Kang and Chang
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Development of Integrated Control Algorithm for Dynamic Lane
Merge and Variable Speed Limit Controls
by
Kyeong-Pyo Kang (Corresponding author)
Advanced Transportation Technology Research Center, Korea Transport Institute
2311, Daehwa-dong Ilsanseo-gu, Goyang-si
Gyeonggi-do 411-701, Korea
Tel:+82-31-910-3177, Fax:+82-31-910-3228, kkyeongpyo@hotmail.com
and
Gang-Len Chang, Ph.D., Professor
Dept. of Civil Engineering, University of Maryland
1173 Glenn L. Martin Hall
College Park, MD 20742
Tel: +1-301-405-1953, Fax: +1-301-405-2585, gang@Glue.umd.edu
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ABSTRACT
To facilitate the merging maneuvers and minimize potential collisions during the
dynamic late merge (DLM) operations, this study has developed a system control
process that can integrate the variable speed limit (VSL) with the DLM so as to
maximize the total effectiveness. The proposed integrated control process has used
the optimal VSL control model as a supplementary strategy of the entire DLM
operations, and coordinated the sequence of variable message signs (VMS) generated
from the DLM and VSL algorithms. From the simulation experiment, the integrated
algorithm of the DLM and VSL controls has shown to respond well to time-varying
traffic conditions and yielded more work-zone throughputs than the DLM control
without VSL. It has also demonstrated that the integrated control results in an
increase in the average speed and a decrease in the speed variation. In particular, the
VSL effect is evident as a supplementary role for the dynamic merge control.
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INTRODUCION
Contending with congestion and incidents in highway work zones has long
been recognized as one of the priority tasks of most highway agencies. An
increasingly popular practice for work zone operations is to recommend or enforce a
reduced speed limit and merge control via variable message signs, which may or may
not respond to the time-varying traffic demand. To properly respond to traffic
conditions and also to increase compliance rate of drivers, traffic professionals have
recently explored the use of dynamic late merge (DLM) and variable speed limit
(VSL) controls in place of the conventional operational strategies. In addition, most
field study results and simulation experiments have indicated that properly regulating
traffic flows with DLM and/or VSL can indeed reduce the potential risk of having
rear-end collisions in highway work zones (1-4).
However, field implementations of DLM and VSL have also revealed that
their independent operations may not best achieve the potential effectiveness.
Besides, most existing practices have been designed in response to traffic safety
concerns, not for improving the operational efficiency, such as maximizing the
throughput, or minimizing the average delay of vehicles traveling through the entire
highway segment plagued by the work-zone incurred traffic queue. Hence, how to
best operate the DLM and VSL controls under various congested work-zone
conditions so as to maximize their compound effectiveness remains an imperative
issue.
This study focuses on exploring the potential of integrating those two control
strategies in work-zone operations and comparing its effectiveness with each
individual control. Section 2 summarizes the key control features, including their
compatibility and potential implementation issues. A detailed description of control
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algorithms for those two models is available elsewhere (5-7). A set of procedures for
integrated operations is proposed in Section 3. Numerical experiments for
performance evaluation of an example integrated control system are reported in
Section 4. Research results and on-going studies are also discussed in the last section.
OVERVIEW OF THE DLM AND VSL CONTROL STRATEGIES
DLM control based on the optimal control threshold model
The DLM control strategy is to dynamically direct drivers’ merging actions,
based on detected traffic conditions and the proper control thresholds. For example,
when traffic data were detected to exceed the specified threshold (i.e., congested
level), the DLM control will function similarly to the static late merge (SLM) control
and display their merging messages (e.g., “USE BOTH LANES” / “TO MEREG
POINT”) at proper upstream locations. During the uncongested period, it will be at
the inactive state, and essentially perform like the conventional merge or static early
merge (SEM) control (e.g., “RIGHT/LEFT LANE CLOSED” or “MERGE HERE”)
(1-2).
