Number of Vehicle in Dill Emma Zone Ate Og

NUMBER OF VEHICLES IN THE DILEMMA ZONE AS A POTENTIAL MEASUREOF INTERSECTION SAFETY AT HIGH-SPEED SIGNALIZED INTERSECTIONS

by

Karl ZimmermanAssistant Research Scientist

Phone: (979) 458-2835Fax: (979) 845-6254

E-mail: [email protected]

James A. BonnesonAssociate Research Engineer

Texas Transportation InstituteTexas A&M University

3135 TAMUCollege Station, TX 77843-3135

Paper prepared for the 83rd Annual Meeting of theTransportation Research Board

Washington, D.C.,January 2004

July 2003

Word count:Abstract: 196Body: 5292Figures: 7 x 250 = 1750Tables: 1 x 250 = 250Total: 7488

TRB 2004 Annual Meeting CD-ROM Paper revised from original submittal.

Zimmerman and Bonneson 2

ABSTRACT

High-speed signalized intersections may have both safety and operational problems. The safetyproblems have traditionally been solved using dilemma zone protection of some form or another. However, dilemma zone protection tends to be associated with an increasing chance of runningthe phase to its maximum allowable duration (i.e., max-out). At max-out, any dilemma zoneprotection that has been provided ceases, and any number of vehicles may be in the dilemmazone, thus creating the safety problem the system was meant to prevent.

Most methods of assessing the safety of intersections do not include an assessment ofsignal operations. Reducing the number of vehicles in the dilemma zone for an intersectionapproach should reduce the number of drivers that do not receive dilemma zone protection,thereby reducing the probability of crashes for those approaches. This paper presents atheoretical method for calculating the number of vehicles in the dilemma zone at the end ofgreen, which can then be used to compare real-world and theoretical performance of differentdetection systems. An illustrative example is provided to show one such comparison. Also, afield data collection method is provided for the assessment of a signal system in operation.



INTRODUCTION

Crashes at high-speed signalized intersections can be a particular problem for traffic engineers. High-speed approaches also create problems for drivers, who must decide whether to proceed orstop when the phase changes from green to yellow based on very limited information. Differences in perception of the situation by drivers tend to create variation among driverdecisions. The greatest variation occurs in the dilemma zone, defined as the area on a high-speedapproach within which 10 percent of drivers stop (typically 2-3 s from the stop line) and 90percent of drivers stop (typically 5-6 s from the stop line) when presented with yellow (1, 2). Bydefinition, the dilemma zone can only occur at the end of green, and both right angle and rear-endcollisions have been associated with the dilemma zone (1, 2, 3, 4). Therefore, the number ofvehicles in the dilemma zone has been directly related to the safety of an intersection.

Recently, there has been an interest in modeling intersection safety using traffic micro-simulation software. Gettman and Head (5) investigated potential safety surrogates for micro-simulation software, including conflicts and red-light-running. These safety surrogates may bevery difficult to build into a traffic simulation because of the large number of variables thatinfluence them. A relatively simple-to-collect safety surrogate would be ideal for use withmicro-simulation.

Because crashes at high-speed signalized intersections have been associated withdilemma zone problems, it seems natural for a safety surrogate to relate to the dilemma zone.This paper proposes using the number of vehicles in the dilemma zone at the end of green as asurrogate safety measure for high-speed intersections and provides a theoretical method forcalculating the expected number of vehicles in the dilemma zone per cycle. It also provides asimple field data collection technique so that the number of vehicles in the dilemma zone can becollected for an operating signal. The same field collection technique can also be extended tomicro-simulation software.

BACKGROUND

Dilemma zone protection has long been used on high-speed approaches to minimize the risk ofcollisions to high-speed traffic. This section briefly describes some of these systems and themeasure of effectiveness associated with them.

