Sayed et al 1994

Pergamon Accid. Anal. and Prev., Vol. 26, No. 5, 593-607, 1994 pp.

Copyright 0 1994 Elsevier Science Ltd Printed in the USA. All rights reserved

0001-4575/94 $6.00 + .00

0001_4575(94)E0002-3

SIMULATION OF TRAFFIC CONFLICTS AT UNSIGNALIZED INTERSECTIONS WITH TSC-Sim

TAREK SAYED, GERALD BROWN, and FRANCIS NAVIN

University of British Columbia, Vancouver, B.C., Canada V6T 124

(Accepted 27 September 1993)

Abstract-This paper describes a traffic conflicts computer simulation model and graphic display for both T and 4-leg unsignalized intersections. The goal of the model is to study traffic conflicts as critical-event traffic situations and the effect of driver and traffic parameters on the occurrence of conflicts. The analysis extends conventional gap acceptance criteria to describe driver’s behaviour at unsignalized intersections by combining some aspects of gap acceptance criteria and the effect of several parameters including driver’s characteristics such as age, sex, and waiting time. The effect of different traffic parameters such as volume and speed on the number and severity of traffic conflicts is also investigated. The model is unique insofar as it uses a technique of importance sampling and stores the traffic conflicts that occur during the simulation for later study. A graphical animation display is used to show how these conflicts occurred and the values of critical variables at the time. Model results were evaluated against previous work in the literature and validated by using field observations from four unsignalized intersections. The simulation results correlated reasonably well with actual conflict observations and should prove useful for assessing safety performance and feasible solutions for other unsignalized intersections.

Keywords-Traffic conflicts, Simulation models, Unsignalized intersections, Driver behavior

INTRODUCTION

Road traffic analysis is becoming more computation- ally intensive in order to better understand the mechanism of traffic operations and road safety dynamics. One emerging area is the study of extreme events, such as traffic crashes, and the conceptual and mathematical techniques that can be used to study such problems (Navin 1991). Traffic crashes at intersections are pervasive road systems failures, but little is presently known about the failure mechanism. Because of well-recognized measurement and statistical problems with accident records and the site- specific focus (“black spots”) of many accident studies, the observation of traffic conflicts as a road- user behavioural factor has been advocated as a procedure to study the vehicle crash failure mechanism from a somewhat broader perspective than accident statistics alone (Brown 1991). However, in- complete conceptualization and the cost of training observers and collecting traffic conflict data have been factors inhibiting extensive application of the technique, and thus successful simulation of traffic conflicts appears to have practical benefits for traffic studies application as well as providing a more complete understanding of the vehicle crash failure

mechanism, particularly the crash-avoidance behaviour of drivers.

The goal of this paper is to outline a traffic conflict simulation model for unsignalized intersections and to report on tests undertaken to validate the model. Computer simulation is employed to study the problem because of the uncertainty and complex relationships associated with human behaviour and the difficulty of controlling different aspects of that behaviour and the parameters of systems operation by the use of conventional mathematical methods. The model is unique insofar as it uses a technique of importance sampling, that is, the model saves characteristic information for only those conflicts that are predefined to be “significant” events and stores these events as they occur during simulation for later study. A graphical animation display is used to show how the conflict occurred and the value of critical variables at that time.

While there is considerable literature on simulation models for unsignalized intersections, most of these models consider intersection capacity and sim- ulate how traffic volume affects level of service and delay. Only a few authors such as Cooper and Fergu- son (1976) and McDowell et al. (1983) consider simu-

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594 T. SAVED et al

lating traffic conflicts at unsignalized intersections. Models that deal with traffic conflicts at intersections tend to oversimplify the driver’s behaviour; they adopt fixed gap-acceptance criteria to describe how drivers make decisions and they neglect to take into account important aspects such as the effect of the stopped delay on the driver’s behaviour. Conse- quently, the simulation model reported on here is multidimensional, incorporating some aspects of gap acceptance criteria as well as the effect of several other parameters that are, a priori, considered useful to describe that behaviour.

TRAFFIC CONFLICTS SIMULATION

The traffic conflicts concept was first proposed by Perkins and Harris (1967). As an alternative to accident data, which in many cases are scarce, un- available, or unsatisfactory, their objective was to define traffic events or incidences that occur fre- quently, can be clearly observed, and are related to accidents. A traffic conflict was defined as any potential accident situation leading to the occurrence of evasive actions such as braking or swerving. This simple definition has since been refined to incor- porate categories of vehicle manoeuvres and measures of time and space proximity between vehicles at the moment of conflict. An internationally accepted definition of a traffic conflict is given by Amundson and Hyden (1977), “A conflict is an observable situation in which two or more road users approach each other in space and time to such an extent that there is a risk of collision if their movements remain unchanged.” An expanded concept can be found in Brown (1994).

