation results. This report describes the TRAVEL/2 model, and provides an overview of both the model update and model validation studies. Background Montgomery County Department of Park and Planning is a unit of the Maryland-National Capital Park and Planning Commission (M-NCPPC). M-NCPPC is a bi-county planning agency with responsibility for a regional system of parks and the preparation and administration of a general plan for the physical development of most of the non-incorporated portions of Montgomery and Prince George’s counties, the two Maryland suburban counties adjacent to Washington, DC. Montgomery County is a member of the Metropolitan Washington Council of Governments (MWCOG). The Metropolitan Planning Organization (MPO) for the Washington, D.C. region is the MWCOG Transportation Planning Board. In contrast with M-NCPPC’s county-level focus, MWCOG’s model is used to analyze regional travel conditions and to perform air quality conformity analysis. As shown in Figure 1, Montgomery County is located north of Washington DC and south of Baltimore. The county is the most populous jurisdiction in Maryland, home to roughly 825,000 residents making up 308,000 households. There are approximately 500,000 jobs in the county. It is also one of the wealthiest counties in the U.S. with a median household income of $68,500. As shown in Figure 2, the County is bisected by two interstates: the Capital Beltway (I-495), providing for east-west travel, and I-270, providing for north-south travel in the county. There are a number of North-South major highways fanning out from the District of Columbia into the county. There is a more limited number of East-West arterials connecting suburban activity centers. The County is served by 12 stations of the Red Line of the Metrorail system. Bus service is provided by regional Metrobus and the Montgomery County Ride-On bus sytem. Commuter rail connects 11 stations in Montgomery County with Union Station in downtown D.C. 3 4 5 Overview of TRAVEL/2 TRAVEL/2 is a regional transportation planning model with a focus on Montgomery County. The model region for TRAVEL/2 encompasses the combined Washington and Baltimore metropolitan areas as shown in Figure 1 – Location Map. Trips made to/from neighboring jurisdictions, particularly Washington D.C., make up a significant portion of county travel and must be accounted for. There are 677 TAZ’s in the model region covering 15 counties, with a population of 6.25 million and 4 million jobs. Montgomery County has a much more detailed zone system than the remainder of the region with 318 TAZs. The existing transportation network is represented in EMME/2 with 18,500 directional links and 5565 nodes. A detailed description of the model development process, structure, and parameters is contained in TRAVEL/2 A Simultaneous Approach to Transportation Modeling, Draft Report (February 1993). Data sets from the MWCOG Household Travel Survey, Montgomery County Planning Department (MCPD) Trip Generation Studies, MCPD Census Update Survey, MCPD Travel Time and Delay Study, Metrorail Passenger Surveys, and MCPD traffic counts database were used to estimate, calibrate, and validate the model. Three unique aspects of the model include: P.M. peak period travel (generation, distribution, and mode choice). Travel demand is forecast for a three-hour peak period rather than for daily travel. The P.M. peak period was chosen because local studies found it to contain the most widespread congestion, and the highest percentage of the rapidly-growing non-work trip purpose. Inclusion of non-motorized (walk & bike) trips (generation, distribution, and mode choice). Although bike/walk trips are not assigned to the transportation network, the model can be used to test the impact of land use and transportation policies on the share of non-motorized trips. Equilibration using a feedback loop that takes congested times from assignment for use in distribution and mode choice. Improvements to the feedback loop process are described in the next section. Travel patterns in the P.M. peak period tend to be more complex than in the A.M. peak period, with travelers much more likely to stop off for other purposes on the commute home from work. TRAVEL/2 accounts for these linked work trips as a separate trip purpose. There are seven trip purposes: Work-to-Home (unlinked), Work-to-Other (linked), Other-to-Home (linked), Home-toWork, Home-to-Other, Other-to-Home (unlinked), and Other-to-Other. Direction is explicitly identified (i.e. no productions and attractions) because of the use of a specific time period. TRAVEL/2 follows the traditional four-step/UTPS approach, but