Conventional Dilemma Zone Protection Designs

For a high-speed intersection, detection is typically placed upstream of the intersection fordilemma zone protection. This conventional type of dilemma zone protection system isfrequently used in the United States, although the detector layout may vary considerably fromlocation to location. A conventional dilemma zone protection system will gap out (i.e., end thegreen phase because no vehicles are extending the phase) if a headway occurs that is greater thana certain maximum amount for all approach lanes. Bonneson and McCoy (6) defined themaximum allowable headway (MAH) that will allow a detection system to gap out as:



(1)

whereMAH = maximum allowable headway of the detection design for the approach (s),

MAHa = maximum allowable headway of the dilemma zone protection system (s),MAHs = maximum allowable headway of the stop line detectors (s),

PT = passage time setting in the controller (s),CEn = call-extension setting for detectors in the dilemma zone protection system (s),

D1 = distance from the stop line to the leading edge of the dilemma zone detectorfurthest from the stop line (ft),

Dn = distance from the stop line to the leading edge of the dilemma zone detectornearest the stop line (ft),

Ld = length of the dilemma zone detectors (ft),Lv = detected length of vehicle (ft),Va = average running speed on the intersection approach (ft/s),

CEs = call-extension setting for the stop line detectors (s), andLds = length of stop line detectors (ft).

Equation 1 describes the maximum allowable headway for a dilemma zone protection systemwhere the stop line detector remains active throughout the green phase. If the stop line detectoris instructed to stop detecting after it gaps out once, then MAHs would be equal to zero. Equation 1 assumes that vehicles are only carried through the dilemma zone, not to the stopline. Bonneson and McCoy also provide a variation on Equation 1 for carrying vehicles to thestop line (6). If a vehicle headway larger than MAH does not occur before the green phasereaches it preset maximum time, the phase maxes out and ends without regard for traffic in thedilemma zone. Therefore, max-out should be avoided if possible.

Dynamic Dilemma Zone Protection

A dynamic dilemma zone protection system attempts to intelligently allocate dilemma zoneprotection based on vehicle needs at a particular time rather than as a result of a fixed detectionscheme. Examples of dynamic dilemma zone protection systems include European systems suchas MOVA (7), LHOVRA (7), and SOS (8), as well as the Detection-Control System or D-CS,developed at the Texas Transportation Institute (9). This section will briefly describe D-CS as anexample of these types of systems.

Unlike conventional dilemma zone protection, D-CS does not use fixed detection near theintersection, except for stop line detection. Instead, the speed of each arriving vehicle ismeasured 800 to 1000 ft upstream of the intersection. Based on each vehicles measured speed,its travel time to the beginning and end of its individual dilemma zone is predicted. Examples ofthese predictions are shown in Figure 1. The green phase is then intelligently ended when the



number of vehicles in their dilemma zones are at a minimum. D-CS features a two-stageoperating scheme specifically to reduce the occurrence of max-out. In Stage 1, the green phasecan not end if there is a vehicle in the dilemma zone in any lane. This stage allows for the safestoperating condition. After a predetermined number of seconds after the first call on a conflictingphase, D-CS changes to Stage 2 operation to avoid max-out. In Stage 2, D-CS will allow thegreen phase to end with as many as one passenger car in the dilemma zone per lane. However,D-CS also attempts to reduce the total number of vehicles in the dilemma zone, so D-CSattempts to find a time in the future that minimizes the number of vehicles in the dilemma zoneto minimize the risk to motorists. For more details on system operation, refer to Bonneson et al(9).

FIGURE 1 Actual dilemma zones used by D-CS (9).

Measures of Effectiveness for Dilemma Zone Protection Systems

There are two different types of measures of effectiveness for signalized intersections:operational and safety. The principal operational measure of effectiveness for signalizedintersections is control delay (10). Other measures of effectiveness may include the number ofstops per hour (or per cycle), the number of completed trips, occupancy, and travel speed.