In review of the operation characteristics and traffic conditions of the early
and late merge controls, it is clear that each of these two controls has its most
applicable traffic conditions. Hence, the best DLM system is to activate one of these
two merge controls, based on the optimal set of control thresholds computed from
detected traffic conditions. Figure 1 illustrates these two control thresholds (i.e., CT 1
and CT 2), which are the criteria for the system to select the SEM, SLM, or SLM+ 
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control, based on their relations with the detected traffic states. Each of these criteria
is briefly discussed below.

CT 1 is to reflect the state that traffic remains at free or moderate flow
condition, where drivers on the open lane are nearly unimpeded by those
changing from the closed to the open lanes when the DLM system activated
the SEM control.

CT 2 is to indicate the boundary of the congested traffic state at a work zone,
over which the open lane cannot provide sufficient merging space for vehicles
on the closed lane to merge onto the open lane under the DLM operation.
Thus, some other control measures (SLM+  ) such as speed control to the
approaching flows will be needed.
To maximize the effectiveness of both merge controls (i.e., SEM and SLM),
the authors have developed an advanced DLM system based on those optimal merge
control thresholds (i.e., CT 1 and CT 2). The proposed optimization model selects the
maximization of the throughputs as the control objective. A more detailed description
for computing the optimal control thresholds is available in the literature (5).
Optimal VSL control
The VSL control strategy aims to properly respond to time-varying traffic
conditions with a dynamically adjusted set of speed control that covers the entire
upstream subsegments impacted by the work zone operations. However, as reviewed
in the literature (8-10), most existing VSL related systems suffer the following two
common limitations in their applications:
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Main control objectives are proposed in response to traffic safety concerns, but
not for operational efficiency, such as to maximize the throughput from a
work-zone segment or to minimize the average delay for vehicles traveling
through the entire highway segment plagued by the work-zone incurred traffic
queue; and

Core control algorithms do not intend to minimize traffic congestion by
dynamically setting the optimal speed limits and coordinating them based on
their spatial relations.
The authors have proposed an optimal VSL control model for addressing the
above limitations, based on the evolution of dynamic traffic states and macroscopic
traffic characteristics (6-7). The proposed VSL system has the following features:
adopting the maximization of work-zone throughput as its control objective which is
subjected to some embedded safety related constraints; computing a sequence of
optimal transition speeds for approaching vehicles, based on dynamic interactions
between the work zone traffic flows and those in upstream highway segment; and
dynamically adjusting the set of displayed optimal speed limits, based on the detected
speed distributions and flow rates so as to effectively respond to potential demand
variation and non-compliance behavior of some drivers.
As shown in Figure 2, the proposed VSL system consists of sensors, variable
speed limit signs, variable message signs and a central processing unit to execute
control actions. The variable message signs (VMS) are used to inform drivers of the
traffic condition ahead and to display the enforced speed limit based on the VSL
control strategies.
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For on-line system applications, some non-linear traffic flow relations have
been approximated with linear functions but updated continuously from on-line
detector data. To reflect the need of improving traffic safety, a set of speed boundaries
has been given as model constraints. Moreover, the normal deceleration rate has been
used in determining the length of each subsegment, which is to ensure that drivers can
reduce their speeds at an acceptable braking rate in response to those displayed VSL
signs. Model components and their mathematical expressions are described in detail in
the reference (7).
Critical issues for integration
To best integrate DLM and VSL, one needs to examine their compatibility and
implementation priority especially with respect to the operational efficiency and
traffic safety. For example,

Are the control objectives of both systems compatible or not? Since the
objective function of both proposed control systems is to maximize the total
throughputs over the upstream subsegments, it is undoubted that one can
operate both systems in a compatible format.

Has any conflict factor embedded in those two control processes that may
degrade their integrated performance? Note that the proposed DLM control is
designed to guide drivers’ merging actions between the open and closed lanes,
while the VSL strategy is to control their approaching speeds to both lanes,
regardless of the merging maneuvers. Thus, their model structures do not
have any conflict components to prevent their integrated operations.
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How to determine the implementation priority between DLM and VSL? Since
the foremost objective of the work zone control is to guide drivers over the
lane-closure segments with proper merging maneuvers, one shall view DLM
as the direct and the first level control. The VSL, designed for the speed
control, can be viewed as a supplementary strategy for improving the safety
and the efficiency during merging operations.
