- Email: [email protected]
An evaluation of freeway lane control signing using computer simulation
Mathl. Comput.
Modelling Vol. 27, No. Q-11, pp. 177-187, 1998 @ 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 08957177/98 819.00 + 0.00
PII:SO?395-7177(98)00058-2
An Evaluation of Freeway Lane Control Signing Using Computer Simulation L. SCHAEFER* Department of Industrial and Management Systems Engineering Arizona State University, Tempe, AZ 85287, U.S.A. lisa.schaeferQI asu.edu J. UPCHURCH Department of Civil Engineering Arizona State University, Tempe, AZ 85287-5306, U.S.A. S. A. ASHUR Department of Civil Engineering University of Texas at El Paso, El Paso, TX 799680516,
U.S.A.
Abstract-Lane
control has been proposed as a traffic congestion alleviation method. For this method to work, a certain minimum percentage of the drivers must comply with the lane signing. The research described here has been performed to analyze the percentage of drivers that must comply with lane control. A simulation model was developed and tested. The simulation results for heavy tragic flow (1550 vehicles per hour per lane-vphpl), medium traffic flow (900 vphpl), and light traffic flow (300vphpl) conditions indicate that lane control has little influence on congestion, regardless of the percentage of drivers that comply with the lane control signing. For heavy flow, the congestion level remains high even when all drivers comply. For medium and light flow, the congestion level remains low even when no drivers comply. The region between heavy and medium traffic flow is, however, sensitive to lane control. Four flow rates between medium and heavy flow were tested. The impsct of lane control under these conditions is described. @ 1998 Elsevier Science Ltd. All rights reserved. Keywords-
Lane use control, Traffic,Simulation,Driverbehavior,Microscopic. 1.
INTRODUCTION
1.1.Background Lane control is the use of traffic management technology to slow trafllc and manage lane usage on a freeway upstream of lane closures, traffic accidents, or other trafhc incidents. This is accomplished by posting speed limits or notices to vacate a lane on individual electronic signs above each lane. The purpose of the electronic signs is to decrease vehicle speed upstream of existing traffic congestion and incidents to prevent vehicles from having to brake suddenly and risk causing more accidents. This method has been used on freeways in The Netherlands, as shown in Figure 1, and in Germany for several years, however, it has not been used in the United States. The Dutch have experienced the following benefits with lane control: a reduction in total accidents of 24 percent, a reduction in secondary accidents of 50 percent, 30 percent fewer vehi*Address all correspondence
to this author.
177
L. SCHAEFERet 41.
178
Figure 1. Lane control signs on a freeway in The Netherlands. The signs indicate a speed limit of 70 kilometers per hour in the three leftmost lanes.. A red X symbol over the fourth lane indicates that lane is closed.
cles involved in accidents, and 15 percent less delay. These advantages suggest it may be very worthwhile to implement lane control on United States freeways. 1.2. Problem
Statement
It is hypothesized that effectiveness of lane control in managing traffic and reducing accidents is dependent on driver response to lane control signals. Based upon observation of driver compliance with other traffic regulations (speed limits, for example), not all drivers comply. The levels of driver compliance with lane control which are required for effective operation, versus congestion, are unknown. The problem is then to identify the levels of compliance needed for effective operations. If very high compliance levels are required, then lane control in the United States may not generate the same level of benefits as in The Netherlands. On the other hand, if lane control can operate effectively at a moderate level of compliance, the likelihood of successful implementation in the United States would be high. The goal of this research was to determine what percentage of drivers must comply with lane control signs in order to improve freeway operations. This would depend upon the severity of the downstream traffic conditions under a given set of traffic flow assumptions. Research has already been performed to determine how well drivers would understand the lane control signing [l]. The results would be used to help decide whether lane control could be effectively implemented in freeway management systems across the United States. 1.3. Methodology
Traffic flows under the influence of lane control were simulated to evaluate flows under certain traEc volumes and certain percentages of driver compliance with lane control. The simulated system consisted of one direction of a typical three-lane urban freeway located in the United States. The effect of varying the percentage of drivers complying with the lane control speed limits and signs under light, medium, or heavy traffic volumes was evaluated. An overhead view of the system is shown in Figure 2. The numbers and symbols in boxes are the items displayed on electronic signs. Numbers designate speed limits in miles per hour. The “t” symbol means vacate the lane and the “X” symbol indicates that the lane is closed. A microscopic simulation model of the freeway segment was constructed using the Simulation Language for Alternative Modelling (SLAM) software [2]. SLAM is a general purpose simulation
179
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1501 : lene control s&n Figure 2. Overhead view of freeway system evaluated showing the lane control sign arrangement. Lane control signs are typically blank under normal conditions. There fore, when a driver approaches a blank lane control sign, he/she drives the normal speed limit. The numbers on the lane control signs designate the speed limit for the freeway section ahead.
software which requires input in the form of abstract high-level computer code. SLAM was used because, unlike typical microscopic traffic simulation software, it allows the modeller to control the percent of drivers that comply with speed limit signs and vacate lane signs. This is important since the percent of compliance is the independent variable in this. research. Each vehicle was modelled as a separate “entity” in the general purpose simulation model. A three mile freeway segment was modelled with a blockage in the rightmost lane, i.e., lane 1, as shown in Figure 2. Initially, three traffic flow rates were modelled: light flow (300 vehicles per hour per lane-vphpl), medium flow (900 vphpl), and heavy flow (1550 vphpl). Later in the study, four additional rates between heavy and medium flow were tested.