with significant enhancements and additions. The inputs to the model include the transportation network, land use activity, demographics, and public policies. The primary model steps are shown in the flowchart in Figure 3: 6 FIGURE 3 TRAVEL/2 Flowchart Initialization Steps Set iteration counter at 1 1. Initial set up Free flow speeds and capacities on links Inputs of bimodal trips Volume-delay functions on approaches and cycle-length on intersections Transpose vectors 2. Auto ownership (LOGIT) optional 3. Trip generation optional 4. Initial all-or-nothing auto assignment to generate auto LOV and HOV skims 5. Mode share defaults optional Begin Demand Loop Incrementation of iteration counter 5. Transit skims (Walk connect) 6. Transit skims (Auto connect) 7. Mode choice model (LOGIT) optional 8. Destination choice model (gravity) 9. Departure time choice model (LOGIT) 10. Computation of auto connect to transit matrices (Park& Ride, Kiss& Ride) 11. Computation of sum peak hour trip matrices 12. Full equilibrium multi-class auto assignment 13. Network interim reports [optional] optional Evaluation of stopping criteria 14. Assignment of « averaged » flows on « skim » scenario 15. Computation of intrazonal time End Demand Loop Closing Steps 16. Determine auto connect/walk connect to transit trip matrices 17. Walk connect and auto connect transit assignments 18. Final reports NOTE: Steps listed as optional may be skipped based on the user selected run parameters. However, these steps are skipped only when default values from a previoius run are used instead. 7 Model Update The new release of TRAVEL/2 (officially Release 3 and referred to as TRAVEL/2.3) has generally improved upon the format and implementation of the model. Model structure and parameters used previously in Release 2 (now referred to as TRAVEL/2.2) remain primarily intact. Unlike TRAVEL/2.2, which uses AWK scripts and FORTRAN programs to execute a number of modeling procedures, TRAVEL/2.3 is fully implemented using the EMME/2 macro language and file structures. In addition, a new user interface is used to set up model run parameters either interactively or in batch mode. The changes made in TRAVEL/2.3 are documented by INRO Solutions in two reports: Revised Elements in the Implementation of the Model and User Manual of EMME/2 Macros (June 1998). Key differences in the revised TRAVEL/2.3 model as compared to the TRAVEL/2.2 model include: 1. Modeling of auto connect to transit (bimodal) trips, i.e. park-n-ride facilities 2. Use of multi-class assignment procedures to properly model HOV facilities and truck prohibitions. 3. Revision of the volume-delay functions 4. Definition/implementation of the demand feedback loop. These refinements are described in more detail in the following sections. Modeling Bimodal (Park-and-Ride) Trips TRAVEL/2.3 uses an approach to model bimodal, or park-and-ride trips, that was developed by Heinz Speiss and makes use of Module 3.22 - Matrix Convolutions. The previous release of TRAVEL/2 did have a sophisticated park-and-ride procedure that was implemented with a FORTRAN progam. However, the current approach is implemented fully within EMME/2 and uses parking lot capacities in the process of determining the transfer zone. The park-and-ride procedures are applied to work trips (from work to home in the P.M.) and involve the following steps: (1) Macro t.parkrideimp computes auto-connect to transit impedance matrix (uses legimped.mac, an INRO shared macro developed by Heinz Spiess): Identify intermediate transfer zone (from list of possible park-and-ride lots) Matrix convolutions used to combine 1st leg (transit) with 2nd leg (auto) times Auto time weighted by 3 so that transfer zone is chosen closer to home. Parking cost is also allocated based on best intermediate zone. (2) Mode choice model computes shares for auto-driver to transit (ADT) and auto-passenger to transit (APT) modes. (3) Macro t.bimodaldem implements logit parking choice model with explicit capacities using parkride.mac (INRO shared macro developed by Henz Spiess). For every O-D pair, this Logit model allocates an « utility » to each parking lot based on the impedance of the first leg and second leg of the bimodal trip. The number of trips that use a parking lot k is the based on the ratio of the utility of parking lot k to the sum of utilities of all the parking lots of the model. The mathematical formulation of the algorithm that solves this problem considers the capacities of the parking lots. 8 t.bimodaldem computes the auto-driver connect to transit demand, multiplying its mode share by the sum of the work to home trips and work to home linked