For simulation, a traffic conflict needs to be described and scaled as an unequivocal, observable measure of the systematic variability of risk as perceived by the driver in a given traffic situation. A variety of observation methods have been developed to scale the severity of risk as measured by traffic conflicts. Conventionally, these methods are thought of as subjective methods and objective methods. In the former, one can find terms such as euasive uction or s~~~~~ ~e~uui~ur as part of the definition. These methods include considerable judgement by the observer and are criticised by researchers such as Hauer (1978) and Allen, Shin, and Cooper (1977) because the grading of the severity of the evasive action can vary greatly from one observer to another, particularly if the observers are not well trained. Objective methods incude a cardinal or ordinal time-proximity dimension in the severity scale. Hayward (1972) used the time-to- collision (TTC) measure defined as “the time for

two vehicles to collide if they continue at their pres- ent speed and on the same path.” The value of TTC is infinite if the vehicles are not on a collision course; but if the vehicles are on collision course, the value of TTC is finite and decreases with time. The minimum TTC reached as the vehicles approach on the collision course is taken as the critical conflict severity. Hayward suggested a minimum TTC value of one second as a threshold value. Since Hayward, a number of field and experimental studies using time- based measures indicate a desirable driver safety “space” of 1.5 seconds and a minimum space of 1.0 seconds (van der Horst 1990). A closed-course experiment conducted by van der Horst and Brown (1989) to confirm these values resulted in critical TTC measures of t(,) = 1.6 seconds and t(,inJ = 1.1 seconds. From these results, it was decided to use values of t(,) = 1.5 seconds for the critical event in the simulation process.

THE SIMULATION MODEL

Because there are few applications of traffic conflict studies, there are few data available to develop mathematical safety models; and the lack of conceptual precision of existing models attests to the complexity and stochastic nature of the traffic process. Simulating traffic conflicts assumes that the incidence and severity of traffic conflicts have stochastic event characteristics similar to other critical events of the traffic process such as vehicle arrivals and accidents. The simulation is meant to emulate this traffic process at unsignalized intersections as follows: (i) vehicles with a random set of characteristics are generated on the approaches; (ii) on arriving at the intersection from a subject approach, an acceptance criterion is determined based on a priori, realistic assumptions; (iii) a “consistent” behaviour model assumes a minimum gap that is acceptable to each driver at all times with variation across drivers based on the type of traffic control, approach speed, driver age and sex, and stopped delay. A traffic conflict is recorded by the simulation when a driver accepts a gap, that, given the closing speed of the conflicting vehicles, puts him/her at risk of collision with the other vehicle.

Structure, ussumptions, and input parameters The model is built using a microcomputer ver-

sion of the discrete event simulation language, Gen- eral Purpose Simulation System, or GPSSlH (Wol- verine Software Corporation, Annandale, VA, USA), a specialized language. The basic elements of GPSSlH models are blocks and transactions in which transactions are dynamic entities (such as

Simufation of traffic conflicts 595

road vehicles) that move from one block to another. Blocks are actions (e.g. GENERATE, ADVANCE, QUEUE, LEAVE) that affect the transactions and other system entities, such as statistical, computational, and resource entities. A full description is found in Schriber (1974). The model also has some features not normally part of GPSS/H and therefore has been labelled “TSC-Sim,” for Traffic Systems Conflict Simulation.

The model is microscopic since it deals with individual vehicles as they approach, go through, and depart the intersection. Actions for vehicles in the model include vehicle generation, approach to the intersection, choosing a gap (lag), and proceed- ing to depart. The assumptions of the model TSC- Sim are as follows: (i) there is no overtaking or lane changing allowed at the intersection, (ii) the subject intersection is isolated, (iii) all drivers have an unob- structed view of the intersection, (iv) there is no pedestrian inte~erence, (v) all drivers must maintain at least a minimum headway between their vehicle and the vehicle in front, (vi) all drivers looking for an acceptable gap have perfect knowledge about the movement of vehicles having higher priority and fully understand the rules of the road. A gap is defined at the time headway between two successive vehicles in the major road traffic stream. A lag is defined as the time remaining between an approaching vehicle on the major road and a vehicle entering the major road from a minor road.

The important input parameters to the model include (i) traffic volumes of all traffic streams, (ii> percentage of heavy vehicle traffic to the total traffic volume, (iii) type of intersection control (yield or stop), (iv) speed limit on the major road, (v) percentage of each driver type in the driver population, (vi) number of lanes for both major and minor roads, and (vii) total default simulation time.

Several other input parameters such as move- up time, minimum allowable headway, turning speed of vehicles, and maximum queue lengths are given as constants to the model. However, it is possible to change the values of these parameters between simulation runs.

Vehicle movemenf si~~lat~~~ A shifted negative exponential distribution is

used to generate vehicle headway (t) from the average headway (i) calculated from the traffic volume. The functional form of this distribution is

P(h < t) = 1 - ,-Kt-c)i(i-c)l

for t 2 c (an exogenous fixed time interval) and where 5 = l/h, and X = vehicle arrival rate. A value

of c = 1.5 seconds is used as a minimum allowable headway between vehicles in the same lane. If the generated headway is less than the minimum allowable headway, it is set to the minimum. In this case, the vehicle is considered a member of a platoon. The model uses a random number generator and a shifted exponential function to produce the required headway. Va~ability in the random number generator may generate a vehicle flow rate different from that required. This problem is solved by calculating the llow rate generated by the mode1 every four minutes. The difference between this flow rate and the required one is calculated and then used to adjust the average headway used in the GENERATE block of the model.