2. DATA SOURCES 2.1.
Headway and Capacity
The capacity of a typical freeway is 2300 passenger cars per hour per lane for basic freeway segments. This is based on the 1994 edition of the Highway Capacity Manual [3]. The probability distributions, means, and standard deviations for vehicle interarrival times used in the model were based on Selvia’s work [4]. Selvia showed that the interarrival times of six lane facilities are approximately lognormally distributed.
180
L. SCHAEFERet al.
2.2. Sign Layout Some of the logic and numerical values represented in the modelling of the system were adapted from typical lane control scenarios adopted in The Netherl~~ [5]. Since overhead lane control signs in The Netherlands are usually 700 meters apart, the signs were assumed to be spaced at l/2 mile intervals for a United States freeway. Also, in The Netherlands, lane control signs show speed limits in increments of 20 kilometers per hour (kph), with 50 kph as the minimum and 110 kph as the maximum. For an urban area in the United States, 55mph was used as the maximum speed limit, and the speed limits used in the model are 55, 50,40, and 30 mph. In most lane control scenarios in The Netherl~ds, lane control signals over adjacent lanes show identical messages, i.e., the same speed. The exception to thii would be the lanes that have signs which designate them as being closed. See Figure 2.
3. LOGIC MODEL OF LANE CONTROL 3.1. Assumptions
of This Model
The following describes the information necessary to mathematically lane control. 3.1.1.
Length
construct the model of
of vehicles
All vehicles were assumed to be passenger cars with a length of 20 feet. When applying the simulation results to a real highway, the actual traffic composition must be converted to units of passenger cars [4]. Each truck or bus is equivalent to some number of passenger cars. The conversion factor depends upon the steepness of the roadway grade, and other geometric characteristics. 3.1.2.
Definition
of minimum
acceptable
headway
Every driver allows a certain distance between their vehicle and the vehicle in front of them in order to feel safe while driving. This distance depends upon the speed at which they are driving. The time it takes to drive through this distance is the minimum acceptable headway. The mean headway is taken to be the reciprocal of the capacity of a highway, i.e., 3600 (~/hr}/23~ passenger cars per hour, or 1.57 seconds per passenger car, The ~nimum acceptable headway is assumed to be normally distributed, A random number representing minimum acceptable headway is generated for esch vehicle. 3.13.
Definition
of compliance
Compliance with a speed limit is defined ss driving on a freeway section at a speed that is no more than 6mph above the speed limit of the freeway section. Thus, if the speed limit were 40mph, the driver would be complying if he/she were driving between 40 and 46mph. The percent of driver compliance with the vacate lane sign is taken to be the fraction of drivers in the lane containing the blockage that leave the lane before entering the freeway section designated ss closed by a red “X” symbol. Thus, if a vehicle enters the freeway section in lane 1 designated as closed, the driver is not complying with the red “X” sign, even if the driver changes lanes before reacftmg the incident. 3.1.4.
Road
network
The simulated highway system is split into l/2 mile segments of equal speed limit. Within each l/2 mile segment, the model allows three chances to change lanes, i.e., vehicles have the oppo~u~ty to change lanes every 880 feet.
Lane Control Signing
181
3.2. Logical Description of the Freeway System
Each lane has its own lognormal distribution for time between arrivals of vehicles [4]. The vehicle is assumed to be travelling at approximately the usual speed limit, 55 mph, upon entering the system. When a vehicle enters the freeway system, it is assigned a speed according to a normal distribution. The mean for 55 mph speed limit is 58 mph and the standard deviation is dependent upon the percent compliance [6]. Each vehicle is also assigned a minimum acceptable headway required for the driver’s safety according to a normal distribution. The speed and headway are used to calculate the travel time and minimum acceptable headway each vehicle will use to travel on the next downstream section. Each vehicle is then given the choice to switch lanes or not. If the vehicle entered the system from either the middle or leftmost lanes (lanes 2 or 3 on Figure l), it may either stay in the lane or switch to the adjacent lanes 3 or 2 according to a conditional statement. The conditional statement represents drivers deciding to change lanes due to downstream congestion in the current lane and less congestion in the adjacent lane. A lane change maneuver from lane 2 or lane 3 may occur if the length of the vehicle plus its minimum acceptable headway is greater than the number of feet available on the next downstream section. If this is the case, and there is enough available roadway for the vehicle to safely travel in the adjacent lane, the vehicle will change lanes. Since percent of compliance is the independent variable in this model, the lane changing logic for lane 1 is different than the lane changing logic of lanes 2 and 3. If the vehicle is travellmg in lane 1, a probability, rather than a conditional statement, is assigned to define the percent of vehicles that vacate lane 1. The probabilistic statement represents drivers complying with the vacate lane sign. The probability is dependent upon the percent of compliance, so that the percent of drivers leaving the lane before the red “X” sign can be controlled. After the vehicle chooses a lane, it is placed in a queue for available roadway feet. If there is enough space on the next section for the vehicle, without slowing down, it immediately “takes up space” and travels in the lane for the amount of travel time previously calculated. When the vehicle finishes travelling on the section, it “releases” the feet of roadway it was occupying and is assigned a speed according to the speed distribution of the next section. The vehicle follows the same pattern of headway assignment, feet of roadway and travel time calculation, lane switching options, queue placement, travelling, and speed assignment until it reaches the end of the system. Upon reaching the end of the system, if the vehicle is in lane 2 or 3, it will release the feet of roadway and exit the system. If the vehicle is in lane 1, it will wait in a queue for available roadway space in lane 2, switch to lane 2, drive along the last section, release its assigned road space, and exit the system. A flowchart representing the logic described above is shown in Figure 3. 3.3. Measure of Performance Delay is used as the measure of performance for the freeway system. In the simulation model, delay is defined as the amount of time vehicles wait in a queue for driving space on the next downstream section of freeway. Traffic density in vehicles per mile is normally used to evaluate the performance of freeways [3]. However, when a lane is blocked, density does not adequately describe the performance of the network. In this case, delay per vehicle is a better measure of performance [3]. Delay is quantified as the average time per vehicle to wait for available space in the next downstream section for each section of the freeway. This was compared to the expected time to travel on one section of the freeway to determine if waiting for an acceptable gap is a large portion of the time to travel on one freeway section.