trips. It also computes the auto-passenger connect to transit demand, by multiplying its mode share by the sum of the work to home trips and work to home linked trips. t.bimodaldem runs the parkride.mac macro to generate the auto portion of auto-driver connect to transit trips (second leg demand matrix) and the transit portion of autodriver connect to transit trips (first leg demand matrix). During the validation process, application of the park-and-ride procedures resulted in some unlikely auto-connect transit trips. For example, transit trips between two suburban activity centers, not currently connected by transit, were created in which the transfer point was located close to the work end of the trip, so that the auto leg of the trip was much longer than the transit leg. In order to prevent this from occurring, a constraint matrix is created that caculates whether O-D pairs met certain criteria including: Auto-Connect Transit Leg > 15 minutes Auto-Connect Transit Leg < Walk-Connect Total Transit Time Auto-Connect Auto Leg < SOV Auto Time Auto-Connect Auto Leg < 1/3 of the ACT Total Time Auto-connect to transit mode shares are calculated only for O-D pairs that meet each of the four criteria. Modeling HOV Facilities and Truck Prohibitions TRAVEL/2.3 allows for more flexibility and refinement in the modeling of the HOV facilities. Although currently there are only HOV-2 lanes in Montgomery Country, the model is flexible enough to test four possible HOV configuration options: no HOV facilities; HOV 2+ facilities only; HOV 3+ facilities only; HOV 2+ facilities and HOV 3+ facilities Based on the configuration selected, the TRAVEL/2.3 model is flexible enough to : 1. apply the proper computations of the mode choice model and trip distribution models 2. handle the creation of the appropriate demand matrices; 3. manage the preparation and computation of the appropriate multi-class assignment of the auto demand matrices. Highway links are coded with an auto mode code « c » and auxilliary auto modes « 1 », « 2 » and « 3 » to specifiy the occupant classes allowed. For example, a general use highway lane would be coded with modes « c123 », while an HOV-2+ facility is coded as « c23 ». Multi-class assignment can also be used to model heavy trucks prohibitions on minor roadways. Auxilliary auto mode « s » is associated to the heavy trucks trips. Prohibitions are coded by removing mode « s » on the minor links where the heavy trucks are not allowed. Depending on the user specification, the auto assignments computed by the M-NCPPC transportation model will always assign from three to five classes of vehicles simultaneously: one to three classes of autos depending on the configuration of the HOV network, the light and medium trucks class and the heavy trucks class. 9 Revision of the Volume-Delay Functions (VDFs) A number of refinements were made to the volume-delay functions including Reduction of the number of functions, combining classes with similar speed and capacity assumptions. Use of a logistic volume-delay function to replace the BPR function used on links outside of Montgomery County (to eliminate excessive delay on sketch-level network). Use of a link-based approach to model intersection delay at all signalized intersections in the county. In addition, during the validation study, new freeflow speeds and capacities were applied. Links Outside Montgomery County Test runs of TRAVEL/2.2 showed that the auto assignment was not converging properly to an equilibrium solution. After 100 iterations of auto assignment, the target relative gap of 1% was not achieved. A review of the network identified a number of links with unrealistically high travel times, especially on links in the Baltimore area. This suggested that the sketch-level network used outside Montgomery County is too coarse to handle the demand generated by the large TAZs used for surrounding counties. The selected solution to this problem was to use a logistic function on links outside the county that would set a threshold that speeds could not drop below. The « s » shape functions generate more realistic travel times when the assigned volume exceeds the capacity of the link The logistic vdf have the following form: T=TO+(TS- TO) × ø ß×(v-c)/c/1+ ø ß×(v-c)/c where : TO: the time that corresponds to the free flow speed; TS: time that corresponds to the congested (bottom) speed; v : link flow; c : link capacity; ß : parameter of the vdf that defines the slope of the curve between the free flow and congested link speeds ; a high value of ß generates a steep curve and a low value of ß generates a smooth curve. If the link volumes produced by the model