After vehicles are generated, a lane-selection process is used to ensure that vehicles will reach their desired destination. When a lane is selected, vehicles proceed and try to enter the intersection. The minor road consists of two sections: the approach section and the decelerating and/or queuing section. At the approach section vehicles have lower speeds than the desired speed, as they are preparing to negotiate the intersection. The queuing section is the location in which vehicles decelerate and in some cases have to stop according to the number of vehicles in the queue and the type of intersection control. Vehicles on the major road are either free movers or a platoon member. Free-moving vehicles can, under certain conditions, achieve their desired speed, which is controlled by the speed limit. The speed of all platoon members is set by the platoon leader.

Major road vehicles are assumed to be unaf- fected by minor road vehicles, so they can proceed and enter the intersection directly without any speed change. In some situations vehicles on the major road have to decelerate or stop as other major road vehicles in the same lane attempt to turn into the minor road.

Minor road vehicles have to find a suitable gap (lag) to join or cross the major road. If the intersection is Stop-controiIed, vehicles have to come to a complete stop before looking for a suitable gap (lag). In the case of a Yield-controlled intersection, minor road vehicles may proceed and enter the intersection direction if they can find a suitable gap (lag). The minor road driver decision as to whether the gap (lag) is suitable or not depends on its size compared with his or her critical gap.

Factors affecting driver’s critical gap value The type ofintersection control is important for

the drivers’ decision. At Stop-controlled intersections, drivers usually start from a stop condition,

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Table 1. Mean and standard deviation of the gap acceptance

Yield control Stop control

Mean Std. dev. Mean Std. dev. Group (seconds) (seconds) (seconds) (seconds)

Young males 4.0 0.75 5.0 0.7s Old males 4.5 0.85 5.5 0.85 Young females 5.5 1.00 6.5 1.00 Old females 6.0 1.25 7.0 1.25

while at Yield-controlled intersections some vehicles start from a low speed. It will obviously take the drivers starting from a stop condition longer to complete a manoeuvre. This leads to drivers to accept shorter gaps (lags) at Yield-controlled intersections than those accepted at intersections controlled by a stop sign.

Driver characteristics such as age and sex have been found to have a significant effect on gap-acceptance behaviour. The data reviewed by Cooper f 1976) indicated that younger drivers generally accepted shorter gaps and are more consistent in their driving behaviour than older drivers. Cooper also found that female drivers are often more cautious than male drivers in most traffic situations. Darzen- tas, McDowell, and Cooper (1980) analyzed unpub- lished data by Transport and Road Research Labora- tory on crossing times of different drivers. The data indicate that young male drivers have the shortest crossing times. Both young male and female drivers have much smaller standard deviations than old drivers of the same sex. Darzentas et al. (1980) also found that female drivers were involved in fewer conflict situations than male drivers. Wennell and Cooper (1981) studied the gap acceptance behaviour of men and women drivers at four unsignalized intersections. They found that the median accepted gap for women drivers is longer than that for male drivers in all situations.

The model considers four types of drivers: young males, young females, old males, and old females. The model uses a truncated normal distribution gap acceptance function, Based on the work by Darzentas et al. (1980) and Polus (1983). the gap acceptance values in Table 1 were chosen for the mean and standard deviation for each group. The model allows these values to be changed, with the higher mean gap-acceptance value designating the more cautious driver group. The higher the standard deviation of the gap acceptance value, the less consistent the driver group. The value of the mean and standard deviation of the gap acceptance is considered to be the same for both merging and single-lane crossing manoeuvres.

number of tunes being crussed in the manoeuvre affects the critical value for drivers. Based on the gap acceptance values provided by the Highway Capacity Manual (National Research Council 1985), a correction factor of 0.25 second is added to the critical gap value for each extra lane being crossed.

Heavy vehicles require critical gaps that are about 30% larger than those for cars, because they accelerate and decelerate at slower rates.

The value of the stopped delay significantly modifies a driver’s gap acceptance behaviour. Driv- ers are usually more relaxed and less sensitive to gaps when they experience minimal delay, while they are more alert and more sensitive to gaps when they suffer greater delay. Wagner (1965) introduced the term pressure of trafjc demand, which refers to the pressure that the driver is exposed to after suffering delay. He found that pressure of traffic demand had a very significant effect on driver behaviour. Ashworth and Bottom (1977) divided the gaps presented to drivers into two categories: those gaps presented to drivers who had been waiting at the head of the queue for less than 8 seconds, and those presented to drivers who had been waiting at the head of the queue for more than 8 seconds. He found that the proportion of gaps accepted increased with increased waiting time. Another study by Adebisi and Sama (1989), concluded that drivers showed significant changes in their gap acceptance behaviour when their stopped delay time exceeded the range of 25-30 seconds, and they began to accept shorter than normal gaps.

