Utilization and Timing of Signal Change Interval

Transcription

1 86 TRANSPORTATION RESEARCH RECORD 1114 Utilization and Timing of Signal Change Interval FENG-BOR LIN, DONALD COOKE, AND SANGARANATHAN VIJAYAKUMAR The problem or timing the signal change Interval has received Increased attention In recent years. Mch or this attention is focsed on two Isses: whether a constant yellow interval shold be sed and whether the timing eqations sggested by the Institte or Transportation Engineers (ITE) can realistically refiect driver needs for the change Interval. These two Isses are examined on the basis or observed driver behavior. The 95th percentile yellow Interval reqirements are fond to vary from 3 to 5 sec. Sch reqirements do not have a positive linear correlation with the approach speed. The 85th and 95th total change Interval reqirements have strong linear correlations with vehicle clearance time. The ITE's timing eqations shold be replaced by simpler ones that can better explain driver behavior. A signal change interval is a short time period in a traffic signal cycle between conflicting green intervals. A yellow signal indication is displayed in this interval, which is often followed by an all-red signal indication. There are two major problems in timing the signal change interval for the vehicles on an intersection approach. One is to determine the total change interval reqirement, and the other is to divide this total reqirement into the yellow interval and the all-red interval reqirement. In general, the total-change interval reqirement refers to the length of a change interval needed for a safe transfer of the right-of-way. The yellow interval reqirement represents the length of a yellow interval that is needed to allow a reasonable driver to take proper action before a red signal indication is exhibited. The all-red interval reqirement is the additionai time following a yellow interval that is needed to clear vehicles from the intersection before a green signal indication is displayed for the vehicles on other approaches. Crrent practices in determining these varios reqirements associated with the signal change interval vary among traffic engineering agencies. Nevertheless, the following eqation sggested by the Institte of Transportation Engineers (ITE) (1) has been adopted by many agencies for determining the change interval reqirement: T = t + V/(2a) + (W + L)/V where T = change interval reqirement, in sec; = driver reaction time, in sec; Civil and Environmental Engineering Department, Clarkson University, Potsdam, N.Y (1) V = vehicle approach speed, in ft/sec; a = vehicle deceleration rate, in ftfsec2; W = intersection width, in ft; and L = vehicle length. in ft. The sm of the first two terms on the right side of this eqation has also been sed by a nmber of agencies in determining the yellow interval reqirement. The se of Eqation 1 reqires the selection of representative vales for the driver reaction time, vehicle deceleration rate, and vehicle length. Reported vales of the mean and the 85th percentile reaction times and deceleration rates vary significantly from one intersection to another (2). ITE sggests a vale of 1 sec for the reaction time and 10 ft/sec2 for the deceleration rate. The vale for the vehicle length is commonly assmed to be 20 ft. Eqation 1 has been expanded in several stdies (3, 4). In May 1985, ITE (5) also extended this eqation and proposed a recommended practice in timing the change interval. This recommended practice determines the yellow interval according to Y = t + V/2/(a ± 0.322G) (2) where t, V. and a are as defined for Eqation 1, and Y =yellow interval reqirement, in sec; and G = the grade of approach lane, in percent. ITE recommends that the 85th percentile approach speed always be sed in Eqation 2. In addition, the ITE's proposed recommended practice allows the se of (W + L)/V, or PIV, or (P + L)/V to determine the length of the reqired all-red interval. The notations sed in these terms are to be interpreted as follows: W = width of the intersection, measred from the near-side stop line to the far-side edge of the conflicting traffic lane along the actal vehicle path, in ft; P = width of intersection, measred from the nearside stop line to the far side of the farthest conflicting pedestrian crosswalk along the actal vehicle path, in ft; L = length of vehicle, recommended as 20 ft; and V = speed of the vehicle throgh the intersection, in ft/sec. According to ITE, (W + L)/V is to be sed if there is no pedestrian traffic present; the longer of (W + L)/V and PIV shold be sed if there is the probability of pedestrian crossings, and (P + L)/V shold be sed if there is significant

