A new lost time estimation method for right-turn traffic in Japan considering signal phasing and sneakers

Transcription

1 JOURNAL OF ADVANCED TRANSPORTATION J. Adv. Transp. 2013; 47: Published online 26 January 2012 in Wiley Online Library (wileyonlinelibrary.com)..191 A new lost time estimation method for right-turn traffic in Japan considering signal phasing and sneakers Keshuang Tang 1 *, Takeshi Ono 2, Masao Kuwahara 3 and Shinji Tanaka 4 1 Department of Traffic Engineering, Tongji University, No. 4800, Cao an Road, Shanghai , China 2 Alternative Investment Department, Daido Life Insurance Company, Kaigan, Minato-ku, Tokyo , Japan 3 Graduate School of Information Sciences, Tohoku University, Aoba , Aramaki, Aoba-ku, Sendai , Japan 4 Institute of Industrial Science, The University of Tokyo, Komaba, Meguro-ku, Tokyo , Japan SUMMARY Precise estimation of the capacity for right-turn traffic (comparable to left-turn traffic in the USA) is of great importance to determine signal phasing schemes at signalized intersections in Japan, where the left-hand driving rule is valid. However, in most signal timing procedures across the world, the lost time of right-turn traffic is simply determined by the duration of intergreen intervals and thus lacks considerations of various signal phasing and driver behavior. Meanwhile, sneakers per cycle are usually applied to account for the number of drivers completing right turns during the effective red portion of the clearance-and-change intervals. As a result, an initial cycle length must be hypothesized in order to assess the total number of sneakers within the analysis period. Consequently, a time-consuming iterative calculation process often becomes necessary. Therefore, the present study aims to develop a new lost time estimation method for right-turn traffic to overcome the aforementioned drawbacks. Lost times of right-turn traffic under three conventional phasing plans are theoretically formulated on the basis of a time space diagram and shock-wave theory. The new method is validated using field data, with case studies of its application in the signal timing procedure. Results indicated that the proposed method is capable of offering more accurate estimation than conventional approaches, which leads to shorter cycle length and simplifies signal timing process by eliminating an iterative check to determine the number of sneakers. Copyright 2012 John Wiley & Sons, Ltd. KEY WORDS: lost time; right-turn traffic; sneakers; time space diagram; shock-wave theory 1. INTRODUCTION So that traffic conflicts during the change of phases at signalized intersections can be avoided, intergreen intervals are designed to clear traffic movements released in the previous phase to provide right of way to the traffic released in the subsequent phase. Because of the clearing process, some portion of intergreen intervals is normally left unused by traffic, leading to a clearance lost time L C. Moreover, because of the need to react to the initiation of the green phase and to accelerate, additional time is consumed by the first few vehicles in the queue, leading to a start-up lost time L S. As shown in Figure 1, L S is the sum of the starting response time for the first vehicle in a queue and the additional time required for the first several vehicles in the queue to be discharged. L C refers to the portion of intergreen time during which an intersection is not used by any traffic. Accurate estimation of lost time is crucial for determining the optimal cycle length because a small variation of lost time may cause a large change of cycle length [1]. *Correspondence to: Keshuang Tang, Department of Traffic Engineering, Tongji University, No. 4800, Cao an Road, Shanghai, , China. tang@tongji.edu.cn Copyright 2012 John Wiley & Sons, Ltd.