Intersection safety has historically relied on crash history as its principal measure ofeffectiveness. The two types of crashes most affected by dilemma zone protection are right-angleand rear-end collisions. For example, Zegeer and Dean (2) noted a 54 percent reduction in crashfrequency after installing dilemma zone protection at two high-speed signalized intersections. However, Zegeer and Dean required 8.5 years of before data and 3.7 years of after data tomake the comparison, illustrating one of the drawbacks of using crash data. Wu et al (4) foundan 8 percent reduction in crashes after installing dilemma zone protection. However, the designWu et al selected did not completely protect the dilemma zone, so the modest reduction isunderstandable.



(2)

Another common safety measure is traffic conflicts. A traffic conflict is a suddenmaneuver by the driver of a vehicle to avoid a crash. Zegeer and Dean also investigated trafficconflicts for the same two intersections for which they obtained crash data (2). The number ofconflicts at these intersections decreased by 62 percent after installing dilemma zone protection. Gettman and Head (5) have proposed incorporating traffic conflict models into various micro-simulation software. Gettman and Head listed 19 different factors that would affect intersectionconflicts, ranging from vehicle headways to driver reaction times. Using traffic conflicts as asafety surrogate within a traffic micro-simulation software package would be a fairly difficultprocedure. Hauer (11) points out that conflicts may or may not be directly related to intersectioncrashes at a particular location. Also, conflicts are relatively rare events themselves, andcollecting a sufficient sample may be very time-consuming.

The dilemma zone protection systems studied by Zegeer and Dean and by Wu et al wereintended to reduce the number of vehicles in the dilemma zone. However, the authors did notdirectly use the number of vehicles in the dilemma zone as a measure of intersection safety. Bonneson et al (9) did use the number of vehicles in the dilemma zone to compare the safetyeffectiveness of the Detection-Control System to other detection systems. However, there iscurrently no theoretical method for calculating the number of vehicles in the dilemma zone. Atheoretical method would allow comparison between real-world systems and their theoreticalcapabilities, as well as allowing comparisons between competing alternatives. A theoreticalmethod for calculating the number of vehicles in the dilemma zone for a signalized intersectionis presented in the following section.

MODELING THE NUMBER OF VEHICLES IN THE DILEMMA ZONE

The number of vehicles in the dilemma zone can be modeled directly, without the need for fieldobservation, if the inputs are available. However, the models can be very complicated. Thissection provides a method to calculate the number of vehicles in the dilemma zone directly. Inaddition, a theoretical comparison between a signal with conventional dilemma zone protectionand one with the Detection-Control System is presented to show the potential value of using thenumber of vehicles in the dilemma zone as a measure of safety.

Conventional Dilemma Zone Protection

Dilemma zone protection ceases at max-out. Therefore, the number of vehicles in the dilemmazone at max-out should therefore be proportional to the probability of max-out, the size of thedilemma zone. and the traffic flow rate on the approach. The expected number of vehicles in thedilemma zone can be computed as:

whereE[k] = expected number of vehicles in the dilemma zone at the end of green per cycle,

P(max-out) = probability of max-out,



tBDZ = travel time from the upstream end of the dilemma zone to the stop line (s),tEDZ = travel time from the downstream end of the dilemma zone to the stop line (s),q(t) = approach flow rate between the beginning and end of the dilemma zone (veh/s),

andM = number of vehicles in the dilemma zone per cycle at gap out.

Theoretically, if dilemma zone protection is provided, the number of vehicles in the dilemmazone when the phase gaps out should be zero. Therefore, M would be zero. In practice, dilemmazone protection usually does not protect every possible vehicle approach speed, so some vehiclesmay be in the dilemma zone when the phase gaps out, and M may be non-zero. For the shorttime interval of the dilemma zone, the approach flow rate q(t) is effectively constant. Therefore,Equation 2 can be reduced to the following:

(3)

whereqt = through vehicle flow rate for the subject phase (veh/s),

tDZ = time duration of the dilemma zone (s), andP(max-out) = probability of max-out due to green extension.