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L. SCHAEFER et al.
ENTER SYSTEM
/SECTION
U=RANDOM
SPEED
H=RANDOM
HEADWAY
~=88~/[v(528Oft/mi)/(3600s/hr)] ROADFT=UH*(5280ft/mi)/(36OOs/hr)
LANE
1
LANE 2 OR 3
I ASSIGN LANE CHANGE
SECTIONeROADFf
PROBABILITY
I
UNITS OF ROADWAY
Figure
3.4. Model
3. Logic
UNITS OF ROADWAY
for the movement
of vehicles
UNITS OF ROADWAY
through
the simulated
UNITS OF ROADWAY
freeway
system.
Limitations
The simulation model described above was created with the assumption that no entrance ramps, exit ramps, or weaving areas were present in the freeway section being analyzed. Thus, the results are valid only for basic freeway sections. The data is hard coded into the simulation statements. The simulation model is not designed to be interactive with the user since extensive amounts of code would have to be written to make the model interactive. Further experimentation would require modifying the high-level input code.
Lane Control Signing
183
Only one sign layout was modelled. The model is not able to change signs as the traflic changes. This model also assumes the complying motorists are familiar with the system. 4. EVALUATION
OF LANE
CONTROL
SIGNING
4.1. Flow Rate There were three different flow rates modelled in the first models that were tested: heavy, medium, and light traffic flow. In a later refinement, three flow rates between medium and heavy were tested. Since the difference among heavy, medium, and light traffic flow is how many vehicles pass a point over a certain period of time, interarrival time, or headway, must be specilkd to differentiate among heavy, medium, and light traffic flows. 4.2. Percentage
of Driver
Compliance
Since two types of signs exist in the freeway system being studied, percentage of driver compliance was specified in two ways. Compliance with speed limits and compliance with lane merging were modelled in this study. Percent compliance was specified so that each simulation run had the same percent speed limit violators as merge violators. Percentages for speed limit and lane merging compliance were varied from 0% to 100% in 10% increments, although results for only some of these cases are presented in this paper. The percent of compliance with speed limits was varied by changing the standard deviation of the speed. Since the percent merging is controlled by specifying the probability of drivers switching out of the blocked lane at each point in the model where lane changing is allowed, the percent of vehicles merging at each section must be calculated. An equal fraction of vehicles that originally entered the system in the lane containing the blockage is forced to switch lanes upstream of the blockage at each location where there is a lane changing option. 4.3. Incident
Duration
All models were constructed to produce output after 5 minutes of incident duration and every 10 minutes thereafter up to 45 minutes. These incident durations were analyzed to determine the effect of duration on percentage of delay. 4.4. Summary
of Preliminary
Results
Plots for heavy traffic flow could not be generated since the simulation run halted due to an excess of vehicles in the system. Light traffic flow has very little or no vehicle delay, regardless of the level of compliance. Figure 4 shows the results of the simulation runs for medium traffic flow. According to this plot, the delay on the freeway section with the highest delay, was less than 1.2 seconds per vehicle even after 45 minutes of lane blockage. Thii delay value is very low compared to the expected travel time value of 18 seconds per vehicle to drive over one 880 foot section at 33mph, the mean speed for a 30 mph section. 4.5. Flow Rate
Between
Medium
and Heavy
Traffic
Flow
After five minutes of incident duration under heavy flow conditions, the simulation run stops because there are too many vehicles in the system (i.e., a traffic jam). In contrast, under medium flow conditions, the congestion is so low that at 0% compliance, there is very little delay incurred by each vehicle. These findings prompted the investigation of intermediate flow rates between medium and heavy flow to determine the effects of lane control at 70% and 30% driver compliance. The intermediate flow rates used were 1000, 1150, and 1300vphpl.
L. SCHAEFERet al.
Incident Duration 0.6
5 1
0.6
f
0.4
0.2
0
I
om
40%
20%
Pwcerrt
60?6
6096
100%
Compliance
Figure 4. Delay through most congested 880 foot section versus percent of compliance for medium trafllc flow. In esch simulation run, the same percent of drivers complied with speed limit signs as vacate lane signs (i.e., if 30% of the drivers complied with speed limit signs, 30% of the drivers complied with vacate lane signs). Thus, “percent compliance” on the graphs apply to all signs. This graph shows that delay is very low during medium tra& flow for any incident duration, even when 0% of the drivers comply with the lane control signs. 70 60
Incident Duration
3 50 s 40 : ; 30 5 o 20 10 0 900
1000
1100
1200
1300
now EvpWI Figure 5. Delay versus trafllc flow rate for 30% compliance. At 30% compliance and high flow (1550 vphpl), the trafllc system became so congested that the simulation run quit due to more vehicles in the system than the software would allow. Thii graph suggests that &straffic flow becomes higher, congestion causes delay to grow exponentially. 4.6.
Summary
of Results
for Intermediate
TrafIlc Flows
Figures 5 and 6 show intermediate flow rates between heavy and medium flow. Figure 5 shows that for 30% driver compliance, delay is high for a flow rate of 1300vphp1, even after only 5 minutes. Delay is approximately 4 seconds per vehicle at 1150vphp1, which means it takes 20% longer than it normally would to drive on one uncongested freeway section. Delay is less than 2 seconds for 1OOOvphpl.