2 Lin el al. pedestrian traffic or the crosswalk is protected by pedestrian signals. To determine the entire change interval, the ITE 's proposed recommended practice reqires that the sm of the yellow interval and the all-red interval be calclated twice--once with the 15th percentile speed and again with the 85th percentile speed. If the 15th percentile speed prodces a longer interval, the all-red interval calclated at the 85th percentile speed is to be increased by the difference. Several recent stdies have raised dobt abot the wisdom of sing Eqation 1 or its expanded forms in determining the change interval and of sing Eqation 2, or the sm of t and V/(2a), for determining the yellow interval. For example, Chang et al. have fond that the behavior of the drivers who entered the intersection after the yellow onset did not change significantly with the approach speed (6). Their stdy showed that, over a speed range of 25 to 55 mph, 85 percent of the vehicles entering the intersection after the yellow onset took less than approximately 3.5 to 3.8 sec to reach the stop line. And, over the same speed range, 95 percent of the entering vehicles took less than abot 4.2 to 4.6 sec to reach the stop line after the yellow onset. These findings prompted the three investigators to sggest that the se of a constant yellow interval of 4.5 sec may be warranted. A stdy by Wortman and Fox frther reinforces the notion that the needs for the yellow interval is independent of the approach speed (7). Regarding the length of the change interval, a stdy by Lin has shown that the change interval reqirement can be better estimated as a linear fnction of the time reqired for the vehicles to clear the intersection (2). However, Lin's stdy was based on a rather limited data base. Sbseqent to this stdy, additional data were collected in order to provide a better nderstanding of how the change interval shold be designed. The objective of this paper is to se the available data to discss the tilization and timing of both the yellow interval and the change interval as a whole. YELLOW INTERVAL REQUIREMENTS Faced with a yellow signal indication, a driver will either decide to stop or proceed throgh the intersection. A yellow interval shold be long enogh to allow a proper choice by a driver nder sch a circmstance. Whether or not a yellow interval is adeqate can be evalated in terms of the percent of vehicles entering the intersection after the termination of the yellow interval (5 ). A shorter yellow interval will likely force a larger percent of vehicles to enter the intersection on a red signal indication, or force more drivers to take potentially dangeros actions. The yellow interval reqirement is defined in this stdy as the length of a yellow interval that will allow a specified percent of signal change intervals to be free of vehicles entering the intersection on a red signal indication. To examine the natre of this reqirement, data related to six straight-throgh movements and two left-tm movements at a total of five intersections were collected for analysis. Each of the sbject movements represents the vehiclar flows in one or more traffic lanes. All the five sbject intersections were located in the state of New York. Three were on Central Avene in Albany, one was on Almond Street in Syracse, and the remaining one was on Market Street in Potsdam. The two lefttm movements had their own separate signal phases. As can be observed in Table 1, the clearance widths for the eight movements varied from 77 to 135 ft. Pedestrian interferences were negligible at the time of the data collection. Therefore, for each of the straight-throgh movements, the clearance width was measred from the stop line of the approach lane to the farthest potential conflicting point on the far side of the intersection. Similarly, the clearance widths for the two left-tm movements were measred as the length of a representative trning path from the stop line to the farthest potential conflicting point downstream. The approach speeds given in Table 1 were based on those vehicles approaching the intersection near the end of the green interval. They were measred with stopwatches as the, travel times over a distance of 100 to 150 ft. The lowest mean approach speed was 21.9 mph for Movement 8 and the highest was 32.5 mph for Movement 4. The grades for all the movements were gentle. On average, each