Based on information from those authors and on the function suggested by Tudge (1988) the following stopped delay modification factor is used to alter the driver critical gap value:

DL @‘=Q,,+DLtC

where

on = DL =

QD = C=

stopped delay modification factor the delay value after which driver behaviour begins to change (seconds). the stopped delay value (seconds) constant value (seconds)

Tudge (1988) used a value of 8 seconds for the delay value after which drivers begin to accept shorter than normal gaps based on information reported by Ashworth (1977). However, Ashworth considered only the time drivers wait as head of queue and not the stopped delay. The values of DL

Simulation of traffic conflicts 597

and C were chosen as 27 and 0.5 seconds, respec- tively. These values were selected after examining the data provided by Adebisi and Sama (1989).

The gap acceptance process This process takes place when a vehicle has

to cross or merge with other traffic streams where different traffic streams have different priority levels according to the rules of the road. Generally, major road vehicles have a higher priority than minor road vehicles, and straight-ahead major road vehicles have a higher priority than major road vehicles turning left or right. Each vehicle is assigned a primary critical gap value by testing the gap acceptance function according to the driver type and the intersection type of control. The primary critical gap value is modified according to the vehicle type and the number of lanes to be crossed. Vehicles trying to cross or merge wait for a gap in the conflicting traffic stream (streams) greater than or equal to their critical gap. The critical gap value is obtained by multi- plying the primary critical gap with the delay modification factor 0,. The delay modification factor has an initial value of 1.5 when the vehicle faces no delay, and this value decreases as the vehicle’s stopped delay increases with a minimum theoretical value of 0.5 when the vehicle faces infinite delay. The model assumes that no driver will accept a gap that he/she thinks will certainly lead to a collision. Therefore, a minimum acceptable gap (Gcmin) is used, with a value of 2.0 seconds as a minimum allowable critical gap, based on data provided by Wennell and Cooper (1981). If the critical gap value is less than the minimum acceptable gap, it is set to the minimum.

Vehicle drivers who decide to enter the intersection are assigned a single lane manoeuvre time. This time is sampled from a truncated normal distribution function. The mean and standard deviation of the function depend on the driver type (Darzentas et al. 1980). The sampled manoeuvre time is then corrected according to the number of lanes to be crossed and the vehicle type.

Conflict resolution A conflict occurs when a driver decides to exe-

cute a manoeuvre that puts him/her at risk of collision with another vehicle. Conflicts in the simulation model are classified into three conflict types and two location groups: conflicts within the intersection that result from conflicting vehicles entering the intersection at close interval times and that can mainly be divided into crossing and merging conflicts, and rear-end conflicts that result when conflicting vehicles leave the intersection through the same lane at

close time intervals. Location of the conflict is taken to be where the vehicles originated. The model uses the time to collision (TTC) as a severity measure for traffic conflicts; the smaller the TTC value the more severe the conflict. The model first estimates whether or not the vehicles are on a collision course. If the vehicles are on a collision course, the TTC value is calculated and compared with the threshold value of 1.5 seconds. If the TTC is less than or equal to the threshold value, the model records the conflict, its type, location, and the TTC value. Con- flicts with TTC value less than 1 second are usually considered to be serious conflicts, with nonzero probability of signalling a crash.

Model output The output statistics of the model are included

in the file OUTPUT.LIS, which is produced with each simulation run. These include: (i) the inputed and generated traffic volumes for each direction, (ii) the average vehicle delay for each queue along with the average and maximum queue contents, and (iii) the information obtained from importance sampling, which comprises the total number of conflicts, conflict locations and type, and the TTC values.

MODEL GRAPHICS

The visualization of the simulation at extreme events is an important aspect of this model. Its objective is to show how the model is behaving during traffic conflicts so characteristic behaviour, if any, can be observed. This provides understanding of critical situations and the parameters affecting their occurrence without the necessity of viewing many average events. The general-purpose system animation software PROOF (Wolverine Software Corpo- ration, Annandale, VA, USA) is used to provide the graphical representation of the simulation events.

Two files are needed to run a PROOF animation. The first is the animation trace file which contains the sequence of timing information and other commands that make the animation happen. The second is the layout file that has all the background text and graphics for an animation. The animation trace file is generally written directly by an executing model or program designed to generate syntactically correct PROOF commands. The layout file is cre- ated either by the graphical tool provided by PROOF (as the case of the current model) or other programs, such as CAD programs.

Two animation files are produced during the simulation run. The first is the animation trace file (*.ATF) that has the animation commands for the whole simulation time. The second is the presenta-

598 T. SAVED et al.

tion file (*.PSF), which contains the commands for the animation at the time at which traffic conflicts occur. In the presentation file conflicts are viewed one at a time. The animation lasts one minute for each conflict, 30 seconds before the conflict and 30 seconds after the event. The user may go forward or go back through these conflicts using the “+I’ and “-I’ keys. The information shown with each conflict included driver, vehicle and conflict types, the primary and driver-critical gaps, the stopped delay value, and the time to collision value. This information is used to develop typical profiles of conflict events.