Equation 3 only applies if the volume/capacity ratio for the phase is less than about 0.8. Whenthe volume/capacity ratio is above 0.8, the number of vehicles observed in the dilemma zone maybe higher than Equation 3 predicts due to occasional oversaturation of individual phases. Thethrough vehicle flow rate qt includes only through vehicles. Turning vehicles usually slowconsiderably before completing their movements, which makes them less of a threat for red-light-running and right-angle collisions.

Typically, the dilemma zone is assumed to be between about 5 s and about 2 s from thestop line (2). Dilemma zone research by Bonneson et al (12) and Chang et al (13) showed thatthe dilemma zone boundaries may vary with speed, but the difference between the upstream anddownstream ends of the dilemma zone was still about 3 s. Therefore, tDZ = 3 s is reasonable. Equation 3 also assumes that a vehicles speed remains nearly constant throughout the dilemmazone. This assumption requires further verification, but does not appear to be unreasonable forthrough traffic.

The probability of max-out due to green extension is also required to find the number ofvehicles in the dilemma zone. For a pre-timed phase, the probability of max-out is 1.0. Thesame is true for a coordinated phase that is forced-off. If the phase is actuated, then the phasecan end at a time less than its maximum. For these systems, the probability of max-out must bedetermined.

Bonneson and McCoy (6) developed a model for actuated signal operation that includesthe probability of max-out for an actuated signal phase. They defined the probability of max-outfor each phase of an actuated signal due to green extensions as:



(4)

(5)

(6)

whereP(max-out) = probability of max-out due to green extension,

p = probability of extending the green phase, andn = number of detector extensions required to max-out the green phase.

Equation 4 is the probability of finding a sequence of headways in the approach traffic streamthat will extend the green phase to maximum green. Each of these headways must be less thanthe MAH of the detection system, as described in Equation 1. The probability p of extending thegreen phase is the probability of a headway less than the MAH using a bunched exponential(Cowan M3) distribution (14), or

where$ = minimum vehicle headway (s), andq = vehicle arrival rate for the subject phase (veh/s).

The vehicle arrival rate for the subject phase, q, must include all vehicles that can actuate thedilemma zone protection. For example, vehicles making left turns will cross some or all of thedilemma zone detection prior to entering the left turn lane, so left turning vehicles will extend thethrough green phase as if they were through vehicles. Therefore, left turn vehicles should beincluded in q. The number of detector extensions required to max-out the green phase is

where

R = time between the first conflicting call and queue clearance (s), andh|h


(7)

Equation 7 converges to 0.5MAH as q becomes small, and to zero as q becomes large.

Figure 2 uses Bonneson and McCoys model to illustrate the effect of increasing flow rateon the probability of max-out for three different maximum allowable headways. For a givenflow rate, the likelihood of finding a headway large enough to gap-out the phase decreases as themaximum allowable headway increases. This tendency increases the likelihood of max-out. Also, as the flow rate increases, the number of vehicles arriving on red increases. Consequently,the queue clearance time for the phase increases, reducing the amount of time available to find agap to safely end the phase. At the same time, the likelihood of finding a headway that willallow gap-out also decreases. These two effects of flow rate combine to decrease the likelihoodof gap-out and cause a steep rise in the probability of max-out in Figure 2.

FIGURE 2 Probability of max-out for three different maximum allowable headwaysusing conventional dilemma zone protection.

Figure 3 illustrates the effect of the traffic flow rate on the number of vehicles in thedilemma zone per cycle using the probabilities of max-out shown in Figure 2. The number ofvehicles in the dilemma zone is proportional to the probability of max-out, as shown in Equation2. The equivalent number of vehicles in the dilemma zone for a pretimed phase is also shown. The vertical distance between any two curves represent the amount of improvement provided byone system over another. For example, at virtually any flow rate below saturation, an actuatedphase with dilemma zone protection always results in fewer vehicles in the dilemma zone than a



(8)

pretimed phase. Fewer vehicles in the dilemma zone should correlate directly to fewer crashesand fewer conflicts.

FIGURE 3 Number of vehicles in the dilemma zone for three different maximumallowable headways using conventional dilemma zone protection.