of the sbject movements was observed for abot 2-1/2 hr. The nmber of change intervals encontered in sch an observation period ranged from 68 for Movement 8 to 255 for Movement 6. Not every one of these change intervals was tilized by vehicles either to enter or to clear the intersection after the yellow onset. For each tilized change interval, the elapsed time from the yellow onset to the moment the last entering vehicle reached the stop line was measred with a stopwatch. Sch an elapsed time represents the length of the yellow interval that is needed for a change interval to be free of vehicles entering on a red signal indication. The reslting TABLE 1 CHARACTERISTICS OF MOVEMENTS EXAMINED FOR YELLOW INTERVAL REQUIREMENTS Movement Existing Clearance A22r0ach s12eed, V m12h Grade Movement Type Yellow Width % sec w, ft 15th Mean 85th 1 Straight Straight l. 7 3 Straight Straight o. 7 5 Straight Straight Left Left

3 88 measrements for each sbject movement were sed to constrct a cmlative distribtion of the yellow interval reqirement. Figre 1 shows the cmlative distribtions of the yellow interval reqirements for the eight sbject movements. Based on these distribtions, a yellow interval can be chosen that will allow a reasonably high percent (e.g., 85 or 95 percent) of the signal cycles to be free of vehicles entering on a red signal. The 85th and 95th percentile yellow interval reqirements for the eight sbject movements are given in Table 2 along with related statistics. The 95th percentile yellow interval reqirements varied from abot 3 to 5 sec, and the 85th percentile reqirements were between 2.2 and 4.2 sec. These variations cannot be explained by the differences in the approach speeds of the varios movements. Figre 1 shows that it can be qite erroneos to assme TRANSPORTATION RESEARCH RECORD 1114 that the yellow interval reqirements has a positive linear correlation with the approach speed. Among the eight movements examined, Movement 4 and Movement 8 (fable 1) had the largest difference in approach speed. Ths, if the approach speed governs the yellow interval reqirement in a manner as indicated by Eqation 2, the cmlative distribtions of the yellow interval reqirements of these two movements shold have exhibited the largest difference. To the contrary, Figre 1 shows that they were nearly identical. On the other hand, Movement 4 and Movement 6 had virtally the same approach speed. Yet, their yellow interval reqirements displayed a large difference. Movement 4 and Movement 5 did show an increase in the yellow interval reqirement as the approach speed increased. Bt, the yellow interval reqirements of Movement 7 and Movement 8 ex >- V I o. 8 Ill... c: QI E QI 0. 7 "- :J i 0.6 a:.r:... ~ 0.5 Ill QI > c:.2... " "- a Yellow Interval Reqirement, Y Seconds FIGURE 1 Cmlative freqency distribtions of yellow Interval reqirements. TABLE2 YELLOW INTERVAL REQUIREMENTS Reqirement Mean Chan9e Interval in Seconds Approach Nmber Percent Movement 85th 95th Speed Ub lized Utilized mph

4 Lin I al. hibited a relationship contradictory to that implied in Eqation 2. Ths, a qestion can be raised as to what really acconted for the variations in the cmlative freqency distribtions shown in Figre 1. With each additional hor of field observations made by the athors, it became increasingly clear that the spply of vehicles that were in a position to enter the intersection within 5 sec after the yellow onset was a major sorce of sch variations. At one extreme, Movement 8 (left trns from Wolf Road onto Central Avene in Albany) had freqent carryovers of long qees from one cycle to the next becase of the inability of a rather short green interval to discharge all of the qeeing vehicles in a cycle. As a reslt, the vehicles wold often contine entering the intersection long after the yellow interval (3.9 sec) expired. Similarly, Movement 4 (straight-throgh flows on Almond Street at Harrison Street in Syracse) provided a high level of vehicle spply at the time of the data collection. This movement occpied three straight-throgh lanes and another lane shared by straight-throgh and right-tm vehicles. Dring the evening peak hors in which most of the observations were made, a large nmber of vehicles were freqently within short travel times from the stop line at the yellow onset, and long qees often began to develop immediately after the change interval expired. Conseqently, the yellow interval reqirement of this movement differed very little from that of Movement 8. At the other extreme, Movement 6 (a straight-throgh