Lane Control Signing
185
incident Duration
900
1000
1100
1200
--+-
5 min.
-
15 min.
+
25 min.
-X-
35 min.
-
45 min.
1300
Flow (vphpl) Figure 6. Delay versus traffic flow rate for 70% compliance. At 70% compliance and high flow (1550 vphpl), the traffic system became so congested that the simulation run quit due to more vehicles in the system than the software would allow. This graph suggests that as traffic flow becomes higher, congestion causes delay to grow exponentially. However, when comparing Figure 6 to Figure 5, one would conclude that delay grows exponentially with 30% compliance more quickly than with 70% compliance. 70 T
60 Percent Compliance w 70% n
5 min.
15 min.
35 min.
25 min. Incident
II
30%
45 min.
Duration
Figure 7. Delay versus incident duration for flow rate of 1300vphpl. This figure emphasizes the difference in delay between 70% and 30% driver compliance.
Figure 6 shows delay for 70% driver compliance and different flow rates. Delay is still high for 1300vphpl and low for 1000 vphpl. However, delay is less at all flow rates with the higher level of driver compliance [6]. Figure 7 emphasizes the difference in delay between 30% and 70% compliance when the flow rate is 1300vphpl.
5. CONCLUSIONS
AND
RECOMMENDATIONS
The effect of lane control as a traffic control method has not been well researched in the past. This research evaluated the percentage of driver compliance which would be required to consider lane control as a feasible method to alleviate congestion. To this end, a simulation model was developed and tested, and the output analyzed.
L. SCHAEFER et al.
186
The results obtained
for traffic flows of 300, 900, and 1550 vphpl indicate
with lane control has little influence comply with the lane control signing.
that driver compliance
on congestion, regardless of the percentage of drivers that For heavy flow, traffic queues resulting from a lane blockage
are so long that drivers would benefit only if they were advised to exit the freeway upstream incident.
For medium
for congestion
and light flow, the congestion
of the
is not necessary
alleviation.
For an intermediate
flow rate of lOOOvphp1, at 70% and 30% driver compliance,
little delay up to 45 minutes
after the incident.
not to warrant
for congestion
lane control
does not alleviate
congestion
Thus,
alleviation.
signing.
there
At a flow rate of 1150 vphpl, comply
lane control
with lane control
delay even after only 5 minutes
lane control
signing.
of incident
duration.
Thus,
comply
there is high
at this flow rate, congestion congestion.
At the
of incident
is effective when 70% of drivers
For a flow rate of 1300 vphpl at 70% and 30% compliance,
enough that vehicles should be routed off of the freeway to alleviate the policy to determine when to use lane control.
is very
is minor enough
there is very little delay even up to 45 minutes
at a flow rate of 1150 vphpl,
with lane control
Thus, at this flow rate, congestion
when only 30% of drivers
same flow rate, but 70% compliance, duration.
is very low and lane control
Figure
is heavy 8 shows
90 80 8 z ‘z
60 --
8
50 --
=8
40 --
b n
30 --
no lane control necessary
70 --
20 t 10 0 L
I
300
400
500
I
I
I
600
700
600
900
1000 1100 1200 1300 1400
1500
Flow (vphpl) Figure 8. Policy to determine when to use lane control. The white area means lane control is not necessary for the flow rate and percent compliance given. The black area designates the flow rates and percent compliance for which lane control will not alleviate congestion. The grey area shows the flow rates and percent compliance for which lane control will make a difference.
Recommendations
For
Further
Research
Further research should be conducted to predict the actual percentage of drivers in the United States that would comply with lane control. If one had an estimate of how many drivers would comply with the lane control signs, one may better determine whether lane control’would be feasible in the United States. To be better able to compare the potential effectiveness of lane control in the United States to the effectiveness of lane control in The Netherlands, it would be very useful to know the percent of drivers that comply with lane control in The Netherlands. This model could be improved by using a software that is not based on the typical link-node paradigm. Instead, a program that simulates entities as existing over a two-dimensional area should be used based on emergent behavior algorithms originating in the animation industry [7].
Lane Control Signing
187
Currently, there are no software packages available that use emergent behavior to model traffic over a two-dimensional area, however, a preliminary feasibility study has been performed (81.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
G.L. Ullman, Motorist interpretation of MUTCD freeway lane control signals, Zbansportation Research Record 1408, 49-56 (October 1993). A. Pritsker, An Introduction to Simulation and SLAM II, System Publishing, (1984). Transportation Research Board, Highway Capacity Manual, TRB, National Hesearch Council, Washington, DC, (1995). G. Selvia, Evaluation of probability distributions for multilane facilities, Dissertation, University of New Mexico, (December 1990). Directorate general for public works and water management, In Dynamic Z?ufic Management in The Netherlands, Hotterdam, The Netherlands, (March 1992). L.A. Schaefer, Analysis of driver compliance with lane control through the use of computer simulation, Thesis, Arizona State University, (August 1995). C. Reynolds, Flocks, herds, and schools: A distributed behavioral model, Computer Graphics ;SIGGRAPH ‘87 Conference Proceedings) 21 (4), 25-34 (1987). K.L. Sanford, J.A. Wentworth and S. McNeil, Application of artificial life to traffic modeling, AZ ‘95 Fifteenth International Conference, June 27-30, 1995, pp. 431-440.