MODEL VALIDATION

Any computer simulation model has to show that it (i) is logically correct and (ii) adequately repre- sents the modeled system in the validation process of “assessing the extent to which a test or instrument measures what it purports to measure” (Grayson and Hakkert 1987). Two levels were used for validation: face validity, or whether the model seems to behave correctly; and external validity, which tested the “fit” between the model results and field observations of similar systems.

Face validity was tested by observing TSC-Sim animation. Animation allows observation of the behaviour of individual vehicles at an intersection to decide if the vehicle’s behaviour is logically reason- able. Also, different model variables are displayed during the animation, and these show the internal interaction between different model entities. Re- searchers such as McCormick, De Fanti, and Brown (1987) indicated that the visualization process plays a very important part in model validation. Face validity provides trust in the model and provides some assurance that the model is logically correct.

External validity was tested by comparing traffic conflicts observed at four unsignalized intersections with traffic conflicts predicted by the simulation model for these intersections for the same period of time. The validation data base came from consultants’ studies of traffic confhcts at several intersections in the Greater Vancouver, Canada, area (Hamilton Associates, 1991). Although several more intersection studies were reviewed, the majority of the unsignalized intersections covered by the conflict studies were complex layouts, beyond the simple T and four-way intersections selected for this analysis. All selected intersections were 4-leg intersections with negligible grades, good visibility, and a simple layout.

intersection geometry and traffic control The first intersection, 156th Street and 20th Av-

enue in Vancouver, has four one-lane approaches that intersect at approximately right angles. All four approaches permit left-turn, through, and right-turn movements. The eastbound and westbound approaches on 20th Avenue are controlled by Stop signs. Crossing-sight distances and stopping-sight distances for all traffic movements are adequate. The peak hour traffic volume on 156th Street is about f50 vehicles per hour (vph) and on 20th Avenue is about 80 vph.

The second intersection, Holdom Avenue and Broadway in Burnaby, has four approaches with the two roadways intersecting at approximately 80 degrees. The northbound approach leg has two lanes for left-turn, through, and right-turn movements, and the northbound exit leg, a single lane. The southbound approach leg has a single lane for left-turn, through, and right-turn movements, while the exit leg is two lanes. The eastbound and westbound approach traffic movements on Broadway are controlled by Stop signs. In addition to the Stop signs on Broadway, southbound left-turn movements on Holdom Avenue are restricted between 7:00 AM and 9:00 AM, Monday through Friday. The peak hour traffic volume on Holdom Avenue is about 500 vph and on Broadway, is about 300 vph.

The third intersection, 116th Street and 75A Avenue in Delta, consists of four one-lane approaches that intersect at approximately right angles. Each of the four approaches provides left- turn, through, and right-turn movements. The eastbound and westbound approaches on the 75A Ave- nue are controlled by Stop signs. Both crossing- and stopping-sight distances are adequate. The peak- hour traffic volume on 116th Street is about 460 vph and on 20th Avenue is about 110 vph.

The fourth intersection, Chesterfield Avenue and Keith Road in North Vancouver, consists of four one-lane approaches that intersect at approximately right angles. All movements are permitted on all approaches. The eastbound and westbound approaches on Keith Road are controlled by Stop signs. The crossing- and stopping-sight distances are adequate. The peak hour traffic volume on Chester- field Avenue is about 360 vph and on Keith Road is about 140 vph.

Conflict observation method Traffic conflicts were recorded at the study in-

tersections by trained observers. The observation and recording method is an on-site, online record of the incidence and severity of traffic conflicts. Obser- vations were made for two days at each intersection.


Table 2. Time-to-collision and risk-of-collision scores

TTC and ROC Time to collision scores (TTC)

I 1.6-2.0 seconds 2 I .O- I 5 seconds 3 0.0-0.9 seconds

Source: Brown, G. R. (1991).

Risk of collision (ROC)

Low risk Moderate risk High risk

Two observers were used each day for an eight-hour observation period, giving a total of 32 man-hours at each intersection. The severity of traffic conflicts is determined by the sum of two scores: the TTC score and the risk-of-collision or ROC score. The ROC score is a subjective measure of the risk of collision and is dependent on the perceived control that the driver has over the conflict situation. The TTC and ROC scales were given equal weighting and combined into a 5-point Likert-type scale. The summation of the TTC and ROC scores gives the overall severity score, which ranges between 2 and 6. An overall severity score of 2 signifies a low- risk conflict situation and a score of 6 is a high- risk conflict situation (Table 2). The midpoint of the composite scale registers the critical event, corre- sponding to a TTC of 1.5 seconds or less with a “moderate” ROC.

Reliability tests of the observation method gave 77% accuracy with 95% confidence, with a high of 85% accuracy for assessing the correct TTC. In addition, in a study of 13 intersections to test the validity of a TTC = 1.5 seconds or less for a measure of safety as defined by the number of accidents, it was found that at 8 of I1 intersections conflicts are significantly correlated with accidents at 95% confidence with R2 Z- .64 with three intersections having R2 z .81 (Brown 1994).