Extending the concept further, the number of vehicles in the dilemma zone can also beused to quantify the severity of clipping of the end of a progression band for coordinatedsignals. A recent study of red-light-running found that ending a coordinated phase during aplatoon is a contributing factor (15). The coordinated phases of a signal system are usually eitherpretimed for progression or are forced-off at a predetermined time in the cycle. Again, theprobability of max-out for these phases would be 1.0. In a coordinated system, vehicle arrivalsare not random, so the value of qt in Equation 3 would instead be

whereRp = platoon ratio, andq = total flow rate for the phase (veh/s).

In this way, the safety effects of changes to the progression band can be immediately seen andcompared to the operational effects of the same changes.



(9)

Dynamic Dilemma Zone Protection

Models of behavior for dynamic dilemma zone protection systems are not as readily available. These models are also much more complicated than Bonneson and McCoys model simplybecause the operation of these systems is more complicated than normal traffic signals. Forexample, Zimmerman (16) developed an algorithm of D-CS operation that provides forcalculating the probability of max-out and the number of vehicles in the dilemma zone for aD-CS controlled phase. In a simplified form, Zimmermans algorithm uses the followingcomponent to determine the number of vehicles in the dilemma zone:

wherekR1 = number of vehicles in the dilemma zone per cycle when phase ends during Stage 1

operation, andk2 = number of vehicles in the dilemma zone per cycle when phase ends during Stage 2

operation.

The calculation for kmax is similar to Equation 3. However, D-CS can allow vehicles to be in thedilemma zone under certain circumstances, so the assumption that M equals zero does not hold. D-CS also attempts to minimize the number of vehicles in the dilemma zone during Stage 2operation, adding a further layer of complication to a mathematical algorithm. The two-stageoperation of D-CS greatly complicates the algorithm construction, and as a result the algorithm istoo complicated to be presented here. For more details, please see Chapter IV of Zimmerman(16).

Zimmermans calculation of the number of vehicles in the dilemma zone requires theprobability of max-out, so the algorithm also provides for calculating the probability of max-outfor a D-CS controlled phase. This algorithm is conceptually similar to Bonneson and McCoysmodel, and uses modified forms of Equations 4 through 7. However, the two-stage nature ofD-CS operation complicates the calculation of the probability of max-out. Due to spacelimitations, the algorithm for the probability of max-out for a D-CS controlled phase can not bepresented here. The complete derivation of the probability of max-out for a D-CS controlledphase is shown in Zimmerman (16).

The probability of max-out for D-CS using Zimmermans algorithm is shown in Figure 4. The shape of the curves in Figure 4 are somewhat similar to Figure 2, but they tend to rise moresteeply. D-CS tends to end phases relatively quickly after entering Stage 2, so the probability ofmax-out does not increase substantially until the queue clearance time approaches maximumgreen. Figure 5 illustrates the number of vehicles in the dilemma zone for D-CS usingZimmermans algorithm.



FIGURE 4 Probability of max-out for three different maximum allowable headwaysusing D-CS operation.

FIGURE 5 Number of vehicles in the dilemma zone for three different maximumallowable headways using D-CS operation.



Separately, Figures 4 and 5 are interesting but not very useful. Together, the number ofvehicles in the dilemma zone can be readily compared between different control strategies. Figure 6 shows a comparison between a conventional dilemma zone protection design and D-CSfor the same maximum allowable headway and maximum green. D-CS has fewer vehicles in thedilemma zone than the conventional dilemma zone protection system at flow rates between 1000and 2000 vehicles per hour because of its dynamic allocation of dilemma zone protection and itsspecial features to reduce the frequency of max-out.

FIGURE 6 Comparison of number of vehicles in the dilemma zone for conventionaldilemma zone protection with the Detection-Control System.

From Figure 6, it is clear that D-CS reduces the number of vehicles in the dilemma zoneat the end of green on a per cycle basis. It could also be argued that this improvement is a safetybenefit. This argument would be merely an assumption without determining the number ofvehicles in the dilemma zone first.