Modelling Vol. 27, No. Q-11, pp. 177-187, 1998 @ 1998 Elsevier Science Ltd. All rights reserved Printed in Great Britain 08957177/98 819.00 + 0.00
PII:SO?395-7177(98)00058-2
An Evaluation of Freeway Lane Control Signing Using Computer Simulation L. SCHAEFER* Department of Industrial and Management Systems Engineering Arizona State University, Tempe, AZ 85287, U.S.A. lisa.schaeferQI asu.edu J. UPCHURCH Department of Civil Engineering Arizona State University, Tempe, AZ 85287-5306, U.S.A. S. A. ASHUR Department of Civil Engineering University of Texas at El Paso, El Paso, TX 799680516,
U.S.A.
Abstract-Lane
control has been proposed as a traffic congestion alleviation method. For this method to work, a certain minimum percentage of the drivers must comply with the lane signing. The research described here has been performed to analyze the percentage of drivers that must comply with lane control. A simulation model was developed and tested. The simulation results for heavy tragic flow (1550 vehicles per hour per lane-vphpl), medium traffic flow (900 vphpl), and light traffic flow (300vphpl) conditions indicate that lane control has little influence on congestion, regardless of the percentage of drivers that comply with the lane control signing. For heavy flow, the congestion level remains high even when all drivers comply. For medium and light flow, the congestion level remains low even when no drivers comply. The region between heavy and medium traffic flow is, however, sensitive to lane control. Four flow rates between medium and heavy flow were tested. The impsct of lane control under these conditions is described. @ 1998 Elsevier Science Ltd. All rights reserved. Keywords-
Lane use control, Traffic,Simulation,Driverbehavior,Microscopic. 1.
INTRODUCTION
1.1.Background Lane control is the use of traffic management technology to slow trafllc and manage lane usage on a freeway upstream of lane closures, traffic accidents, or other trafhc incidents. This is accomplished by posting speed limits or notices to vacate a lane on individual electronic signs above each lane. The purpose of the electronic signs is to decrease vehicle speed upstream of existing traffic congestion and incidents to prevent vehicles from having to brake suddenly and risk causing more accidents. This method has been used on freeways in The Netherlands, as shown in Figure 1, and in Germany for several years, however, it has not been used in the United States. The Dutch have experienced the following benefits with lane control: a reduction in total accidents of 24 percent, a reduction in secondary accidents of 50 percent, 30 percent fewer vehi*Address all correspondence
to this author.
177
L. SCHAEFERet 41.
178
Figure 1. Lane control signs on a freeway in The Netherlands. The signs indicate a speed limit of 70 kilometers per hour in the three leftmost lanes.. A red X symbol over the fourth lane indicates that lane is closed.
cles involved in accidents, and 15 percent less delay. These advantages suggest it may be very worthwhile to implement lane control on United States freeways. 1.2. Problem
Statement
It is hypothesized that effectiveness of lane control in managing traffic and reducing accidents is dependent on driver response to lane control signals. Based upon observation of driver compliance with other traffic regulations (speed limits, for example), not all drivers comply. The levels of driver compliance with lane control which are required for effective operation, versus congestion, are unknown. The problem is then to identify the levels of compliance needed for effective operations. If very high compliance levels are required, then lane control in the United States may not generate the same level of benefits as in The Netherlands. On the other hand, if lane control can operate effectively at a moderate level of compliance, the likelihood of successful implementation in the United States would be high. The goal of this research was to determine what percentage of drivers must comply with lane control signs in order to improve freeway operations. This would depend upon the severity of the downstream traffic conditions under a given set of traffic flow assumptions. Research has already been performed to determine how well drivers would understand the lane control signing [l]. The results would be used to help decide whether lane control could be effectively implemented in freeway management systems across the United States. 1.3. Methodology
Traffic flows under the influence of lane control were simulated to evaluate flows under certain traEc volumes and certain percentages of driver compliance with lane control. The simulated system consisted of one direction of a typical three-lane urban freeway located in the United States. The effect of varying the percentage of drivers complying with the lane control speed limits and signs under light, medium, or heavy traffic volumes was evaluated. An overhead view of the system is shown in Figure 2. The numbers and symbols in boxes are the items displayed on electronic signs. Numbers designate speed limits in miles per hour. The “t” symbol means vacate the lane and the “X” symbol indicates that the lane is closed. A microscopic simulation model of the freeway segment was constructed using the Simulation Language for Alternative Modelling (SLAM) software [2]. SLAM is a general purpose simulation
179
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T I
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I 30 I
t
f
r
I
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I
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trflt% AOW
2
mi. t
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I
I
t
2
t I
L"
101 lane2
1501 : lene control s&n Figure 2. Overhead view of freeway system evaluated showing the lane control sign arrangement. Lane control signs are typically blank under normal conditions. There fore, when a driver approaches a blank lane control sign, he/she drives the normal speed limit. The numbers on the lane control signs designate the speed limit for the freeway section ahead.
software which requires input in the form of abstract high-level computer code. SLAM was used because, unlike typical microscopic traffic simulation software, it allows the modeller to control the percent of drivers that comply with speed limit signs and vacate lane signs. This is important since the percent of compliance is the independent variable in this. research. Each vehicle was modelled as a separate “entity” in the general purpose simulation model. A three mile freeway segment was modelled with a blockage in the rightmost lane, i.e., lane 1, as shown in Figure 2. Initially, three traffic flow rates were modelled: light flow (300 vehicles per hour per lane-vphpl), medium flow (900 vphpl), and heavy flow (1550 vphpl). Later in the study, four additional rates between heavy and medium flow were tested.