Comparing results A comparison between the observed conflicts

and the simulated conflicts was carried out. The model was modified to allow for the traffic volume changes through the morning, noon, and afternoon periods. There was further modification to allow the inclusion of the restricted southbound, left-turn movement between 7:00 AM and 9:00 AM hours at the Holdom Avenue and Broadway intersection. The simulated conflicts were averaged over a large number of runs.

Since the simulation model considers only conflicts with TTC values less than or equal to 1.5 seconds, observed conflicts with TTC values greater than 1.5 seconds were excluded from the validation test data. At first the computational speed limit was

set at 50 km/h, which is the legal posted speed limit at the four intersections. The comparisons of observed and estimated conflicts for both intersections are given in Tables 3 through 6.

In the case of the 156th Street and 20th Avenue intersection (Table 3), the model predicted five conflicts compared to eight observed conflicts with a similar distribution of the types of conflicts over the different locations within the intersection. It was observed in the field that typical vehicles’ speeds exceeded the legal 50 km/hr limit along 156th Street, and this was suspected to be a factor contributing to the difference between number of conflicts and those predicted by the model. Increasing the speed limit in the model to 70 km/h caused the model to increase the total number of conflicts to 10 conflicts with a distribution of predicted conflicts very close to that of observed conflicts.

The Holdom Avenue and Broadway intersection model predicted 17 conflicts compared to 19 observed. Increasing the speed by 10 km/h to 60 km/hr produced 21 conflicts. In both cases the predicted conflicts distribution was close to the observed conflicts distribution (Table 4).

In the 116th Street and 75A Avenue intersection, six conflicts were predicted compared to 10 observed with the speed limit set at 50 km/h. Raising the speed limit to 60 km/h resulted in eight predicted conflicts with approximately identical conflicts distribution except for the left-turn crossing conflicts (Table 5).

The Chesterfield Avenue and Keith Road intersection conflict study team observed 15 conflicts. The study also indicated that the major road vehicle speed largely exceed the 50 km/h speed limit. The model predicted nine conflicts out of the 15 observed at 50 km/h speed limit and 12 conflicts at 70 km/h speed limit. Although there is some difference in

Table 3. Observed and predicted conflicts distribution, 156th Street and 20th Avenue intersection

Predicted Predicted Conflict name and Observed conflicts conflicts description conflicts 50 kmihr 70 km/hr

156th Street northbound, 4 2 4 rear-end conflicts

156th Street southbound, 1 1 1 crossing conflicts

156th Street northbound, 2 1 2 left-turn crossing conflicts

156th Street southbound, 1 0 I rear-end conflicts

156th Street northbound, 0 I 2 crossing conflicts

Total 8 5 10

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Table ‘4. Observed and predicted conflicts distribution, Holdom Avenue and Broadway intersection

Conflict name and description Observed conflicts

Predicted Predicted conflicts- conflicts- 50 km/hr 60 km/hr

Left turn crossing conflicts involving westbound left turning motorists and southbound through motorists.

10 I 9

Left turn opposing conflicts involving eastbound through motorists and westbound left turning motorists.

Crossing conflicts involving eastbound through motorists and northbound or southbound through motorists.

1 2 3

2 3 3

Crossing conflicts involving eastbound through motorists and northbound or southbound through motorists.

Right turn (merging) conflicts involving westbound right turning motorists and northbound through motorists.

Rear-end conflicts involving southbound through motorists.

1 2

19 17 21

Left turn opposing conflicts involving southbound through motorists and northbound left turning motorists.

Total

Table 5. Observed and predicted conflicts distribution, 116th Street and 75A Avenue intersection

Conflict name and description Observed conflicts

Predicted Predicted conflicts conflicts 50 kmlhr 60 km/hr

Left turn crossing conflicts involving through northbound vehicles on 116th Street and left turning vehicles on 7SA Avenue.

3 2 2

Left turn crossing conflicts involving through southbound vehicles on 116th Street and left turning vehicles on 75A Avenue.

2 1 1

Rear-end conflicts involving through northbound vehicles on 116th Street.

2 1 2

Right turn conflicts involving westbound right turning vehicles from 7SA Avenue and through northbound traffic on 116th Street.

Rear-end conflicts involving through southbound vehicles on 116th Street

Left turn opposing conflicts involving through southbound vehicles and northbound left turning vehicles on 116th Street.

Total IO 6 8


Table 6. Observed and predicted conflicts distribution, Chesterfield Avenue and Keith Road intersection

Conflict name and description

Crossing conflicts involving northbound through vehicles on Chesterfield Ave- nue and eastbound through vehicles on Keith Road.

Observed conflicts

8

Predicted Predicted conflicts conflicts 50 km/hr 70 km/hr

4 6

Crossing conflicts involving southbound through vehicles on Chesterfield Ave- nue and westbound through vehicles on Keith Road.

4 3 3

Crossing conflicts involving southbound through vehicles on Chesterfield Ave- nue and eastbound through vehicles on Keith Road.

1 1 1

Rear-end confiicts involving southbound through vehicles on Chester- field Avenue.