flow on Market Street at Sandstone Road in Potsdam) had a low flow rate of abot 300 vph and was reglated by a trafficactated signal. The level of vehicle spply at the yellow onset was low becase the vehicles were sally more than 4 sec away from the intersection when the green interval expired. Over a 4-hr observation period, the longest recorded yellow interval reqirement for a cycle was 3.4 sec, and the 95th percentile yellow interval reqirement was only 3 sec. Movement 7 (left trns from Central Avene onto Everlet Avene in Albany) had a similar characteristic. The yellow interval for this movement often began when there were no vehicles within a travel time of less than 4 sec from the stop line. This phenomenon was created by the signal controls for Movement 7 and for the movements at the pstream intersection. The reslting 95th percentile yellow interval reqirement of 3.7 sec was significantly lower than that of Movements 4 and 8. Althogh it is evident that the level of vehicle spply at the yellow onset is a governing factor of the yellow interval reqirement, there are crrently no qantitative methods for defining sch a casal relationship. The percent of change intervals tilized by vehicl~s to enter the intersection may be a potential measre of the level of vehicle spply. Figre 2_shows that sch a measre has an apparent correlation with both the 95th and 85th percentile yellow interval reqirements of the eight movements. Let F be the proportion of change intervals tilized by vehicles to enter the intersection after the yellow onset. Then, the 95th percentile yellow interval reqirements of the eight movements given in Table 2 can be related to F according to Y = F (3) where Y represents the specified percentile yellow int.erval reqirement This eqation has an R 2 vale of and a standard error of estimate of 0.33 sec. The corresponding eqation for the 85th percentile yellow interval reqirement is Y = F (4) 89 5 I 4.. c Ill Ill' c: c E c... 5 O" c c:: "iii... >... c c: - 2 s 85th Percentile 95th Percentile :!:.2 4 a; >- 3 - I I I I I I Change Intervals Utilized, Percent FIGURE 2 Variation of yellow Interval reqirement with the rate of change Interval tilization. -.

5 90 The R 2 vale of this eqation is 0.60 and the standard error of estimate is 0.42 sec. CHANGE INTERVAL REQUIREMENTS The signal change intervl may comprise only a yellow interval or inclde a yellow interval and an all-red interval. The crrent Uniform Vehicle Code (8) allows vehicles to enter the intersection dring the yellow interval and to clear the intersection after the red interval begins. This "permissive rle" has a greater need for the all-red interval in comparison with the "restrictive rle," which reqires vehicles to clear the intersection by the end of the yellow interval. Regardless of which rle drivers shold follow, the change interval reqirement can be defined as the length of a change interval that is needed to allow all vehicles to clear the intersection in a specified percent (e.g., 85 percent) of signal cycles. In order to analyze the natre of this reqirement, data related to the interactions between the change intervals and the vehicles of 22 movements were collected. These 22 movements were associated with 15 intersections in 5 rban areas in the state of New York. Five of the intersections were located in Syracse, for in Albany, one in Rochester, three in Potsdam, and two in TRANSPOKTATION RESEARCH RECORD 1114 Canton. For of the 22 movements were the same as Movement 1 throgh Movement 4 described previosly in Table 1. As can be observed in Table 3, all bt one of the movements had clearance widths between 74 and 135 ft. The grades of the approach lanes were within ±4 percent. The mean approach speeds varied from 21.9 to 43.9 mph, and the mean trning speeds of the left-tm movements were abot 20 mph. At the time of the data collection, none of the 22 movements had vehicles blocking the intersections becase of congestion downstream of the stop lines. The "permissive rle" was in place at all the intersections for the se of the change interval. Pedestrian interferences with the vehiclar movements at all the intersections were negligible at the time of the data collection. Therefore, the clearance widths were also measred according to the definitions described previosly. The traffic conditions in an approach lane of a signalized intersection may vary sbstantially within a signal cycle becase of the formation and dissipation of qees. Conseqently, the speeds of those vehicles that may interact with the change interval may be significantly affected by sch changing conditions. For this reason, the determination of the vehicle speeds took into consideration only those vehicles approaching or crossing the intersection near the end of the green interval or immediately after the yellow onset. Stopwatches were sed to measre the travel times of sch vehicles over a distance of 100 TABLE3 CHANGE IN'IERVAL REQUIREMENTS Clearance A1212 roach s12eed, m12h c. I. Reg irement, s e c % of c. I. Movement Width Grade Utilized ft % 15th Mean 85th 85th 95th l B l l l llo (14. 