DEVELOPMENT OF THE INTEGRATED ALGORITHM
As mentioned previously, the purpose of an integrated DLM/VSL operation is
to dynamically control drivers’ merging activities and speeds, with the optimal
merging control thresholds and speed limits based on detected traffic conditions.
Since there exists no compatibility and implementation issues between those two
algorithms, this study has proposed the following procedures for their integrated
operations.
Step-1: Compute the potential maximum queue length
The purpose of this step is to approximate the maximum queue length, based on the
difference in maximum flow rates between the upstream segment and the work zone,
as the computed queue length will be used as the target control segment for the DLM
and VSL operations. If the actual traffic queue caused by the work zone operations
exceeds the target segment, then one should extend the target control boundaries to
cover the entire roadway segment potentially impacted by the work zone traffic
queue.
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Step-2: Set the initial speed boundaries for the VSL control
This step is designed to set an initial speed boundary that reflects the free flow speed
for each subsegment i. This boundary is designed to prevent the optimal speed limit
of subsegment i from exceeding the boundary of its upstream subsegment (i+1).
Thus, a set of optimal VSL, based on these speed boundaries, will enable drivers to
smoothly adjust their speed when approaching the work zone. Such speed boundaries
will be revised dynamically by the central control unit, based on the detected speed
data.
Step-3: Locate the DLM and VSL trailers
The locations of DLM and VSL trailer set should be determined on the basis of the
average decelerating rate of drivers when they perceive each displayed VSL or DLM
sign. By using a normal deceleration rate (e.g., a=3.3mph/sec), one can divide the
target segment into n subsegments. This is to ensure that when perceiving the DLM
and VSL signs, drivers need not to experience an uncomfortable and unsafe
deceleration rate.
Step-4: Initialize all PCMS and VSL systems
The integration system is initialized by setting VSL with a set of initial speed
boundaries and DLM to be at the Early Merge (or conventional static merge) state.
Such an initialization can be done only when the lane-closure operations are started
under the free flow traffic condition. Each sensor should also be activated for
measuring the traffic data (e.g., volume and speed) at this initialization stage.
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Step-5: Execute Dynamic Late Merge control
The proposed DLM control can be executed by identifying the detected traffic states
(e.g., moderate, congested, and heavily congested traffic conditions), and then
followed by displaying the optimal merging directions on PCMS (Portable
Changeable Message Sign) or VMS (Variable Message Sign).
Step-6: Update the speed boundaries
One can also employ the measured traffic data (i.e., speeds) for the DLM control to
update the speed boundaries (see Step-2).
Step-7: Execute the optimal VSL control model
The final step is to optimize a set of speed limits over all subsegments during each
control time interval (e.g., 1min.). As mentioned in Step-1, if the actual queue length
is longer than the projected maximum queue length, then go to Step-1. Otherwise, the
system shall repeat Steps 5, 6, and 7 with the data detected from the sensors.
Figure 3 presents the principal steps for integrated operations of the DLM and
VSL controls, including the interactions between sensors, DLM, VSL, and the
feedback process. The entire process is designed to ensure that the VSL can always
reflect the traffic states controlled by DLM and take into account the embedded safety
constraints (e.g., speed boundary and sign locations).
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EVALUATION OF THE INTEGRATED CONTROL
Design of experiments
To simulate the on-line work-zone control with the proposed integrated
operations (see Figure 3), this study has designed the experimental scenarios with
CORSIM-RTE (CORridor SIMulation – Rune Time Extension), a program designed
to capture the interactions between the simulated vehicles and the execution of the
integrated DLM/VSL control under the time-varying traffic conditions. Figure 4
illustrates an example work-zone system for simulation experiments, in which one left
lane was closed on a two-lane highway segment, and drivers are all assumed to
cooperate with the displayed messages.
Performance evaluation
The evaluation task is focused on comparing the integrated control (called
DLM/VSL) with the DLM control (called DLM) and the DLM control by Mn/DOT
(called Mn-DLM) same as those conduced in the previous study (2). The
performance evaluation includes both the operational efficiency and traffic safety.