2. DATA SOURCES 2.1.
Headway and Capacity
The capacity of a typical freeway is 2300 passenger cars per hour per lane for basic freeway segments. This is based on the 1994 edition of the Highway Capacity Manual [3]. The probability distributions, means, and standard deviations for vehicle interarrival times used in the model were based on Selvia’s work [4]. Selvia showed that the interarrival times of six lane facilities are approximately lognormally distributed.
180
L. SCHAEFERet al.
2.2. Sign Layout Some of the logic and numerical values represented in the modelling of the system were adapted from typical lane control scenarios adopted in The Netherl~~ [5]. Since overhead lane control signs in The Netherlands are usually 700 meters apart, the signs were assumed to be spaced at l/2 mile intervals for a United States freeway. Also, in The Netherlands, lane control signs show speed limits in increments of 20 kilometers per hour (kph), with 50 kph as the minimum and 110 kph as the maximum. For an urban area in the United States, 55mph was used as the maximum speed limit, and the speed limits used in the model are 55, 50,40, and 30 mph. In most lane control scenarios in The Netherl~ds, lane control signals over adjacent lanes show identical messages, i.e., the same speed. The exception to thii would be the lanes that have signs which designate them as being closed. See Figure 2.
3. LOGIC MODEL OF LANE CONTROL 3.1. Assumptions
of This Model
The following describes the information necessary to mathematically lane control. 3.1.1.
Length
construct the model of
of vehicles
All vehicles were assumed to be passenger cars with a length of 20 feet. When applying the simulation results to a real highway, the actual traffic composition must be converted to units of passenger cars [4]. Each truck or bus is equivalent to some number of passenger cars. The conversion factor depends upon the steepness of the roadway grade, and other geometric characteristics. 3.1.2.
Definition
of minimum
acceptable
headway
Every driver allows a certain distance between their vehicle and the vehicle in front of them in order to feel safe while driving. This distance depends upon the speed at which they are driving. The time it takes to drive through this distance is the minimum acceptable headway. The mean headway is taken to be the reciprocal of the capacity of a highway, i.e., 3600 (~/hr}/23~ passenger cars per hour, or 1.57 seconds per passenger car, The ~nimum acceptable headway is assumed to be normally distributed, A random number representing minimum acceptable headway is generated for esch vehicle. 3.13.
Definition
of compliance
Compliance with a speed limit is defined ss driving on a freeway section at a speed that is no more than 6mph above the speed limit of the freeway section. Thus, if the speed limit were 40mph, the driver would be complying if he/she were driving between 40 and 46mph. The percent of driver compliance with the vacate lane sign is taken to be the fraction of drivers in the lane containing the blockage that leave the lane before entering the freeway section designated ss closed by a red “X” symbol. Thus, if a vehicle enters the freeway section in lane 1 designated as closed, the driver is not complying with the red “X” sign, even if the driver changes lanes before reacftmg the incident. 3.1.4.
Road
network
The simulated highway system is split into l/2 mile segments of equal speed limit. Within each l/2 mile segment, the model allows three chances to change lanes, i.e., vehicles have the oppo~u~ty to change lanes every 880 feet.
Lane Control Signing
181
3.2. Logical Description of the Freeway System
Each lane has its own lognormal distribution for time between arrivals of vehicles [4]. The vehicle is assumed to be travelling at approximately the usual speed limit, 55 mph, upon entering the system. When a vehicle enters the freeway system, it is assigned a speed according to a normal distribution. The mean for 55 mph speed limit is 58 mph and the standard deviation is dependent upon the percent compliance [6]. Each vehicle is also assigned a minimum acceptable headway required for the driver’s safety according to a normal distribution. The speed and headway are used to calculate the travel time and minimum acceptable headway each vehicle will use to travel on the next downstream section. Each vehicle is then given the choice to switch lanes or not. If the vehicle entered the system from either the middle or leftmost lanes (lanes 2 or 3 on Figure l), it may either stay in the lane or switch to the adjacent lanes 3 or 2 according to a conditional statement. The conditional statement represents drivers deciding to change lanes due to downstream congestion in the current lane and less congestion in the adjacent lane. A lane change maneuver from lane 2 or lane 3 may occur if the length of the vehicle plus its minimum acceptable headway is greater than the number of feet available on the next downstream section. If this is the case, and there is enough available roadway for the vehicle to safely travel in the adjacent lane, the vehicle will change lanes. Since percent of compliance is the independent variable in this model, the lane changing logic for lane 1 is different than the lane changing logic of lanes 2 and 3. If the vehicle is travellmg in lane 1, a probability, rather than a conditional statement, is assigned to define the percent of vehicles that vacate lane 1. The probabilistic statement represents drivers complying with the vacate lane sign. The probability is dependent upon the percent of compliance, so that the percent of drivers leaving the lane before the red “X” sign can be controlled. After the vehicle chooses a lane, it is placed in a queue for available roadway feet. If there is enough space on the next section for the vehicle, without slowing down, it immediately “takes up space” and travels in the lane for the amount of travel time previously calculated. When the vehicle finishes travelling on the section, it “releases” the feet of roadway it was occupying and is assigned a speed according to the speed distribution of the next section. The vehicle follows the same pattern of headway assignment, feet of roadway and travel time calculation, lane switching options, queue placement, travelling, and speed assignment until it reaches the end of the system. Upon reaching the end of the system, if the vehicle is in lane 2 or 3, it will release the feet of roadway and exit the system. If the vehicle is in lane 1, it will wait in a queue for available roadway space in lane 2, switch to lane 2, drive along the last section, release its assigned road space, and exit the system. A flowchart representing the logic described above is shown in Figure 3. 3.3. Measure of Performance Delay is used as the measure of performance for the freeway system. In the simulation model, delay is defined as the amount of time vehicles wait in a queue for driving space on the next downstream section of freeway. Traffic density in vehicles per mile is normally used to evaluate the performance of freeways [3]. However, when a lane is blocked, density does not adequately describe the performance of the network. In this case, delay per vehicle is a better measure of performance [3]. Delay is quantified as the average time per vehicle to wait for available space in the next downstream section for each section of the freeway. This was compared to the expected time to travel on one section of the freeway to determine if waiting for an acceptable gap is a large portion of the time to travel on one freeway section.