2 A NEW LOST TIME ESTIMATION METHOD FOR TURNING TRAFFIC 705 Figure 1. Start-up loss time and clearance time. C ¼ 5 þ 1:5L 1 l (1) where C is the optimal cycle length (s), L the lost time of one cycle (s), and l the demand ratio. In Japan, capacity estimation for right-turn traffic (comparable to left-turn traffic in the USA) at signalized intersections is of great importance for determining signal phasing schemes in the planning stage. However, the lost time of right-turn traffic is simply determined by the duration of intergreen intervals and therefore lacks considerations of various signal phasing and driver behavior. Meanwhile, sneakers at the end of a permitted phase are usually applied to account for the number of drivers completing right turns during the effective red portion of the clearance-and-change interval. As a result, an initial cycle length must be hypothesized to assess the total number of sneakers within the analysis period, and thus a time-consuming iterative calculation process often becomes necessary. In view of that, the primary objective of this study is to develop a new lost time estimation method for right-turn traffic in Japan to better account for the characteristics of distinct signal phasing schemes and driver behavior, as well as to integrate sneaker assessment into signal timing procedure to avoid iterative calculations. Note that the proposed method can also be adopted for left-turn traffic in other countries, where the right-hand driving rule is applied. The rest of the paper is organized as follows. Past research on lost time estimation and treatment of sneakers in the current signal timing procedures is reviewed in the next section. The proposed method is then introduced while incorporating three conventional signal phasing plans adopted at signalized intersections in Japan, followed by its validation based on field data. Subsequently, a series of case studies are presented to demonstrate the application of the new method in signal timing procedure. Conclusions and future works are summarized at the end of the paper. 2. LITERATURE REVIEW 2.1. Lost time estimation For the planning stage, lost time estimation methods vary across the world because of distinguished traffic circumstances. In the USA, Japan, Germany, and Australia, for example, a fundamental assumption that the extension of the effective green time, e, which is equal to the start-up lost time, L S,is applied when estimating lost time [2 5]. Thus, the total lost time, L, can be approximated as the sum of the intergreen times, I, that is, L = I. However, some minor modifications have also been suggested. In the USA, an extra 1 or 2 s may be added to L for each change of phase that is applied a restrictive yellow law, which means that a vehicle may not enter an intersection when the indication is yellow unless the vehicle can clear the intersection by the end of yellow or when it is impossible or

3 706 K. TANG ET AL. Table I. Conventional signal phasing plans and sneaker assessment in Japan. Phasing plan Sneakers Note Protected-only dual-lagging right turn NA Permitted-only right turn 1 2 K = 2 veh/cycle for small intersections; K = 3 veh/cycle for large intersections Permitted-and-protected right turn KER = 1 veh/cycle for small intersections; K ER = 2 veh/cycle for large intersections (D = waiting area length) (D = waiting area length) NA, not applicable.