FIELD MEASUREMENT OF THE NUMBER OF VEHICLES IN THE DILEMMAZONE

A field measurement technique is also necessary to assess the number of vehicles in the dilemmazone at the end of green for an operating intersection and to compare actual results to thetheoretical predictions. The technique described in this section is a result of the experience ofcollecting the number of vehicles in the dilemma zone to evaluate the effectiveness of theDetection-Control System (9).



Field Measurement Technique

The field measurement technique for the number of vehicles in the dilemma zone is straightforward and easy to set up. It requires at least two traffic cones and a video camera. Theupstream and downstream boundaries of the dilemma zone on a high-speed approach are markedwith a cone, as shown in Figure 7. The video camera is set up so that all high-speed lanes andthe traffic signal indications are in the field of view. The approach is then videotaped. Duringreplay, when the signal indications change from green to yellow, stop the tape and count thenumber of through vehicles between the cones. Turning vehicles (left or right) should beexcluded. The number of vehicles in the dilemma zone per cycle is simply the following:

(10)

wherekm = observed number of vehicles in the dilemma zone at the end of green for phase m,

andm = number of cycles observed, with one green phase per cycle.

FIGURE 7 Field data collection design for number of vehicles in the dilemma zone.

The number of vehicles in the dilemma zone is assumed to be Poisson distributed (i.e.,random), so the number of vehicles observed to be in the dilemma zone may vary considerablyfrom cycle to cycle. The following equation can be used to ensure that the number of phasesobserved is sufficient to obtain the number of vehicles in the dilemma zone per cycle at 95percent confidence:



(11)

wherem = number of cycles observed,z = standard normal distribution value,

= 1.96 at 95 percent confidence level,s2 = ,

E[k]* = qttDZ, ande = acceptable error range, vehicles per cycle.

The variance of a Poisson distribution equals its mean, so the variance s2 in Equation 10 equalsthe expected value of the number of vehicles in the dilemma zone. E[k]* is the expected numberof vehicles in the dilemma zone if the phase maxed out every cycle. As a result, the number ofcycles necessary for 95 percentile confidence will usually be conservative for an actuated signal. An error rate of 0.5 vehicles per cycle is suggested to keep the necessary number of cycles to areasonable amount at very high flow rates. For example, 118 cycles would be necessary at atraffic volume of 2000 vehicles per hour (both directions) and the error rate of 0.5 vehicles percycle. Because traffic conditions are not static, four hours of observation is a practical uppertime limit if the number required of cycles calculated using Equation 10 becomes very large.

The field measurement technique just described would appear to be inaccurate because ituses only the dilemma zone for the average speed. The dilemma zone is defined as a particularnumber of seconds of travel time from the stop line. As shown in Figure 1, the dilemma zonevaries with speed. If an observer could measure vehicle speeds for every vehicle on a high-speedapproach, then a more accurate assessment of the number of vehicles in the dilemma zone couldbe obtained. Bonneson et al (9) measured the speed of each vehicle as it approached theintersection using a tape switch speed trap placed upstream of the dilemma zone, as well asvideotaped the intersection. After analyzing both sets of data, it was found that the videotapealone would have been adequate. Matching the tape switch data to vehicles was time-consumingand did not materially improve the accuracy of the count. The videotape was also be used tocollect control delay without any additional equipment or setup. Based on this experience, theuse of videotape and a dilemma zone based on the average speed is recommended as shown inFigure 7 instead of a more sophisticated technique measuring vehicle speeds.

While measuring every vehicles speed proved impractical in the field, it is possible to doso with simulation. A traffic micro-simulation model is designed to track the locations and speedof every vehicle at all times. Zimmerman (16) used simulation to find the number of vehicles inthe dilemma zone at the end of every cycle. Zimmerman parsed the animation files for thealgorithm calibration runs on a second-by-second basis, then compared each vehicles locationwith the boundaries of the dilemma zone for its speed. The same technique could be used withthe animation files of any traffic micro-simulation package. Alternatively, a function could bebuilt into micro-simulation packages that can determine the number of vehicles in the dilemma



zone as each phase ends, so the calculation could be done internally rather than as a post-processing task.