9) (18. 0) (22. 7) 20 l (17. 4) (20. 0) (24. 4) (17. 9) (20. 2) (23. 2) (16. 2) (18.8) (21.1) Note : Vales in parentheses are trning speeds

6 Lin et al. to 150 fl For the straight-throgh movements, the approach speeds determined in this manner were eqivalent to the speeds at which the vehicles cleared the intersection. For the left-tm movements, the approach speeds were not a good approximation of the clearance speeds. Therefore, both approach speeds and clearance speeds were determine for the left-trn movements. The major task of the data collection was to se stopwatches to measre, on a cycle-to-cycle basis, the elapsed time from the yellow onset to the moment the last entering vehicle cleared the intersection. Only those vehicles entering the intersection after the yellow onset were inclded in the data collection. This task was performed for an average of abot 2 hr for each sbject movement. The reslting data were sed to constrct a cmlative freqency distribtion of the change interval reqirement for each sbject movement. The 85th and 95th percentile change interval reqirements determined from sch distribtions are smmarized in Table 3 along with other relevant statistics. The data given in Table 3 can be sed to examine alternative models for estimating the change interval reqirement. One sch model sggested by Lin (2) can be written as T = A + B(W + L)/V (5) where T = specified percentile reqirement of the change interval, in sec; A, B = coefficients to be calibrated; W = clearance width, in ft; L = representative vehicle length, 20 ft; and V = mean clearance speed, in ft/sec. This model implicitly assmes that the relationship between the change interval reqirement and the average clearance time (W + L)/V is linear. Figre 3, which is based on the 95th percentile change interval reqirements given in Table 3, confirms the existence of a strong linear relationship between T and (W + L)/V. A least-sqare regression based on the 85th percentile change interval reqirement given in Table 3 reslts in the following eqation: T = (W + L)/V (6) This eqation has an R 2 vale of 0.75 and a standard error of estimate of 0.58 sec. When the 95th percentile reqirements are sed for the regression, the reslting eqation is T = (W + L)/V (7) The R2 vale of this eqation is 0.74 and the standard error of estimate is 0.64 sec. No attempt was made to analyze the confidence intervals of these regression eqations and the variances of the regression coefficients. Sch an analysis reqires the assmption that the 85th and 95th percentile change interval reqirements are distribted normally. The existing data do not spport sch an assmption Cl) "' c "' Cl) 9 E Cl)... :J er 8 Cl) a: iii >... Ill c Cl) 7 Ol c.s::. "' Linear Correlation Coefficient = o (W + L) IV, sec FIGURE 3 Variation of the 95th percentile change Interval reqirement with clearance time.

7 92 TRANSPORTATION RESEARCH RECORD 1114 For the sbject movements, the last term of Eqation 7 is virtally the same as the clearance time determined from the 15th percentile clearance speed. Similarly, the last term of Eqation 6 has vales that are on the average only 0.2 sec shorter than the clearance times determined from the 15th percentile clearance speeds of the varios movements. Therefore, if the last terms of these two eqations are sed to determine the all-red interval reqirement, they wold satisfy the clearance needs of abot 85 percent of the entering vehicles. Eqations 6 and 7 are capable of explaining abot 74 percent of the variations in the 85th and the 95th percentile change interval reqirements. The nacconted-for variations can be attribted to differences in vehicle speeds, vehicle lengths, vehicle spply patterns at the yellow onset, and so forth. Becase the yellow interval reqirement is linearly correlated to some extent with the proportion F of change intervals tilized, Eqation 5 can be improved by adding onto it another term as follows: T = A + CF + B(W + L)/V (8) The reslting regression eqation