4 A NEW LOST TIME ESTIMATION METHOD FOR TURNING TRAFFIC 707 unsafe to stop [2]. In Japan, 1 s is subtracted from L for each change of phase when Y 4 s or (Y + AR) 5 s. These modifications intend to account for the impacts on driver behavior of yellow law and long signal change and clearance intervals. Unlike other countries, the UK adopts a method in which the sum of L S and the unused yellow is assumed to be 2 s, which leads to a lost time of (I 1) because Y is standardized at 3 s [2,6]. This is because of the 2-s duration of the yellow-and-red signal indicated before the onset of the green signal, which can significantly reduce the start-up lost time [7]. For the operation stage, in addition to theoretical investigations [8,9], a number of empirical studies have investigated the influence of signal display sequences, signal phasing, and signal timing on lost time. Bonneson and McCoy [10] evaluated the driver s starting response time to the leading left-turn indication. No significant difference among five protected permitted/permitted protected left-turn signal displays was found. Sheffer and Bruce [11] compared L S between lead and lag protected-only phasing. They found it to be smaller for locations with lag phasing than for those with lead phasing. Noyce et al. [12 15] found no significant difference in L S due to the type of the protected permitted/permitted protected left-turn signal display. Early studies by Tang and Nakamura [16,17] showed that the signal display sequence has significant effects on the starting response time and that signal timing significantly affects L C as well. There was also some research on lost time of right-turn traffic under various phasing plans in Japan, where left-hand traffic is valid. Shikata et al. [18] compared L S for the permitted-and-protected and protected-only right-turn phases; they found that L S goes up by 0.5 s with the increase of one vehicle waiting inside the intersection. In addition, the whole yellow interval is frequently used, and part of the all-red interval is sometimes used. Ono et al. [19] analyzed lost time under the protected-only right-turn phase and found that the observed total lost time is smaller than the estimated value based on the current method in Japan Treatment of sneakers Sneakers are defined by the Highway Capacity Manual 2000 as the drivers who complete left turns (equivalent to right turns in the case of Japan) during the effective red portion of the clearance-and-change interval at the end of a permitted phase [20]. There are different treatments of sneakers in the current signal timing procedures. The following introduces those in Japan and the USA. Methods applied in other countries are more or less similar. In the USA, a practical minimum value is imposed on the left-turn adjustment factor f m to account for sneakers. The number of sneakers per cycle is estimated as (1 + P L ), where P L refers to the proportion of left turns in the shared lane. It becomes two vehicles per cycle given an exclusive left-turn lane corresponding to P L = 1. Assuming an average headway of 2 s in an exclusive lane on a protected phase, the practical minimum value for f m may be estimated as 2(1 + P L )/g. In general, sneakers are considered to be part of the left-turn count for the corresponding green interval, even though they may discharge from the intersection during the yellow or red intervals. Overall, there is no term in the formulation of the effective green time to account for sneakers, and the effect of sneakers was approximated by imposing a lower limit on the left-turn adjustment factor, f LT. In Japan, the conventional signal phasing plans include the protected-only dual-lagging right turn, the permitted-only right turn, and the permitted-and-protected right turn, as summarized in Table I. In the first case, right turners wait ahead of the stop line for the onset of the right-turn green arrow. In the latter two cases, right turners wait inside the intersection for suitable gaps in the opposing traffic flow and discharge after the opposite traffic clears away. A vehicle-based concept has been applied to assess the number of sneakers at the end of the permitted right-turn phase, K and K ER [3]. Given an exclusive right-turn lane, K = 2 vehicles per cycle for small intersections and K = 3 vehicles per cycle for large intersections are recommended for the second case. K ER = 1 vehicle per cycle for small intersections and K ER = 2 vehicles per cycle for large intersections are recommended for the third case. The preceding treatments of sneakers in the USA and Japan are basically identical and inevitably result in an iterative calculation process in signal timing procedure. Figure 2 depicts the current signal timing procedure in Japan, which is quite close to that described in the Traffic Signal Timing Manual [2]. According to the figure, sneakers are considered as gained capacity, and this part of capacity is excluded from the total demand prior to calculating the demand ratio in step 4. As a result, an initial cycle length has to be hypothesized to assess the number of sneakers per cycle before step 4. Afterwards,

5 708 K. TANG ET AL. Figure 2. Current signal timing procedure in Japan. an optimum cycle length is calculated according to Equation (3) in step 6. Split ratios and green times are then calculated in step 7, on the basis of the optimum cycle length obtained in step 6. If all the rightturning vehicles can be discharged at a reasonable degree of saturation, which is normally less than 0.90, the signal timing process is completed. Otherwise, the cycle length and/or signal phasing plan is adjusted, and the previous steps are repeated until the goal is reached. This type of iterative calculation is rather time consuming. In summary, although empirical studies have discovered several factors that influence the lost time, they have not been taken into consideration when estimating lost time in the planning stage. So far, lost time is solely calculated by the length of the intergreen intervals. Driver behavior as well as the consequent lost time could be greatly different for signal phasing schemes. Its considerable impacts on traffic operation have been recognized by a few researchers, such as Lam et al. [21] and Wong et al. [22]. Therefore, lost time needs to be more sophisticatedly assessed for more accurate capacity estimation. Moreover, the treatment of sneakers in the current methods requires a time-consuming iterative calculation process in signal timing procedure. This treatment needs to be simplified for practical use. 3. PROPOSED METHOD 3.1. Protected-only dual-lagging right-turn phasing As shown in Figure 3, the protected-only right turners can anticipate the start of the right-turn green arrow (3) via the previous yellow interval for the through and left-turn traffic (2). It is very possible that they start to move before the onset of the right-turn green arrow. Therefore, the start-up lost time for right-turn traffic movement L S1 (i.e., start-up lost time of the protected right-turn phase) could be very small. Moreover, studies have reported that many right turners enter intersections even after the start of the red interval (5), which leads to a large extension of the effective green time e 1 for the protected