1 0 1

Left turn crossing conflicts involving southbound vehicles on Chesterfield Avenue and left turning vehicles on Keith Road.

1 1 1

Total 15 9 12

the total number of conflicts between predicted and observed conflicts, the distribution of predicted conflicts is very close to the observed conflicts espe- cially for the 70 km/h speed limit (Table 6).

A comparison, while limited to a small number of intersections, shows that the model results compare very well with the observed field data, espe- cially the internal distributions of predicted and observed conflicts. The comparison implies a reasonably successful external validation process, which leads to the conclusion that the model can be used in similar situations with some degree of confidence. Further validation is necessary, if the model is applied to other types of intersections, but for this model structure and conflicts definition, the results are encouraging.

Ferguson (1976) state that the number of conflicts occurring at a certain location is proportional to the product of conflicting volumes. The same result was recorded by Hodge and Richardson (1978). Spicer, Wheeler, and Older (1979) indicated that at relatively low traffic volumes, the total number of observed conflicts is proportional to the square root of the product of the conflicting volumes. Darzentas et al. (1980) propose that conflicts linearly increase as a function of the traffic volume. None of the above researchers considered intersections with high traffic volumes.

DISCUSSION

Since traffic conflicts offer a potentially rich source of behavioural information, the possibility of successful traffic-conflicts simulation opens up areas of practical research into the manner in which different road users interact with various traffic situations. Some research implications, using TSC-Sim, are given below.

Volume and conflicts

Figures 1 and 2 are examples of the relationship between traffic volume and the simulated conflict rate obtained from the model. These figures indicate that over a wide range of traffic volumes, including congested conditions, an exponential function seems to give a good fit. However, if only low traffic volumes are considered (volumes less than the warrants for a traffic signal), conflicts may appear to be proportional to the square root of the conflicting volumes as suggested by Spicer et al. (1979). The large increase in simulated conflicts at high traffic volumes is probably the result of allowing drivers in the model to accept shorter gaps as their delay time increases. However, usually unsignalized intersections operate at lower volumes, reducing this effect.

Several researchers suggest that traffic volume The curves representing conflicts for Yield- and flow has a significant effect on conflicts. Cooper and Stop-controlled intersections (Figures 1 and 2) were

T. SAVED et al.

Fig. f. Relationship between traffic volume and conflicts for 8 T-intersection.

very close at low traffic volumes and the difference Speed and conjicls between them increases rapidly as traffic volume Early research by Cooper, Starr, and Wennell increases. This outcome tends to confirm the engi- (1977) indicates that risk of an accident increases as neering practice of setting a volume warrant that the approach speed of major road vehicles increases, limits the volume after which Yield signs should not which would suggest that traffic conflicts also in- be used to control unsignalized intersections. crease under the same speed conditions. Darzentas

100 150 200 250 300 350 Volume (VEHIHR)

~ I__- ql - kq k- 0.3

Approroh rpood 40 km/hr 1 tan@ for bath m@or and minor road*

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Fig. 2. Relationship between traffic vofume and conflicts for a it-leg intersection.


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=40 45 50 55 60 65 70 Speed (Km/hr)

q1 - kq k-O.3 2 Ianw approach for both major and minor rods

nti wntr~ikd I-

Fig. 3. Relation between approaching speed and conflicts at a Stop-controlled 4-leg intersection.

et al. (1980) suggests a rapid increase of traffic con- model is shown in Figures 3 and 4. The figures indi- flicts rate (at a fixed flow) as the mean speed on the cate an increase in the number of conflicts as the major road increases. mean approach speed increases for a fixed volume,

The relationship between the mean approach with the increase proportional to the traffic volume. speed and number of conflicts from the current A slight increase was obtained at low traffic volume

60

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SDeed /Km/hr) ql = kq k=O.3 No turning vohklr

1 lane approach for both major and minor road8 Stop controlled intemaction

Fig. 4. Relation between approach speed and conflicts at a Stop-controlled 4-leg intersection

604 T. SAVED et al.

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Fig. 5. Relation betw-een approaching speed and severe conflicts for a Yield-controlled T-intersection.

and a significant increase at high traffic volumes. There was no significant effect of the intersection type of traffic control (Yield, Stop) on the value of this increase.

The number ofconflicts estimated by the model increased as the dispersion of speeds on the main road increased. This agrees with the published research that indicates a driver’s error of judgement associated with vehicles having speeds different from the mean speed (Brian 1962; Cooper et al. 1976). These results suggest that a decrease in major road vehicles speeds and the dispersion of these speeds can result in adecreasing number of conflicts. A decrease may be achieved by police activity at the intersection as reported by Cooper and McDowell (1977).

The overall severity of traffic conflicts repre- sented by the average time-to-collision (TTC) value increased as the mean approach speed of the major road vehicles increased in the model (see Figures 5 and 6). The same results were reported by Cooper et al. (1976, 1977) and Darzentas et al. (1980). This indicates that the percentage of injury accidents at unsignalized intersections may increase as the major road mean speed increases.