based on the 95th percentile reqirements is T = F (W + L)/V (9) with an R 2 vale of 0.84 and a standard error of estimate of 0.52 sec. The corresponding eqation for the 85th percentile reqirements is T = F + 1.lO(W + L)/V (10) This eqation bas an 'ff vale of 0.82 and a standard error of estimate of 0.51 sec. Althogh Eqations 9 and 10 are mor.e powerfl than Eqations 6 and 7 in explaining the length reqirements of the change interval, the improvements do not appear to be large enogh to warrant the se of either Eqation 9 or Eqation 10. In fact, the inclsion of F in these eqations wold make the eqations difficlt and expensive to se becase data for F wold have to be collected at each intersection. For the same reason, Eqations 3 and 4 presented earlier wold have little se for timing applications. An alternative to Eqations 5 and 8 for estimating the change interval reqirements is ITE 's proposed recommended practice. For movements that have little pedestrian interference, this practice implies a model form of T = t + V/2/(a ± 0.322G) + (W + L)/V (11) As described previosly, the se of Eqation 11 reqires two calclations: once with the 15th percentile speed and once with the 85th percentile speed. However, ITE is vage abot how sch calclations are to be performed for protected left trns. The last two terms in Eqation 11 are a fnction of vehicle speed. If both terms are determin~ from the same percentile approach speed for left-tm movements, it can be shown that the reslting T vales and the 95th percentile change interval reqirements given in Table 3 have a linear correlation coefficient of If the approach speed is sed for the second term on the right side of Eqation 11 and the trning speed is sed for the last term, the reslting linear correlation coefficient wold become 0.79 (Figre 4). This level of correlation with the observed 95th percentile reqirements is respectable, bt it is still below that which can be achieved by a mch simpler model sch as Eqation 7 (Figre 3). Therefore, there is no reason to adopt ITE's proposed recommended practice nless it has a sperior theoretical basis for explaining driver behavior. The sondness of the theoretical basis for Eqation 11 can be addressed by rewriting this eqation as Z = T - (W + L)/V = t + V/2/(a ± 0.322G) (12) The term Z in this eqation represents the yellow interval reqirement. H Eqation 11 is a valid representation of the behavior of drivers in their se of the change interval, the vales of Z determined as T - (W + L)/V from field observations shold be strongly and positively correlated with the approach speed. Figre 5 shows that sch a linear correlation does not exist between Z and the approach speed as far as the 22 sbject movements are concerned. In this figre, the vales of Z are determined as T - (W + L)/V from Table 3 based on the mean clearance speeds and the 95th percentile change interval reqirements. A least-sqare regression of these Z vales on the mean approach speeds (in mph) reslts in the following eqation: Z = V (13) The K vale of this eqatfon is 0.10 and the standard error of estimate is 0.62 sec. As can be observed from Figre 5, there is only one Z vale for mean approach speeds exceeding 34 mph. This Z vale is weighted more heavily in Eqation 13 than the other vales. If this vale is deleted, the reslting regression eqation becomes Z = V (14) for mean approach speeds ranging from 22 to 33 mph. Eqation 14 has an If vale of 0.34 and a standard error of estimate of 0.54 sec. The regression coefficients of both Eqation 13 and Eqation 14 are qite different from the vales recommended by the ITE. According to ITE, the constant terms in Eqations 12 and 13 shold have been 1.0 sec and, for the sbject movements, the coefficient of V shold have been in the range of to Therefore, even if Z is really a linear fnction of the approach speed, the swn oft and V/2/(a ± 0.322G) is a poor representation of driver behavior. The negative signs of the coefficients of Vin Eqations 13 and 14 frther indicate that an increase in the approach speed tends to case a redction instead of an increase in the yellow interval reqirement. It is ncertain, however, whether this negative correlation between Zand Vreally exists becase ther 2 vales of Eqations 13 and 14 are rather small and data are lacking for mean approach speeds exceeding 32 mph and for speeds below 26 mph. Overall, it is evident that the casal relationship between Z and V is very weak and; ths, it is meaningless to treat the yellow interval reqirement as a fwiction of the approach speed.