6 A NEW LOST TIME ESTIMATION METHOD FOR TURNING TRAFFIC 709 Figure 3. Signal displays and time space diagram of protected-only right-turn traffic. right-turn phase. Consequently, L S1 may significantly vary from e 1, which is inconsistent with the fundamental assumption of the existing methods, as discussed earlier. Thus, L S1 should be modeled as a function of signal change and clearance intervals before the rightturn green arrow (2), and e 1 should be dependent upon intergreen times after the right-turn green arrow (45). L S1 ¼ fðy B ; AR B Þ (2) e 1 ¼ gy ð A ; AR A Þ (3) where Y B and AR B are the yellow and all-red times before the onset of the right-turn green arrow and Y A and AR A are the yellow and all-red times after the right-turn green arrow Permitted-and-protected right-turn phasing The permitted-and-protected right turners are allowed to enter the intersection after the start of the permitted right-turn phase (1), as illustrated in Figure 4. However, they usually cannot pass the intersection right away because of the existence of the opposing flow. They either find acceptable gaps to traverse through the intersection during the permitted right-turn phase or after the opposing flow clears. In the latter case, right turners can move immediately after the clearance of the opposite through and left-turning vehicles without the need to wait for the onset of the right-turn green arrow. More specifically, possible time intervals for the discharge of the permitted-and-protected right turners include the unsaturated period of the opposing flow in the permitted right-turn green phase (1), the intergreen interval before the right-turn green arrow (2), the following protected right-turn phase (3), and the intergreen interval after the right-turn green arrow (4). If the stop bar of the waiting area is regarded as the starting point of right-turn traffic discharge, the start-up lost time of the protected right-turn phase (3)isL S1, as shown in Figure 4. Because right turners can start to move immediately after the opposite through and left-turn traffic clear, L S1 could be fairly small and may even be negative, similar to the case of the protected-only right-turn phasing. However, if the stop bar of the approach is regarded as the reference, the start-up lost time of the protected right-turn phase (3) becomes L S2, which excludes the vehicles in the waiting area. The relationship between L S2 and L S1 can be expressed by Equation (4). The extension of the effective green time of the protected right-turn traffic e 1 is basically the same as the previous case.

7 710 K. TANG ET AL. Figure 4. Signal displays and time space diagram of permitted-and-protected right-turn traffic. L S2 ¼ L S1 D v (4) where D is the waiting area length (km) and v the free flow speed of the right-turn traffic (km/h) Permitted-only right-turn phasing The permitted-only right turners are also allowed to enter the intersection at the beginning of the permitted right-turn phase (1). However, they normally cannot immediately cross the intersection because of the presence of the opposing flow and have to stay in the waiting area, as illustrated in Figure 5. They then seek suitable gaps in the opposing flow to cross during the permitted right-turn phase, or after the opposing traffic flow completely clears at the end of the phase, or during the intergreen interval after the phase (23). Figure 5. Signal displays and time space diagram of permitted-only right-turn traffic.