The overall severity of conflicts was higher in the case of Yield-controlled intersections than Stop- controlled intersections. This may result because of

the tendency of drivers to accept shorter gaps at Yield-controlled intersections. This increased conflict severity may put a constraint on using Yield signs to control intersections with relatively high major road speeds, even though other warrants for using a Yield sign such as traffic volume and sight distance are satisfied.

The number of severe conflicts approximately increased exponentially with speed (Fig. 7) compared with a linear increase in the case of all conflicts. This signifies that there is an effect of speed on severe conflicts and agrees with research into accidents in which a nonlinear relationship between speed and severe accidents is found.

Conflicts and driver type The values for the mean and standard deviation

of the gap acceptance function and manoeuvre time for different driver types were chosen based on the data provided by Cooper (1976), Darzentas et al. (1980), and Polus (1983). The model results agreed with their findings, which indicated that female drivers are generally less involved in conflict situations than male drivers and that older drivers are less consistent in their driving behaviour. This contri- butes to the face validity of the model and indicates that these variables give a good description of driver behaviour, at least as replicated by the model. The model can perhaps be useful in investigating the effect of changing these variable values. For exam-

Simulation of traffic con!? icts 605

1.25

Speed WM/HRl

ql -4 k=O.S 2 kwia~ appwch for both major and minor roadr

yield controll8d Intersection I

Fig. 6. Effect of approaching speed on conflicts severity for a Stop-controlled T-intersection

ple, the number of conflicts predicted by the model can be reduced by increasing the median acceptance gap (i.e. make drivers more cautious). This would follow research by Cooper and McDowell (1977) which indicated that police activity near an intersection makes drivers turning from a minor road more cautious and consequently decreases the number of conflicts.

CONCLUSIONS AND FURTHER RESEARCH

This paper describes a microscopic traffic conflicts simulation model, TSC-Sim, for both T- and 4-leg intersections using the commercially available GPSS/H. The model considers different aspects of driver behaviour and several other parameters on a driver’s entry or crossing decision at unsignalized intersections. The model employs importance sampling to save characteristic information for only those conflicts that are predefmed to be “significant” events. Graphics is a very important part of the model as it shows how the model behaves at extreme values: that is, during traffic conflicts, and gives a clearer understanding of these critical situations and the parameters affecting their occurrence. The validation process showed that the model results correlate reasonably well with the field observations from the area of Vancouver, British Columbia.

In practice, observing traffic conflicts is expen- sive, since it requires trained people. An alternative to direct observation is to utilize the results provided by a simulation model, such as a first estimate of driver behaviour, to better understand the traffic process in incipient crash conditions. This model offers a way of estimating traffic conflicts and can also provide an in-depth study of conflicts as critical traffic events, The resuhs of the simulation may eventually reduce the cost for direct observation of all except the most complex intersections.

The model is intended to be used to meet two traffic analysis objectives. The first is to assess the safety and performance of unsignalized intersections. The safety measure may be expressed by the number and the location of conflicts predicted by the model, while the performance can be expressed by the intersection level of service as a function of the average delay to minor road vehicles. The second use of the model is as a tool for investigating how to reduce driver risk. Several researchers emphasize the value of behavioural studies and driver education in reducing road user risk and the model may be a useful tool in identifying the parameters for these kind of studies.

The research attempts to contribute to road safety studies in two ways. The measure used in the research to delineate the conflict has been quantified as a time proximity value, allowing road safety to be studied in the context ofgap acceptance research;

606 T. SAVED eta1

40

n I,

. Confllot looatlonr e

q-yTf=F

“40 45 50 55 60 Speed (Km/hr)

ql - kq k-0.3 2 bnes approach for both major and minor roada

Weld controlled interwction

65 70

Fig. 7. Effect of approaching speed on conflicts severity for a Yield-controlled intersection.

and the resultant stimulation model using this measure appears to replicate, with an acceptable degree of accuracy, field observations of traffic conflict behaviour using time proximity to collision. However, the study has pointed to several areas of further research. First, the severity definition used is specific to the field procedure, and this constrains the wider evaluation of the model, particularly the relationship among conflicts, flow volume, and speed. A larger inventory of conflict studies, using the time proximity definition, is needed to further investigate these relationships. Secondly, more research is needed to confirm the conceptual linkage of traffic conflicts to safety and risk. The model simulates conflicts (as defined here) and cannot be evaluated against accident statistics nor other measures of road user risk. The authors are reasonably confident that the time proximity definition of traffic conflict will prove to be a measure of driver risk, but to date, this contention is still tentative.

Lastly, simulation has been suggested as a useful tool for the study of road safety, but there is no attempt to compare simulation with analytical or statistical methods. Until the road safety problem can be described unambiguously, and the complex relationship between driver behaviour and roadway and traffic parameters delineating driver risk is known, perhaps computer simulation will prove useful.

Acknowledgements-The financial support for this study comes from F. Navin’s Natural Science and Engineering Research Council of Canada Operating Grant. P. deLeur provided details of the study reports used in the research. Hamilton Associates kindly supplied their study reports for selection and analysis.

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