8 Lill el al "' ; E 8.. c: 5 O'" a: 1J > c 0 6 Linear Correlation Coefficient = Design Vale by ITE, sec FIGURE 4 Correlation between the 9Sth percentile change Interval reqirements and vales determined from the ITE's proposed recommended practice 5 :!l 111 lj N'... 0 ~ IO 3 > Mean Approach Speed, mph FIGURE 5 Variation of Z with mean approach speed. TIMING DESIGN APPLICATIONS The cmlative freqency distribtions of the yellow interval reqirement shown in Figre 1 are bonded by the distribtions of Movements 6 and 8, which had vehicle spply patterns of opposite extremes at the yellow onset. The corresponding 95th percentile yellow interval reqirements are between 3 and 5 sec and the 85th percentile reqirements are between 2.2 and 4.2 sec. The Z vales shown in Figre 5, which approximate the 95th percentile yellow interval reqirements of 22 movements, also lie between 3 and 5 sec. The same Z vales plotted in Figre 6 against the percentage of change intervals tilized frther show that the Z vales remain above 3 sec even when the rate of change interval tilization drops to as low as 13 percent. Therefore, a reasonable range of the design vales for

9 94 TRANSPOIUATION RESEARCH RECORD Qj t/i N' Qj :J "' 4.. > Change Intervals Utilized, Percent FIGURE 6 Variation of Z with the rate of change Interval tilization. the yellow interval is 3 to 5 sec. Yellow intervals shorter than 3 sec are not recommended becase they may case some drivers to apply excessively high decelerations in order to avoid entering the intersection on red. The variations in the change interval reqirements cannot be acconted for by the differences in the approach speeds. Relating sch variations to another traffic or signal variable is likely to make the reslting timing method difficlt to apply. Therefore, it is preferred that simple gidelines be established in the ftre for the choice of the yellow interval. Meanwhile, the yellow interval may be determined according to Y= C 1 (15) in order to satisfy the 95th percentile reqirements. In this eqation, C 1 is a correction factor with a vale between -1.0 and sec. A vale between +0.5 and +1.0 sec may be chosen for C 1 if one of the following vehicle spply patterns exists: (a) freqent carryovers of long qees from one cycle to the next; (b) a rapid bild-p of long qees immediately after the change interval expires; and (c) the percent of change intervals tilized exceeding 70 percent. On the other hand, a reasonable choice of C 1 wold be between-1.0 and--0.5 sec if (a) the movements of concern have low flow rates and are reglated by trafficactated controls; or (b) the vehicle spply to the intersection at the yellow onset is freqently ct off de to cyclic flow patterns created by signal coordination; or (c) the rate of change interval tilization is less than 30 percent. For movements with vehicle spply patterns in between the two extremes, C 1 may be set to 0 sec. To reflect the actal reqirements of individal movements, the lengths of the change interval determined from either Eqation 6 or Eqation 7 may be adjsted pward or downward. For the 95th percentile reqirements, the adjstment may take the form of T = (W + L)/V + C 2 where C 2 is a correction factor. (16) For the 22 sbject movements given in Table 3, the vales of C 2 range from abot -1.0 to sec. These vales correspond to the deviations of the measred 95th percentile reqirements from the regression line shown in Figre 3. Again, a reasonable choice of C 2 is between +0.5 to sec for movements with high levels of vehicle spply at the yellow onset (e.g., Movements 1, 7, 13, 14, 15, 16, 19, and 22). In contrast, C 2 wold most likely assme a vale between -1.0 and -0.5 sec for movements with very low levels of vehicle spply (e.g., Movements 3, 5, 8, 9, 11, and 20). For timing applications, C 1 and C 2 can be considered to be the same. Therefore, given a yellow interval and a change interval as determined from Eqations 15 and 16, the all-red interval R can be calclated as R = (W + L)/V + C C 1 = 1.17 (W + L)/V (17) It shold be noted that the all-red interval reqirements determined from Eqation 17 do not take into consideration a safety margin that may be provided by the cross traffic. This safety margin is the amont of time reqired for the first vehicle in the cross traffic to reach the conflicting point after the change interval expires. If qeeing vehicles are present on the cross street after the change interval expires, the safety margin wold eqal the