8 A NEW LOST TIME ESTIMATION METHOD FOR TURNING TRAFFIC 711 Thus, the start-up lost time of the permitted right-turn phase can be regarded as that of the priority through and left-turn traffic. With respect to the clearance lost time, a part of the intergreen times at the end of the phase is usually used by the opposing through traffic and left-turn traffic to clear the intersection, that is, the extension of effective green time e TL. The rest of the intergreen interval is used by sneakers. If the stop bar of the approach is considered as a reference line, the necessary time for clearing sneakers e 2 can be computed by Equation (5) according to the fundamental diagrams and shock-wave theory [8,23]. Therefore, the clearance lost time of the permitted right-turn phase L C2 may be calculated by Equation (7), which takes sneakers into consideration and is thus different from the conventional methods. e 2 ¼ D u þ D v (5) where D is the waiting area length (km), u the shock-wave speed for the discharge flow of right-turn traffic (km/h) as derived by Equation (6), and v the free flow speed of right-turn traffic (km/h). S R u ¼ k J S (6) R v where S R is the saturation flow rate of right-turn traffic (veh/h), k J the jam density (veh/km), and v the free flow speed of right-turn traffic (km/h). L C2 ¼ ðy A þ AR A Þ e TL e 2 (7) where e TL is normally assumed as 2 or 3 s if Y 4 s or (Y + AR) 5 s in the current method. 4. VALIDATION OF THE PROPOSED METHOD 4.1. Data collection and reduction Seven intersections located in the urban area of Japan were selected to collect field data to validate the proposed method. Three of them were from Tokyo and four from Nagoya. The subject intersections are all typical four-leg intersections and have exclusive right-turning lanes at all approaches. Among these intersections, Hibiya (HY) and Sakurayama (SY) have protected-only right-turn phasing (Pro.); Tokyo Kokusai Forum Nishi (TN) has permitted-only right-turn phasing (Per.); and Kawana, Aoyama Ichome (AI), Suemori Tori, and Sunadabashi have permitted-and-protected right-turn phasing (Per. Pro.). The vast majority of vehicles consisted of passenger cars and small trucks; the pedestrian volumes were quite small at the subject intersections. Thus, the effects of heavy vehicles on discharge headway and that of pedestrians on right-turn behavior during changes in phases can be neglected. Table II outlines the relevant information of the subject intersections. Table II. Outline of the subject intersections and approaches. Inter. App. Phasing Observation time # of lanes Size (m) D (m) Y B (s) AR B (s) Y A (s) AR A (s) C (s) HY NB Pro. 7:00 9: SY NB 7:20 8: TN NB Per. 7:00 10: KN NB Per. Pro. 7:20 8: AI SB 7:00 10: ST SB 9:00 10: SB NB 17:00 19: HY, Hibiya; SY, Sakurayama; TN, Tokyo Kokusai Forum Nishi; KN, Kawana; AI, Aoyama Ichome; ST, Suemori Tori; SB (Inter.), Sunadabashi; NB, northbound; SB (App.), southbound; size, the distance between the opposite stop lines of the approaches; C, cycle length; D, waiting area length; Y B, yellow time before the permitted or protected right-turn phase; AR B, all-red time before the permitted or protected right-turn phase; Y A, yellow time after the permitted or protected right-turn phase; AR A, all-red time after the permitted or protected right-turn phase.