are unrealistic (which is likely to occur in areas of the network that do not constitute the object of extensive study and analysis) this type of function will ensure that the delays associated to the volumes are more realistic. The minimum speed of major links was set at 6 minutes/mile or 10 mph (vdf 50-58) on highways and major arterials and at 8 minutes/mile or 7.5 mph (vdf 61-86) on minor arterials. For example, a freeway with a capacity of 2100 vehs/lane-hour and freeflow speed of 60 mph would have the VDF: Time=length*(60/60+ 5 / (1+5 / ((volau +1)/(2100*lanes))^5)) 10 Modeling Intersection Delay The presence of intersections is a major factor of delay and congestion for trips during the peak periods. In some dense urban areas, the intersections will have more impact on the delay than the link itself. Therefore, it is more realistic to estimate the travel time due to the intersection separately from the actual travel time on links between intersections. The previous release of TRAVEL/2 calculated intersection delay based on detailed intersection data using the 1985 Highway Capacity Manual (HCM) procedures, and predicted turning movements for 517 of the county’s 750 signalized intersections. The process required numerous inputs such as the number of turning lanes and signal phasing that were subject to change and difficult to maintain. While this HCM approach is appropriate for sub-area studies, it is not practical for regional forecasts. The revised process requires fewer inputs and can be implemented for all signalized intersections in the county. The approach implemented in TRAVEL/2.3 is an adaptation of the Chicago Area Transportation Study (CATS) strategy. This approach is much less data consuming, it does not even require the characterization of the phases of a cycle (identification of the turning movements, number of phases etc..). It also relies on simpler computation operations. CATS uses the Webster equation to model intersection delays in their EMME/2 transportation model. This intersection delay has uniform and incremental components. This equation is the result of regression analysis performed for a range of cycle lengths and green time to cycle length ratios. The intersection delay is computed on the approach links of the designated intersections. On these links, the approach delay is added to the travel delay on link. Here follows an example of the definition of a volume delay function modified for the computation of the intersection delay on an approach link : vdf = (60 * length / A) * (1 + (volau / (B * lanes)) ^ 4) + ((6.0*volau/(B * lanes)+2.7*(volau/(B * lanes))^8+ul2).min.ul3) The first part of this function is a regular BPR volume-delay function where A is the free flow speed and B is the capacity per lane of the link. The second part is actually the intersection delay where ul3 is the cycle length (1.5 or 1.0 minute) and ul2 is a fix term of the intersection delay function equal to : ul2 = ((( 3.4 – 0.39*(G*ul3*60) + 0.35*ul3*60 – 4.5 – 7.3*G) .max. 0) / 60) where G is the green phase duration for this approach. The expression of the fix term is compared to zero to avoid - possible - negative values. This intersection delay is defined such that it will never exceed the cycle length. It is also adapted from the intersection delay function presented in the theory to estimate intersection delays in seconds rather than minutes. In TRAVEL/2.3, these functions are implemented using the same capacity for the end-node of a link (intersection) as for the link itself since it is assumed that the capacities associated to the links in the model account for the presence of traffic lights or of any other type of intersection delay. 11 Feedback Loop Structure TRAVEL/2.3 has adopted the link averaging method as described in a presentation made at the Tenth Annual EMME/2 Users’ Group Conference by Walker et al. of Portland Metro. The Portland paper demonstrated that, using different performance criteria, the link averaging method was shown to converge faster than two other approaches. The link averaging method, averages the equilibrium flows of the auto assignments as follows : vk = ½ volauk + ½ vk-1 The demand model implemented is an iterative model in which demand matrices are estimated until one of two stopping criterias of the demand loop is satisfied. At each iteration, auto and transit demand matrices are estimated and assigned on their respective networks. Then, following a « successive average » strategies, the flows that result of the auto assignment are weighted with those of the previous iterations and assigned on a separate scenario. The auto trip times matrix that results