182
L. SCHAEFER et al.
ENTER SYSTEM
/SECTION
U=RANDOM
SPEED
H=RANDOM
HEADWAY
~=88~/[v(528Oft/mi)/(3600s/hr)] ROADFT=UH*(5280ft/mi)/(36OOs/hr)
LANE
1
LANE 2 OR 3
I ASSIGN LANE CHANGE
SECTIONeROADFf
PROBABILITY
I
UNITS OF ROADWAY
Figure
3.4. Model
3. Logic
UNITS OF ROADWAY
for the movement
of vehicles
UNITS OF ROADWAY
through
the simulated
UNITS OF ROADWAY
freeway
system.
Limitations
The simulation model described above was created with the assumption that no entrance ramps, exit ramps, or weaving areas were present in the freeway section being analyzed. Thus, the results are valid only for basic freeway sections. The data is hard coded into the simulation statements. The simulation model is not designed to be interactive with the user since extensive amounts of code would have to be written to make the model interactive. Further experimentation would require modifying the high-level input code.
Lane Control Signing
183
Only one sign layout was modelled. The model is not able to change signs as the traflic changes. This model also assumes the complying motorists are familiar with the system. 4. EVALUATION
OF LANE
CONTROL
SIGNING
4.1. Flow Rate There were three different flow rates modelled in the first models that were tested: heavy, medium, and light traffic flow. In a later refinement, three flow rates between medium and heavy were tested. Since the difference among heavy, medium, and light traffic flow is how many vehicles pass a point over a certain period of time, interarrival time, or headway, must be specilkd to differentiate among heavy, medium, and light traffic flows. 4.2. Percentage
of Driver
Compliance
Since two types of signs exist in the freeway system being studied, percentage of driver compliance was specified in two ways. Compliance with speed limits and compliance with lane merging were modelled in this study. Percent compliance was specified so that each simulation run had the same percent speed limit violators as merge violators. Percentages for speed limit and lane merging compliance were varied from 0% to 100% in 10% increments, although results for only some of these cases are presented in this paper. The percent of compliance with speed limits was varied by changing the standard deviation of the speed. Since the percent merging is controlled by specifying the probability of drivers switching out of the blocked lane at each point in the model where lane changing is allowed, the percent of vehicles merging at each section must be calculated. An equal fraction of vehicles that originally entered the system in the lane containing the blockage is forced to switch lanes upstream of the blockage at each location where there is a lane changing option. 4.3. Incident
Duration
All models were constructed to produce output after 5 minutes of incident duration and every 10 minutes thereafter up to 45 minutes. These incident durations were analyzed to determine the effect of duration on percentage of delay. 4.4. Summary
of Preliminary
Results
Plots for heavy traffic flow could not be generated since the simulation run halted due to an excess of vehicles in the system. Light traffic flow has very little or no vehicle delay, regardless of the level of compliance. Figure 4 shows the results of the simulation runs for medium traffic flow. According to this plot, the delay on the freeway section with the highest delay, was less than 1.2 seconds per vehicle even after 45 minutes of lane blockage. Thii delay value is very low compared to the expected travel time value of 18 seconds per vehicle to drive over one 880 foot section at 33mph, the mean speed for a 30 mph section. 4.5. Flow Rate
Between
Medium
and Heavy
Traffic
Flow
After five minutes of incident duration under heavy flow conditions, the simulation run stops because there are too many vehicles in the system (i.e., a traffic jam). In contrast, under medium flow conditions, the congestion is so low that at 0% compliance, there is very little delay incurred by each vehicle. These findings prompted the investigation of intermediate flow rates between medium and heavy flow to determine the effects of lane control at 70% and 30% driver compliance. The intermediate flow rates used were 1000, 1150, and 1300vphpl.
L. SCHAEFERet al.
Incident Duration 0.6
5 1
0.6
f
0.4
0.2
0
I
om
40%
20%
Pwcerrt
60?6
6096
100%
Compliance
Figure 4. Delay through most congested 880 foot section versus percent of compliance for medium trafllc flow. In esch simulation run, the same percent of drivers complied with speed limit signs as vacate lane signs (i.e., if 30% of the drivers complied with speed limit signs, 30% of the drivers complied with vacate lane signs). Thus, “percent compliance” on the graphs apply to all signs. This graph shows that delay is very low during medium tra& flow for any incident duration, even when 0% of the drivers comply with the lane control signs. 70 60
Incident Duration
3 50 s 40 : ; 30 5 o 20 10 0 900
1000
1100
1200
1300
now EvpWI Figure 5. Delay versus trafllc flow rate for 30% compliance. At 30% compliance and high flow (1550 vphpl), the trafllc system became so congested that the simulation run quit due to more vehicles in the system than the software would allow. Thii graph suggests that &straffic flow becomes higher, congestion causes delay to grow exponentially. 4.6.