9 712 K. TANG ET AL. Field surveys were conducted during the peak hours and in good weather conditions. In addition to signal timing parameters, traffic volumes, and geometric parameters, data collection is carried out to observe the crossing time of right-turning vehicles at the stop bars of the approach and the waiting area. Data were reduced by using a lab-developed image processing software at a 1/30-s frame rate. With the use of the acquired data, speed, extension of the effective green time, saturation flow rate, and start-up and clearance lost times of the right-turn traffic were estimated cycle by cycle. Start-up and clearance lost times were calculated according to the HCM 2000 method, as described in the following. L S ¼ 4 H 1 þ...þ H 4 4 H 5 þ...þ H n n 4 (8) where H i is the time headway of the ith queued vehicle (s) and n the total number of queued vehicles. L C ¼ Y þ AR T E (9) where Y is the yellow time (s), AR the all-red time (s), and T E the entry time of the last cleared vehicle (s); the start of the intergreen time is regarded as the beginning time Validation results Table III compares the observed start-up lost times (M(L S1 ), M(L S2 )) and the observed extensions of the effective green times (M(e 1 )) with their corresponding estimates (E(L S2 ), E(e 2 )) Protected-only dual-lagging right-turn phasing. Intersections HY and SY were used to validate the proposed lost time estimation method for the protected-only dual-lagging right-turn phasing plan. As shown in Table III, the observed L S1 (i.e., M(L S1 )) of 0.40 and 0.08 s at the two intersections is much lower than the observed e 1 (i.e., M(e 1 )) of 1.73 and 2.62 s. The average difference between L S1 and e 1 is 2.33 s. This implies that the current methods tend to overestimate lost time. The observed L S1 at HY is slightly smaller than that at SY. This may be because there is no all-red interval (AR B ) between the right-turn green arrow and the yellow interval for through and left-turn traffics, which makes right turners feel safer in entering the intersection. A slightly longer yellow time (Y B ) at HY may also have contributed to the difference. e 1 at HY was almost 1 s shorter than that at SY. This might be due to the longer intergreen times after the right-turn green arrow (Y A, AR A ) at SY, which can possibly induce more aggressive stop-line-crossing behavior. Table III. Observed and estimated start-up lost times and effective green time extensions of right-turn traffic. Inter. Phasing D (m) v (m/s) u (m/s) M(L S1 ) (s) M(L S2 ) (s) M(e 1 ) (s) E(e 2 ) (s) E(L S2 ) (s) HY Pro (n = 21) (n = 24) SY (n = 18) (n = 16) TN Per KN Per. Pro (n = 15) (n = 30) AI (n = 15) (n = 21) ST (n = 31) (n = 34) SB (n = 28) (n = 31) HY, Hibiya; SY, Sakurayama; TN, Tokyo Kokusai Forum Nishi; KN, Kawana; AI, Aoyama Ichome; ST, Suemori Tori; SB, Sunadabashi; Pro., protected-only right-turn phasing; Per., permitted right-turn phasing; D, waiting area length; v, free flow speed; u, shock-wave speed; L S1, the start-up lost times of right-turn traffic in the protected-only right-turn phase; L S2, the start-up lost times of right-turn traffic in the permitted right-turn phase; e 1, the effective green time extensions of right-turn traffic in the protected phase; e 2, the effective green time extensions of right-turn traffic in the permitted right-turn phase; n, sample size.