Comparison of Field Measurements to Model Predictions

Table 1 shows a comparison of the field data collected for the two high-speed signal locationsinvestigated by Bonneson et al (9). Data was collected at these sites on only one approach at atime, so the hourly flow rate shown in Table 1 is for the southbound approaches only, and wascollected during off-peak times, explaining the low flow rates observed. The northboundapproach at Site 1 had a considerable amount of platooning, so this approach is not consistentwith the assumption of random arrivals embedded in Equation 3. As Table 1 indicates, themodel predictions from Equation 3 match closely to the observed number of vehicles in thedilemma zone for the low flow rates at these sites. Obviously, more research is necessary for amore conclusive comparison, especially at higher volume locations.

TABLE 1 Comparison of Field Measurement and Model PredictionsSite Control P(max-out)1 Hourly flow rate

(vph)2Number of Vehicles in Dilemma Zone/Cycle3

Model prediction4 Observed number5

1 Semi-actuated 1.00 353 0.29 0.26

2 Actuated 0.10 262 0.02 0.02Notes1 - Site 1 was semi-actuated, so the high-speed green phase always maxed out. Site 2 had full dilemma zoneprotection with an MAH of approximately 11 s, and maxed out during about 10 percent of cycles observed.2 - Hourly flow rates were calculated using southbound traffic only and are for one direction only.3 - The number of vehicles in the dilemma zone per cycle assumes a 3 s dilemma zone and uses traffic flow in onlyone direction, consistent with the data collection method.4 - The model prediction uses Equation 3: k = q ttDZP(max-out), with tDZ = 3 s and q t = hourly flow rate/3600.5 - The observed number is the number of vehicles observed to be in the dilemma zone per cycle on average for thestudy period, for southbound traffic only.

CONCLUSIONS AND RECOMMENDATIONS

The number of vehicles in the dilemma zone at the end of green indicates the frequency thatdrivers are forced to make an uncertain decision whether to go or stop at the end of green. Giventhat many crashes at intersections are at least partly a result of these decisions, the number ofvehicles in the dilemma zone should have a relationship with intersection safety. The goal ofdilemma zone protection has been to reduce the number of vehicles in the dilemma zone at theend of green. Measuring the number of vehicles in the dilemma zone therefore gives a directmethod of assessing the effectiveness of any dilemma zone protection scheme. This paperproposes the use of the number of vehicles in the dilemma zone as a potential intersection safetymeasure. Using the number of vehicles in the dilemma zone also makes intuitive sense.

This paper also presents a relatively easy way to determine the number of vehicles in thedilemma zone at the end of green in the field. Using this method, a traffic engineer could quickly



assess whether a particular intersections dilemma zone protection system is functioning properlyor not. The number of vehicles in the dilemma zone can also be readily incorporated into trafficmicro-simulation packages using vehicle locations and speeds when the green phase ends ratherthan using the field measurement technique. However, there is currently no connection betweencrashes and the number of vehicles in the dilemma zone. This connection must be developedbefore the number of vehicles in the dilemma zone can be widely used as a safety surrogate. Also, Equation 3 is appropriate for volume/capacity ratios below about 0.8. The effect ofvolume/capacity ratios higher than 0.8 on the number of vehicles in the dilemma zone alsorequires further investigation.

Because the number of vehicles in the dilemma zone is relatively easy to collect andinterpret, and because of the connection between dilemma zone protection and crash reduction inthe literature, it is recommended that the number of vehicles in the dilemma zone be consideredas a potential intersection safety surrogate. It is also recommended that the relationship betweencrashes and the number of vehicles in the dilemma zone be established in future research. Research into the relationship between the number of vehicles in the dilemma zone andvolume/capacity ratios above 0.8 is also recommended. Finally, if and when the link betweencrashes and the number of vehicles in the dilemma zone is established, incorporation of thenumber of vehicles in the dilemma zone into traffic micro-simulation packages is recommendedbecause of the ease with which this can be done.