of this « dummy » assignment and the transit impedance matrix obtained from the transit assignment are then used to re-estimate the demand matrices of each mode considered. The « successive average » strategy « smoothes » the flows assigned on the auto network and accelerates the convergence to a good solution. At the end of each iteration of the demand loop, the convergence of the solution is evaluated. The two stopping criterias of the demand loop are : maximum number of iterations; relative difference between the Vehicle Hours Traveled (VHT) resulting from auto assignments on consecutive iterations of the demand loop. 12 Model Validation After completing the model refinements described in the previous section, a study was undertaken to evaluate and improve the model’s ability to replicate existing travel, also know as model validation. The base year against which the model results were compared was updated to 1998. While the model components were not fully re-calibrated, some adjustment of model parameters was performed based on validation results. The first step of this study involved assembling validation data from a number of sources. Figure 4 displays four different types of data sources including: Travel surveys: A regional household survey was condicted in 1994 and this can be used to obtain estimates of trips generated as well as trip length distribution. Unfortunately, the sample size of this survey (and most regional travel surveys) was not sufficient to obtain detailed origindestination flows within Montgomery County. The sample would have been even more limited if only P.M. peak trips were used. Instead, the 1990 Census Transportation Planning Package (CTPP) data provided a better sample of work trips within the county. In order to use the CTPP, trips were factored to reflect 1998 conditions during the P.M. peak period. Traffic Counts: The county has maintained a fairly extensive database of traffic counts, although the counting program has been more limited in recent years. Traffic counts are primarily intersection turning movements for the A.M. and P.M. peak hours on arterials. In addition, tube counts were available for the Interstate roadways. Traffic counts from 1994 through 1998 were assembled and reviewed for the extent of the coverage. One future source of traffic counts will be the county’s Advanced Traffic Management System (ATMS) that automatically collects counts using loop detectors. Transit Ridership Counts: Rail boardings and alightings for each station in the county were availble from the transit agency. The ridership counts did include the mode of arrival/departure so that estimates of the auto-connect to transit shares for each station could be calculated. Bus ridership counts were also available and were aggregated by line and for corridors. Travel Time Data: A 1994 survey contained travel times on selected arterials obtained using the floating car approach. These times were useful for reasonableness checks, although the limited sample of roadways and the lack of multiple survey times reduces their reliablity. Future surveys of travel times will be needed given the importance of travel time in the equilibration/feedback loop process. The study has taken a top-down approach to model validation. Figure 5 illustrates the steps used to validate the model. Checks are applied for each of the individual model components, before assessing the overall results of the model. This approach ensures that modeling error is not propagated between steps in the model chain. Travel survey data provided the primary source for assessing the trip generation, distribution, and mode choice components of the model. Traffic and transit counts were used to assess assignment results. In order to evaluate county-wide travel patterns, a set of screenlines were developed. Auto volumes on the links crossing these imaginary lines are aggregated to determine how close the model replicates actual traffic patterns. The screenlines selected for Montgomery County are shown in Figure 6. and capture most of the key north-south and east-west movements. Some smaller cutlines were also used to assess corridor forecasts. 