10 A NEW LOST TIME ESTIMATION METHOD FOR TURNING TRAFFIC Permitted-only right-turn phasing. Intersection TN was used to validate the proposed lost time estimation method for the permitted-only right-turn phasing. Because queue length of the subject right-turn traffic is shorter than eight vehicles per cycle at intersection TN, the real saturation flow rate could not be directly measured. Hence, when estimating e 2, a saturation flow rate of 1800 veh/h, a vehicle length of 4.5 m, and a stopping space of 1.5 m were assumed on the basis of the current manual in Japan [3]. Also, the free flow speed of right-turning vehicles was measured to be 28 km/h, and the waiting area length was 20 m at intersection TN. With the use of these parameters, the propagation speed u of the shock wave was calculated to be 4.87 m/s using Equation (6); thus, the estimated e 2 (i.e., E(e 2 )) was 6.68 s based on Equation (5). This result is understandable if one recognizes that, in the proposed method, e 2 is totally dependent upon the time that is required to clear the right turners in the waiting area, not necessarily the sum of Y and AR, that is, (Y + AR). An e 2 greater than (Y + AR) translates that right turners cannot clear from the intersection before the green onset of the next phase. According to the current manual, the estimated number of sneakers, K, at intersection TN is two vehicles per cycle in terms of intersection size. Assuming 2 s for the saturation headway, the equivalent e 2 based on the current method is 4 s, which is significantly smaller than the estimated value of 6.68 s based on the proposed method. This indicates that the current method may underestimate the capacity for sneakers. In contrast, the proposed method offers better estimation by accounting for the waiting area length and free flow speed. According to the proposed method, it is possible that the estimated e 2 is larger than (Y + AR). In the case of permitted-only right-turn phase, the effective time used by right-turn traffic is dependent upon the time that is required to clear the right turners in the waiting area Permitted-and-protected right-turn phasing. Intersections Kawana, AI, Suemori Tori, and Sunadabashi were used to validate the proposed lost time estimation method for the permitted-and-protected right-turn phasing. L S1 at intersection HY was measured to be 0.40 s, which was used to estimate L S2 at the four intersections. This was because the yellow and all-red intervals before the onset of the rightturn green arrow (Y B, AR B ) at the four intersections were closer to those at intersection HY. In addition, the measured free flow speeds and waiting area lengths at the four intersections were applied as well. The differences between the observed L S2 (i.e., M(L S2 )) and the estimated L S2 (i.e., E(L S2 )) were found to fall in the range of 0.39~1.19 s. Such discrepancies can be attributed to the measurement errors in v and/or L S1. First, there may be an error in the measurement of v because of the limited sample size and complex maneuver of a turning vehicle. Second, the measured L S1 at intersection HY might not be exactly identical to those at the four intersections. At intersection HY, although some aggressive right turners start to move after the opposing flow is cleared, most of the right turners comply with the signals and do not move until the onset of the right-turn green arrow. However, at the four intersections, right turners can move as soon as the opposing flow clears without the need to wait for the onset of the rightturn green arrow. Thus, different driver behaviors may also contribute to the difference in L S1. In contrast, the measured e 1 (i.e., M(e 1 )) at the four intersections was found to be very close to one another. The slightly lower value at intersection AI may be due to its relatively short intergreen time after the right-turn green arrow (Y A + AR A ). The measured e 1 values at the four intersections were almost identical to that at intersection SY with (Y A + AR A ) of 7 s, but they were a bit higher than that at intersection HY, which had (Y A + AR A ) of 5 s. This result suggests that the extension of the effective green time for right-turn traffic is greatly influenced by the length of the intergreen time (Y A + AR A ) after the right-turn green arrow. 5. APPLICATION OF THE PROPOSED METHOD For a demonstration of the application of the proposed method, this section presents a series of case studies comparing signal timing parameters based on the current procedure illustrated in Figure 2 and the modified procedure by incorporating the proposed method Base assumptions of case studies Table IV presents the assumed conditions for case studies, including design traffic volumes, design speeds, signal phasing plans, intersection sizes, and basic intersection configurations. To avoid