The experimental results on those two regards are summarized below.
Operational efficiency
The operational efficiency of the target work zone system (see Figure 4) is
evaluated with two measures of effectiveness (MOE), the work zone throughput and
average speed.
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
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Figure 5 compares the work zone throughputs between those three control
strategies under the time-varying traffic conditions. The DLM/VSL and DLM
controls produced 1750 vphpl and 1670 vphpl throughputs, respectively under
the average volume of 2000 vph (see Figure 5a); and 1870 vphpl and 1720
vphpl, respectively under the average volume of 2400 vph (see Figure 5b).
These results indicate that with the complemental VSL control, the DLM
operations can indeed yield a more throughput than that when it works alone.

Figure 6 represents the average speeds detected from the upstream
subsegments (e.g., Links 1 to 5, see Figure 4). Overall, there exists no
significant difference in the average speeds between the DLM/VSL and DLM
controls. It seems that the implementation of VSL does not contribute to any
reduction in the average flow speed, which instead may actually improve the
average flow speed on the upstream subsegments (e.g., Links 1 to 3 at Figure
6a, and Links 1 and 4 at Figure 6b).
Traffic safety
Traffic safety is one of the most important issues during work-zone operations,
especially under the congested and fluctuating traffic conditions. Under the integrated
operations, the VSL control is expected to help drivers properly adjust their speeds on
their merging and lane-changing maneuvers so as to increase the performance of the
DLM control. The simulation results with respect to traffic safety are summarized
below.

Figure 7 compares the patterns of speed changes detected over the upstream
subsegments (e.g., Links 1 to 3, see Figure 4) under the time-varying traffic
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conditions of average volume equal to 2000 vph. As highlighted in Figure 7a,
the average speeds drop or changes drastically and inconsistently under the
DLM control. In contrast, Figure 7b shows that under the DLM/VSL control,
the speeds on those links at a relatively smooth and consistent rate, despite the
fluctuating traffic conditions. During the example operational period, their
numerical comparison of speed changes between the initial and latter time
intervals is reported in Table 1.

Under the other time-varying traffic conditions of average volume equal to
2400 vph, Figure 8 compares the patterns of speed changes detected over three
upstream subsegments (i.e., Links 1 to 3) during the specified time intervals
(e.g., highlighted circles). Figure 8a shows the fluctuating and inconsistent
pattern of speed changes under the DLM control. Under the DLM/VSL
control, however, Figure 8b indicates that their average speeds are maintained
smoothly and consistently, with corresponding to the time-varying traffic
condition. Likewise, the numerical example of speed changes during the
specified time intervals is also compared in Table 1.

As compared in Figures 8(a) and (b), particularly, it should be noted that as the
simulation time interval increases, the DLM/VSL still maintains higher speeds
(approx. 10.0 mph) around the merge point (i.e., Link 1) than those (approx.
5.0 mph) under the DLM control. This indicates that the integrated control
retards the impacts of traffic congestion and merging conflict on the merge
point by the effective speed control of VSL, during the work zone operation
period.

Consequently, the integrated control is expected to help drivers pass the
upstream segment of the work zone area with smooth speed changes. This is
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supported by the results shown in Figure 9, where the speed variations over
the upstream subsegments (i.e., Links 1 to 5, see Figure 6.4.1) are overall
lower under the DLM/VSL control than under the DLM control. This result
means that the integrated control can mitigate the impacts of the frequently
changed merge strategies by DLM on the speed variations, and enhance the
performance of the DLM control with the help of VSL.
CONCLUSIONS
To facilitate the merging maneuvers and minimize potential collisions during
the DLM operations, this study has developed a system control process that can
integrate the VSL with the DLM so as to maximize the total effectiveness. The
proposed integrated control process has used the optimal VSL control model as a
supplementary strategy of the entire DLM operations, and coordinated the sequence
of VMS messages generated from the DLM and VSL algorithms.