13 Figure 4 14 Figure 5 15 Figure 6 16 Validation targets were based in part on Federal Highway Administration guidelines that set the maximum error by functional type: Freeways within 7% Principal arterials within 10% Minor Arterials within 15% Other within 25% Table 1 lists the 1998 observed and simulated traffic volumes for the P.M. peak hour at 12 screenlines. The overall target for screenline volumes was to match counts within 10%. The results show that most screenlines are within this range. In particular, assigned volumes crossing the major north-south screenlines of the Beltway and Montrose/Randolph Road are both only 3% over the traffic counts. Table 1 Comparison of Observed and Simulated Screenline Volumes 1998 P.M. Peak Hour No. 1 2 3 4 5 6 7 8 9 10& 11 12 Screenline Potomac River D.C. Line P.G. County Line Frederick County Line Howard County Line Beltway Montrose Rd/Randolph Rd Norbeck Rd Shady Grove Rd Seneca Rd/Darnestown Count 16,305 30,122 39,837 8,547 9,389 52,707 53,948 18,490 29,496 22,026 Assigned Vol 15,593 34,497 42,467 8,409 10,347 54,326 55,874 21,180 35,639 24,419 Ratio of Assn/Count 0.96 1.14 1.07 0.98 1.10 1.03 1.03 1.15 1.21 1.11 Rock Creek 19,914 19,529 0.98 17 Next Steps The model improvement program is a continuous process and model validation will need to be performed as additional refinements to the process are made. Three areas that will continue to demand attention in the future include: GIS/Travel Model Linkages: There is a continuing need to interface between the MNCPPC data that is stored in ARC/Info and the data formatted for EMME/2. GIS is cuurently used to develop some of the zonal inputs to the model, and for displaying final results. The development of a comprehensive database of transportation facilities, traffic counts and speed data, and other travel data will be critical for the continued update and maintenance of the travel demand model. Coordination with Metropolitan Planning Organizations: As a county planning agency, M-NCPPC depends on the work of the two regional MPO’s, MWCOG and Baltimore Metropolitan Council, for collecting regional land use forecasts and the regional transportation network. To avoid duplication of data collection and model development, M-NCPPC will benefit from greater consistency between the regional and county modeling practices. Development of A.M. Peak and Daily Analytical Tools: While TRAVEL/2 is an excellent tool for assessing the P.M. peak conditions, there is a need to forecast A.M. and daily travel conditions. The addition of other time periods may require some changes to the current model components, particularly trip generation. 18 References Barton-Aschman Associate, Inc. and Cambridge Systematics, Model Validation and Reasonableness Checking Manual, Travel Model Improvement Program, February 1997. Chicago Area Transportation Study, Procedures for Multiple Time Period Daily Highway Assignments, Memorandum from Ronald W. Eash to Interested Parties, July 17, 1997. INRO Consultants, EMME/2 User’s Manual Release 9, August 1998, Montreal. Ismart, Dane, Calibration and Adjustment of System Planning Models, U.S. DOT Federal Highway Administration, Publication No. FHWA-ED-90-015, December 1990. Levinson, D.M. and A. Kumar. Multimodal Trip Distribution: Structure and Application. In Transportation Research Record 1466, TRB, National Research Council, Washington, D.C., 1994, pp. 70-77. Levinson, D.M. and A. Kumar. Integrating Feedback into the Transportation Planning Model: Structure and Application. In Transportation Research Record 1413, TRB, National Research Council, Washington, D.C., 1992, pp. 70-77. Levinson, D.M. and A. Kumar. Specifying, Estimating and Validating a New Trip Generation Structure: A Case Study of Montgomery County, Maryland. In Transportation Research Record 1413, TRB, National Research Council, Washington, D.C., 1992, pp. 107-113. Levinson, David M., TRAVEL/2 Flow Chart, Montgomery County Planning Department, Transportation Planning Division, Transportation Modeling Group, 1995, Silver Spring. Levinson, David M., TRAVEL/2 Model : User’s Guide, Montgomery County Planning Department, Transportation Planning Division, Transportation Modeling Group, 1991, 1994 update, Silver Spring. Montgomery County Planning Department, TRAVEL/2 Draft Report, A Simultaneous Approach to Transportation Modeling, Montgomery County Planning Department, Transportation Planning Division, Transportation Modeling Group, 1993, Silver Spring. Spiess Heinz, A Logit Parking Choice Model with Explicit Capactities, EMME/2 Support Center, 1996, Aegerten. Tremblay Pierre, Appréhension de la congestion routière dans un modèle statique de simulation, le cas du Modèle de Transport de la Région de Montréal (MOTREM), Revue de l’AQTR, Hiver 1993, pp. 12-21, Montréal. Walker R., Pederson C. and Higgins S., Equilibrating the Input and Output Impedances in the Demand Modeling Process, Portland Metro, prepared for the Tenth Annual EMME/2 Users’ Group Conference, November 1995, Portland, Oregon. Webster F.V and Cobbe B.M., Traffic Signals, Road Reseach Laboratory, Ministry of Transport Road Research, Technical Paper No. 56, 1966. 19