Summary
of Results
for Intermediate
TrafIlc Flows
Figures 5 and 6 show intermediate flow rates between heavy and medium flow. Figure 5 shows that for 30% driver compliance, delay is high for a flow rate of 1300vphp1, even after only 5 minutes. Delay is approximately 4 seconds per vehicle at 1150vphp1, which means it takes 20% longer than it normally would to drive on one uncongested freeway section. Delay is less than 2 seconds for 1OOOvphpl.
Lane Control Signing
185
incident Duration
900
1000
1100
1200
--+-
5 min.
-
15 min.
+
25 min.
-X-
35 min.
-
45 min.
1300
Flow (vphpl) Figure 6. Delay versus traffic flow rate for 70% compliance. At 70% compliance and high flow (1550 vphpl), the traffic system became so congested that the simulation run quit due to more vehicles in the system than the software would allow. This graph suggests that as traffic flow becomes higher, congestion causes delay to grow exponentially. However, when comparing Figure 6 to Figure 5, one would conclude that delay grows exponentially with 30% compliance more quickly than with 70% compliance. 70 T
60 Percent Compliance w 70% n
5 min.
15 min.
35 min.
25 min. Incident
II
30%
45 min.
Duration
Figure 7. Delay versus incident duration for flow rate of 1300vphpl. This figure emphasizes the difference in delay between 70% and 30% driver compliance.
Figure 6 shows delay for 70% driver compliance and different flow rates. Delay is still high for 1300vphpl and low for 1000 vphpl. However, delay is less at all flow rates with the higher level of driver compliance [6]. Figure 7 emphasizes the difference in delay between 30% and 70% compliance when the flow rate is 1300vphpl.
5. CONCLUSIONS
AND
RECOMMENDATIONS
The effect of lane control as a traffic control method has not been well researched in the past. This research evaluated the percentage of driver compliance which would be required to consider lane control as a feasible method to alleviate congestion. To this end, a simulation model was developed and tested, and the output analyzed.
L. SCHAEFER et al.
186
The results obtained
for traffic flows of 300, 900, and 1550 vphpl indicate
with lane control has little influence comply with the lane control signing.
that driver compliance
on congestion, regardless of the percentage of drivers that For heavy flow, traffic queues resulting from a lane blockage
are so long that drivers would benefit only if they were advised to exit the freeway upstream incident.
For medium
for congestion
and light flow, the congestion
of the
is not necessary
alleviation.
For an intermediate
flow rate of lOOOvphp1, at 70% and 30% driver compliance,
little delay up to 45 minutes
after the incident.
not to warrant
for congestion
lane control
does not alleviate
congestion
Thus,
alleviation.
signing.
there
At a flow rate of 1150 vphpl, comply
lane control
with lane control
delay even after only 5 minutes
lane control
signing.
of incident
duration.
Thus,
comply
there is high
at this flow rate, congestion congestion.
At the
of incident
is effective when 70% of drivers
For a flow rate of 1300 vphpl at 70% and 30% compliance,
enough that vehicles should be routed off of the freeway to alleviate the policy to determine when to use lane control.
is very
is minor enough
there is very little delay even up to 45 minutes
at a flow rate of 1150 vphpl,
with lane control
Thus, at this flow rate, congestion
when only 30% of drivers
same flow rate, but 70% compliance, duration.
is very low and lane control
Figure
is heavy 8 shows
90 80 8 z ‘z
60 --
8
50 --
=8
40 --
b n
30 --
no lane control necessary
70 --
20 t 10 0 L
I
300
400
500
I
I
I
600
700
600
900
1000 1100 1200 1300 1400
1500
Flow (vphpl) Figure 8. Policy to determine when to use lane control. The white area means lane control is not necessary for the flow rate and percent compliance given. The black area designates the flow rates and percent compliance for which lane control will not alleviate congestion. The grey area shows the flow rates and percent compliance for which lane control will make a difference.
Recommendations
For
Further
Research
Further research should be conducted to predict the actual percentage of drivers in the United States that would comply with lane control. If one had an estimate of how many drivers would comply with the lane control signs, one may better determine whether lane control’would be feasible in the United States. To be better able to compare the potential effectiveness of lane control in the United States to the effectiveness of lane control in The Netherlands, it would be very useful to know the percent of drivers that comply with lane control in The Netherlands. This model could be improved by using a software that is not based on the typical link-node paradigm. Instead, a program that simulates entities as existing over a two-dimensional area should be used based on emergent behavior algorithms originating in the animation industry [7].
Lane Control Signing
187
Currently, there are no software packages available that use emergent behavior to model traffic over a two-dimensional area, however, a preliminary feasibility study has been performed (81.
REFERENCES 1. 2. 3. 4. 5. 6. 7. 8.
G.L. Ullman, Motorist interpretation of MUTCD freeway lane control signals, Zbansportation Research Record 1408, 49-56 (October 1993). A. Pritsker, An Introduction to Simulation and SLAM II, System Publishing, (1984). Transportation Research Board, Highway Capacity Manual, TRB, National Hesearch Council, Washington, DC, (1995). G. Selvia, Evaluation of probability distributions for multilane facilities, Dissertation, University of New Mexico, (December 1990). Directorate general for public works and water management, In Dynamic Z?ufic Management in The Netherlands, Hotterdam, The Netherlands, (March 1992). L.A. Schaefer, Analysis of driver compliance with lane control through the use of computer simulation, Thesis, Arizona State University, (August 1995). C. Reynolds, Flocks, herds, and schools: A distributed behavioral model, Computer Graphics ;SIGGRAPH ‘87 Conference Proceedings) 21 (4), 25-34 (1987). K.L. Sanford, J.A. Wentworth and S. McNeil, Application of artificial life to traffic modeling, AZ ‘95 Fifteenth International Conference, June 27-30, 1995, pp. 431-440.