ACKNOWLEDGMENT

The authors would like to thank Dr. Carroll Messer of Texas A & M University, CivilEngineering Department. He provided thoughtful guidance and insight on the development ofthis research. He also served as the chair of the lead authors doctoral committee and supervisedthe research the culminated in a dissertation and this paper.

REFERENCES

1. ITE Technical Committee 18 (P.S. Parsonson, chair). Small Area Detection atIntersection Approaches. Traffic Engineering, Vol. 44, No. 2, February 1974, pp. 8-17.

2. Zegeer, C. V. and R. C. Deen. Green Extension System at High-Speed Intersections. ITEJournal, Vol. 48, No. 11, November 1978, pp. 19-24.

3. Pline, J. L., ed. Traffic Engineering Handbook, 5th ed. Institute of TransportationEngineers, Washington, D.C., 1999.

4. Wu, C .S., C.E. Lee, R. B. Machemehl, and J. Williams. Effects of Multiple-PointDetectors on Delay and Accidents. In Transportation Research Record 881,Transportation Research Board, National Research Council, Washington, D.C., 1982, pp.1-9.



5. Gettman, D., and L. Head. Surrogate Safety Measures From Traffic Simulation Models.Report No. FHWA-RD-03-050, Federal Highway Administration, Washington, D.C.,2003.

6. Bonneson, J. A., and P.T. McCoy. Manual of Traffic Detector Design, 1st ed. Institute ofTransportation Engineers, Washington, D.C., 1994.

7. Kronborg, P., and F. Davidsson. MOVA and LHOVRA: Traffic Signal Control ForIsolated Intersections. Traffic Engineering and Control, vol. 34, no. 4, April 1993, pp.193-200.

8. Kronborg, P., F. Davidsson, and J. Edholm. SOSSelf Optimising Signal Control:Development and Field Trials of the SOS Algorithm for Self-Optimising Signal Control atIsolated Intersections. TFK (Transport Research Institute) Report 1997:2E, Stockholm,Sweden, 1997.

9. Bonneson, J. A., D. A. Middleton, K. H. Zimmerman, H. A. Charara, and M. Abbas.Intelligent Detection-Control System for Rural Signalized Intersections. Report No.FHWA/TX-03/4022-2. Texas Transportation Institute, College Station, Texas,September 2002.

10. Highway Capacity Manual 2000. 4th ed. Transportation Research Board, NationalResearch Council, Washington, D.C., 2000.

11. Hauer, E., Observational Before-After Studies in Road Safety, Pergamon Press, ElsevierScience, Inc., Tarrytown, New York, 1997.

12. Bonneson, J. A., P. T. McCoy, and B. A. Moen. Traffic Detector Design and EvaluationGuidelines. Report TRP-02-31-93. Nebraska Department of Roads, Lincoln, Nebraska,1993.

13. Chang, M.S., C.J. Messer, and A.J. Santiago. Timing Traffic Signal Change IntervalsBased on Driver Behavior. In Transportation Research Record 1027, TransportationResearch Board, National Research Council, Washington, D.C., 1985, pp. 20-30.

14. Cowan, R .J. Useful Headway Models. Transportation Research, Vol. 9, No. 6,November/December 1975, pp. 371-375.

15. Bonneson, J.A., K. Zimmerman, and M. Brewer. Engineering Countermeasures toReduce Red-Light-Running, Report No. FHWA/TX-03/4027-2. Texas Department ofTransportation, Austin, Texas, August 2002.

16. Zimmerman, K. Development of a Performance Prediction Algorithm for Evaluation of aTraffic Adaptive Signal System for Isolated High-Speed Intersections. Dissertation,Texas A&M University, College Station, Texas, August 2003.


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