From the simulation experiment, the integrated algorithm of the DLM and
VSL controls has shown to respond well to time-varying traffic conditions and
yielded more work-zone throughputs than the DLM control without VSL. It has also
demonstrated that the integrated control results in an increase in the average speed and
a decrease in the speed variation. In particular, the VSL effect is evident as a
supplementary role for the dynamic merge control.
However, it should be mentioned that this type of the advanced control
systems cannot guarantee the performance in field applications unless the sufficient
number of sensors required for the DLM and VSL control models function properly
with respect to their accuracy and reliability. Thus, a further study is to consider the
limitations caused by the sensor system in field applications, based on the actual
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traffic flow data and the lessons observed from the previously tested DLM systems.
One also needs to properly identify the locations of VMS and the displayed messages
so as to increase the compliance rate of drivers.
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REFERENCES
1.
Taavola, D., Jackels, J., and Swenson, T., Dynamic Late Merge System
Evaluation: Initial Deployment on US-10, Summer 2003, Minnesota
Department of Transportation, 2004.
2.
Chang, G. L. and Kang, K. P., Evaluation of Intelligent Transportation System
Deployments for Work Zone Operations. Report MD-05-SP, Department of
Civil Engineering, University of Maryland (UMCP), Sponsored by Maryland
State Highway Administration, August 2005.
3.
Lyles, R. W., Taylor, W. C., Lavansiri, D., and Grossklaus, J., A Field Test
and Evaluation of Variable Speed Limits in Work Zones, Transportation
Research Board Annual Meeting (CD-ROM), Washington, D.C., 2004.
4.
Park, Byungkyu and Yadlapati, S. S., Development and Testing of Variable
Speed Limit Logics at Work Zones Using Simulations, Transportation
Research Board Annual Meeting (CD-ROM), Washington, D.C., 2003.
5.
Kang, K. P. and Chang, G. L., Development of an Advanced Dynamic Late
Merge Control Model and Algorithm, Transportation Research Board Annual
Meeting (CD-ROM), Washington, D.C., 2006.
6.
Lin, P. W., Kang, K. P., and Chang, G. L., Exploring the Effectiveness of
Variable Speed Limit Controls on Highway Work Zone Operations. In
Journal of Intelligent Transportation Systems, Vol. 8 (3), July 2004.
7.
Kang, K. P., Chang, G. L., and Zou, N., An Optimal Dynamic Speed Limit
Control for Highway Work Zone Operations. In Transportation Research
Record 1877, TRB, National Research Council, Washington, D.C., 2004, pp.
77-84.
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8.
17
Wilkie, J. K., Using Variable Speed Limit Signs To Mitigate Speed
Differentials Upstream of Reduced Flow Locations. In Compendium of
Graduate Student Papers on Advanced Surface Transportation System; Texas
Transportation Institute Report SWUTC/97/72840-00003-2. August 1997.
9.
Coleman, J. A. et al., FHWA Study Tour for Speed Management and
Enforcement Technology. FHWA-PL-96-006. Federal Highway
Administration, U.S. Department of Transportation, February 1996.
10.
Smulders, S., Control by Variable Speed Signs: Results of the Dutch
Experiment. 6th International Conference on Road Traffic Monitoring and
Control. 1992.