time needed for the driver in the first qeeing vehicle to accelerate the vehicle to the conflicting point. If no qeeing vehicles are pre.c;ent, it will also take the first vehicle arriving on the cross street some time to reach the conflicting point. If this vehicle approaches the intersection at a speed V 0 and has an intended deceleration b, then the minimm safety margin provided by this vehicle can be approximated by V J(2b). The deceleration rate b can be as high as 18 ft/sec2 (6). Using this rate and measring V 0 in ft/sec gives a safety margin of V J36 sec. This safety margin can be determined by choosing an appropriate vale (e.g., the 15th percentile approach speed) for V 0 The safety margin allowed for the timing design cold be taken as the lesser of V J36 and the minimm (or near

10 Lin et al. minimm) time for the first qeeing vehicle in the cross traffic to reach the conflicting point. CONCLUSIONS The yellow interval reqirement correlates poorly with the approach speed. This reqirement appears to be governed by the vehicle spply pattern at the yellow onset. When freqent canyovers of long qees from one cycle to the next exist. the 95th percentile yellow interval reqirement can reach S sec. This reqirement can be redced to abot 3 sec if vehiclar movements with low flow rates and nder the control of trafficactated signals are involved. A constant yellow interval of 4.5 sec wold be able to accommodate the 90th to the looth percentile reqirements at nearly all the intersections. However, becase the 95th percentile yellow interval reqirement can vary from 3 to S sec, the se of a constant yellow interval may not appeal to some traffic engineering agencies. On the other hand, introdcing additional variables into a timing procedre in order to accont for sch a variation wold certainly make the reslting procedre impractical. Therefore, it is recommended that simple gidelines be established to assist in the choice of the yellow interval. Sch gidelines may evolve on the basis of Eqation 15. At intersections where grades are within ±4 percent, the change interval reqirements are strongly and linearly correlated with the vehicle clearance time. Therefore, simple regression eqations sch as Eqations 6 and 7 can adeqately serve as a basis for timing design. The ITE's proposed recommended practice lacks a sond theoretical basis and is nnecessarily tedios to apply. Eqation 17 provides a convenient and logical tool for determining the all-red interval reqirements. The coefficients of this and other regression eqations presented previosly can be modified if additional data become available. The existing data base can be enhanced in several respects. Of particlar interest are vehiclar movements with mean approach speeds exceeding 32 mph, intersections with clearance widths of more than 130 ft, and intersections where grades are steep. ACKNOWLEDGMENT Parts of the analyses and the data collection efforts described in this paper are spported by the National Science Fondation in connection with the development of a simlation model. REFERENCES 1. TrQ/ISportation and Traffic Engineering Handbook. Institte of Transportation Engineers, Washington, D.C., F. B. Lin. Tning Design of Signal Change Inrerval. In Transportation Resem-clt Record 1069, TRB, National Research Concil, Washington, D.C., 1986, pp. 46-SO. 3. W. L. Williams. Driver Behavior Dring the Yellow Interval. In TrQ/ISportalion Research Record 644, TRB, National Research Concil, Washington, D.C., 1977, pp P. S. Paraonson and A. J. Santiago. Dcaign Standards for Tning the Traffic-Signal Clcanmoe Period Mst be Improved to Avoid Liability. In Compendim of Tecltnical P~r:r, Institte of Tn111sportation Engineers, 1980, pp rie Technical Committee 4A-16. Determining Vehicle Change Intervals. Proposed Recommended Practice. OE JoMnUJl, May 1985, pp M. S. Chang, C. J. Messer, and A. J. Santiago. Timing Traffic Signal Change Intervals Based on Driver Bebavi~. Presented at the 64th Annal Meeting of the Transportation Research Board, Washington, D.C., Jan R. H. Wortman and T. C. Fox. Reassessment of the Traffic Signal Change lnrerval. In Tran:rportalfon Researclt Record 1069, TRB, National Rcacarch Concil, Washington, D.C., 1986, pp Uniform Vehicle Code alld Model Traffic Ordinances. The Michie Company, National Comminec on Unifonn Traffic Laws and Ordinances, Revised 1968, Charlottesville, Va., Pblication of this paper 1pon:rore.d by Commiltee on Traffic Control Devices. 95