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LISTS OF TABLES AND FIGURES
TABLE 1 Comparison of Speed Changes between DLM and DLM/VSL
(unit: mph) ---------------------------------------------------------------------- 18
FIGURE 1 Interrelations between the Optimal Control Thresholds
(CT 1 and CT 2) -------------------------------------------------------------- 19
FIGURE 2 Configuration of a VSL System ------------------------------------------- 20
FIGURE 3 An Integrated Algorithm of DLM and VSL Controls ---------------- 21
FIGURE 4 Configuration of the Integrated Control System ---------------------- 22
FIGURE 5 Comparison of Work Zone Throughputs under Time-Varying
and Congested Traffic Conditions ---------------------------------------23
FIGURE 6 Comparisons of Average Speeds under Time-Varying and
Congested Traffic Conditions -------------------------------------------- 24
FIGURE 7 Comparison of Speed Changes over the Upstream Segment
(Ave. = 2000 vph) ------------------------------------------------------------25
FIGURE 8 Comparison of Speed Changes over the Upstream Segment
(Ave. = 2400 vph) ------------------------------------------------------------26
FIGURE 9 Comparison of Speed Variations over the Upstream Segment
under Time-Varying and Congested Traffic Conditions ----------- 27
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TABLE 1 Comparison of Speed Changes between DLM and DLM/VSL (unit: mph)
Upstream
subsegments
Link 1
Link 2
Link 3
Figure 7 (operational period)
DLM
DLM/VSL
Initial / Latter
Initial / Latter
15.0 / 6.0
22.0 / 13.0
41.0 / 12.0
42.0 / 30.0
27.0 / 29.0
51.0 / 37.0
19
Figure 8 (specified time intervals)
DLM
DLM/VSL
From / To
From / To
5.0 / 9.3
10.0 / 11.0
48.0 / 6.0
30.0 / 35.0
41.0 / 42.0
38.0 / 40.0
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Vol. = 0 vphpl
Vol. = 2200 vphpl
Range available for SEM
?
Range available for SLM
?
DLM control
DLM control
SEM
SLM +
SLM
CT 1
CT 2
FIGURE 1 Interrelations between the Optimal Control Thresholds (CT 1 and CT 2)
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VMS
21
Sen 1
Sen 2
Sen 3
Sen 4
Sen 5
VSL 1
VSL 2
VSL 3
VSL 4
VSL 5
VSL 6
Central porcessing unit
FIGURE 2 Configuration of a VSL System
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Step-1: Compute the potential Max. queue lentgh
 Traffic flow rate between the upstream and work zone
 Target section controlled by DLM and VSL
Step-2: Set the initial speed boundaries
 Speed data between the upstream and work zone
 Expected free flow speed of each subsection
Step-3: Locate the PCMS and VSL trailers
 Normal deceleration rate
 Length of subsection between trailers
t=0
Estimated data of
upstream and
downstream
 Flow rate
 Density
Step-4 : Initialize all PCMS and VSL messages
 A Set of initial speed boundaries
 Early merge state or Conventional static signs
t = t+1
t=0
Step-5 : Execute the optimal DLM control
 Determine the traffic conditions
(Moderate, Congested, Heavy congested status)
 Display the merge strategies to maximize the work-zone throughputs
(Early or Late or Traffic Back-up)
Step 6 : Update the speed boundaires
 Changed to cooperate with the DLM control
 Determined based on the thresholds of each state and location
Actual data from
the sensors
 Volume
 Speed
Yes
Step 7 : Execute the optimal VSL control
 Measure the traffic conditions for the determined merge strategy
 Compute a set of speed limits to maximize the work-zone throughputs
Actual queue length
 Maximum queue length
FIGURE 3 An Integrated Algorithm of DLM and VSL Controls
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VSL5
VSL4
Link 5
SPEED
LIMIT
65 MPH
VSL3
Link 4
VSL2
Link 3
WORK
ZONE
45 MPH
VSL1
Link 2
WORK
ZONE
45 MPH
Link 1
WORK
ZONE
45 MPH
1000 ft
1 mile
2 miles
EARLY MERGE
SIGNS
LEFT LANE
CLOSED
2 MILES
LEFT LANE
CLOSED
1 MILE
TAKE YOUR TURN
/ MERGE HERE
LATE MERGE
SIGNS
USE BOTH
LANES
USE BOTH
LANES
TAKE YOUR TURN
/ MERGE HERE
FIGURE 4 Configuration of the Integrated Control System
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Work zone throughputs (a)
under the time-varying traffic condition (Ave. = 2000 vph)
2000
Work zone throughput (vphpl)
DLM/VSL
= 1750 vphpl
DLM/VSL
1800
DLM
1600
DLM
= 1670 vphpl
Mn-DLM
1400
1200
Mn-DLM
= 1510 vphpl
1000
800
600
400
200
0
1
4
7
10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58
Time intervals (1 min.)
Work zone throughputs (b)
under the time-varying traffic condition (Ave. = 2400 vph)
2000
Work zone throughput (vphpl)
DLM/VSL
= 1869 vphpl
DLM/VSL
1800
DLM
1600
Mn-DLM
1400
DLM
= 1720 vphpl
1200
1000
Mn-DLM
= 1393 vphpl
800
600
400
200
0
1
4
7
10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58
Time intervals (1 min.)
FIGURE 5 Comparison of Work Zone Throughputs under Time-Varying and
Congested Traffic Conditions
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Average speeds over the upstream segment (a)
under the time-varying traffic conditin (Ave. = 2000 vph)
70
60
Speeds (mph)
50
DLM/VSL
DLM
Mn-DLM
40
30
20
10
0
Link 1
Link 2
Link 3
Link 4
Link 5
Upstream subsegment
Average speeds over the upstream segment (b)
under the time-varying traffic condition (Ave. = 2400 vph)
70
60
Speeds (mph)
50
DLM/VSL
DLM
Mn-DLM
40
30
20
10
0
Link 1
Link 2
Link 3
Link 4
Link 5
Upstream subsegments
FIGURE 6 Comparisons of Average Speeds under Time-Varying and Congested
Traffic Conditions
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Evolution of speed changes over the upstream segment
under the DLM control (Ave. = 2000 vph) (a)
80
2200
Link 1
70
Link 2
Link 3
Time-varying Up. Vol.
2000
1600
50
1400
1200
41.0
40
1000
30
29.0
27.0
800
600
20
15.0
12.0
6.0
10
0
400
Upstream Volume (vphpl)
Speeds (mph)
1800
60
200
0
1
6
11
16
21
26
31
36
41
46
51
56
Time intervals (1 min.)
Evolutionn of speed changes over the upstresm segment
under the DLM/VSL control (Ave. = 2000 vph) (b)
80
2200
Link 1
Link 2
Link 3
Time-varying Up. Vol.
1700
Speeds (mph)
60
50
51.0
40
42.0
1200
37.0
30
30.0
700
22.0
20
13.0
10
0
200
-300
1
6
11
16
21
26
31
36
41
46
51
56
Time intervals (1 min.)
FIGURE 7 Comparison of Speed Changes over the Upstream Segment
(Ave. = 2000 vph)
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Upstream Volume (vphpl)
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Evolution of speed changes over the upstream segment
under the DLM control (Ave. = 24000 vph) (a)
2600
Link 1
Link 2
Link 3
Time-varying Up. Vol.
60
2200
2000
50
Speeds (mph)
2400
1800
48.0
1600
42.0
41.0
40
1400
1200
30
1000
20
800
10
600
400
9.3
6.0
5.0
Upstream Volume (vphpl)
70
200
0
0
1
6
11
16
21
26
31
36
41
46
51
56
Time intervals (1 min.)
Evolution of speed changes over the upstream segment
under the DLM/VSL control (Ave. = 24000 vph) (b)
2600
Speeds (mph)
Link 1
Link 2
link 3
Time-varying Up. Vol.
2400
60
2200
2000
50
1800
40
1600
40.0
35.0
38.0
1400
1200
30.0
30
1000
20
800
10
600
400
11.0
10.0
200
0
0
1
6
11
16
21
26
31
36
41
46
51
56
Time intervals (1 min.)
FIGURE 8 Comparison of Speed Changes over the Upstream Segment
(Ave. = 2400 vph)
27
Upstream Volume (vphpl)
70
Kang and Chang
28
Speed variations over the upstream segment (a)
(Link 1 to Link 5, Ave. = 2000 vph)
35
30
Standard deviation
DLM
25
20
15
DLM/VSL
10
Stdev. Under the DLM/VSL control
5
Stdev. under the DLM control
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
Time intervals (1 min.)
Speed varation over the upstream segment (b)
(Link 1 to Link 5, Ave. = 24000 vph)
40
DLM
35
Standard deviation
30
25
20
DLM/VSL
15
10
Stdev. under the DLM/VSL control
5
Stdev. under the DLM control
0
1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59
Time intervals (1 min.)
FIGURE 9 Comparison of Speed Variations over the Upstream Segment under TimeVarying and Congested Traffic Conditions
28