11 714 K. TANG ET AL. Table IV. Assumed traffic conditions for case studies. Design traffic volumes (veh/h) Intersection size (m) EB SB WB NB L T R L T R L T R L T R Protected only, dual 1-A (D = 15.0) lagging 1-B (D = 22.5) 1-C (D = 30.0) Permitted only 2-A (D = 10.0) 2-B (D = 15.0) 2-C (D = 20.0) 3-A (D = 15.0) 3-B (D = 22.5) 3-C (D = 30.0) Intersection configuration Permitted and protected SB SB SB WB V=60km/h EB WB V=60km/h EB WB V=60km/h EB NB Protected-only (Pro.) NB Protected-only (Pro.) NB Protected-only (Pro.) EB, eastbound; SB, southbound; WB, westbound; NB, northbound; T, through; L, left; R, right.

12 A NEW LOST TIME ESTIMATION METHOD FOR TURNING TRAFFIC 715 complex calculations due to gap acceptance, we maintained design traffic volumes for through traffic at a level where gap acceptance was impossible. A flow of over 1000 veh/h was used in the case studies according to the current manual in Japan. Demand ratios were set between 0.65 and To investigate the sensitivity of the lost time and signal timing parameters to the length of the waiting area, we included various intersection sizes, which are denoted by A, B, and C. Intersection configurations were considered to be completely symmetrical for simplicity. The lengths of the waiting area were calculated on the basis of intersection size; the distance between the opposite stop bars for the waiting areas was assumed to be 10 m. A basic saturation flow rate of 1800 veh/h per lane was assumed for the exclusive right-turning lanes and 2000 veh/h per lane for the other lanes. The adjustment factors for lane width, grade, and heavy vehicles were 1, 1, and 0.97, respectively. In addition, when adopting the current procedure, the number of sneakers, K and K ER, was determined to be two vehicles per cycle on the basis of the intersection sizes. For the modified procedure, L S1 and e 1 should be modeled by Y B, AR B, Y A, and AR A in an ideal case. However, this was not realistic in this study because of insufficient observation data. Thus, a simplified method was used in the case studies in which the observed value for L S1 at intersection HY, 0.40 s, and the average ratio of e 1 to (Y A + AR A ), 0.39, observed at all subject intersections except TN were used to estimate L S1 and e 1. An average stopping distance of 1.5 m, mean vehicle length of 4.5 m, and free flow speed of 30 km/h were assumed to estimate the shock-wave speed u according to Equation (6) Signal timing results of case studies Given the inputs presented in Table IV, the yellow and all-red times were first determined by intersection size and speed limit for each type of phasing plan. For the permitted-and-protected right-turn phasing plan, there was no all-red time inserted between the yellow interval for through and left-turn traffic and the right-turn green arrow. Saturation flow rate for each traffic movement was then estimated in accordance with the current manual [3]. The lost times of the right-turn traffic were estimated using the current and proposed methods separately. However, when adopting the modified procedure, the start-up lost time for the through and left-turn traffic was assumed to be 2 s, and the extensions of the effective green time dependent upon the intergreen times were assumed to be 2 or 3 s. Subsequently, the optimum cycle length calculated by Equation (1) or the closest value was used to allocate green times. Table V presents the signal timing results. For the protected-only dual-lagging right-turn phasing, the difference in the total lost time estimated by the two methods was found to be between 1.5 and 3 s; the difference increased with intersection size. Although the differences in lost time were not very remarkable, they can cause noticeable variations in the cycle length ranging from 10 to 21 s. As the demand ratios are the same, the calculated green times for the two procedures are close. For the permitted-only right-turn phasing, the estimated lost times of the proposed method were significantly lower than that of the existing method. The differences increased with the intersection size because the proposed method is more sensitive to the length of the waiting area D. On the other hand, the demand ratio was higher in the modified procedure because sneakers were excluded from the calculation of the demand ratio in the current procedure. These two effects cancelled each other out, leading to the result that the cycle lengths based on the modified and current procedures were fairly close for case 2-A, whereas the modified procedure produced a cycle length almost half that produced by the current method for cases 2-B and 2-C. For the permitted-and-protected right-turn phasing, a similar trend as the previous phasing plan was found. The modified procedure estimated considerably shorter lost times than the current procedure, while producing higher demand ratios. As a result, the calculated cycle lengths based on the current and modified procedures were close for case 3-A. However, the modified procedure reduced the cycle length by 10% for case 3-B and by 24% for case 3-C. 6. CONCLUSIONS AND FUTURE STUDIES A new lost time estimation method, based on the time space diagram and shock-wave theory, was presented for the left-turn traffic at signalized intersections. It accounts for the various signal phasing and

13 716 K. TANG ET AL. Table V. Signal timing results of case studies. Ф1 (s) Ф2 (s) Ф3 (s) Ф4 (s) G Y AR G Y AR G Y AR G Y AR C P (Y + AR) l 1 L S + L C l 2 L S + L C l 3 L S + L C l 4 L S + L C P l P (LS + L C ) Pro. 1-A Existing Proposed B Existing Proposed C Existing Proposed Per. 2-A Existing Proposed B Existing Proposed C Existing

14 A NEW LOST TIME ESTIMATION METHOD FOR TURNING TRAFFIC 717 Ф2 (s) Ф3 (s) Ф4 (s) G Y AR G Y AR G Y AR G Y AR C P (Y + AR) Ф1 (s) P P l1 LS + LC l2 LS + LC l3 LS + LC l4 LS + LC l (L S + LC) Proposed Per. Pro. 3-A Existing Proposed B Existing Proposed C Existing Proposed Pro., protected-only right-turn phasing; Per., permitted right-turn phasing.

15 718 K. TANG ET AL. driver behavior more elaborately. It also integrates sneaker assessment into signal timing process in closed form. The method was developed, validated, and demonstrated, focusing on right-turn traffic in Japan, where left-hand traffic is applied. Results showed that, as compared with previous methods, the proposed method offers more accurate lost time estimation by considering the waiting area length and vehicle speed. Its application in signal timing procedure allows for the avoidance of iterative calculations to estimate the sneaker capacity and thus simplifies signal timing process. In addition, the proposed method can also produce shorter cycle lengths, especially for permitted-only and permitted-and-protected right-turn phasing plans. Future studies are necessary to improve the proposed method, such as its modeling and prediction of the start-up and clearance lost times of the protected right-turn phase L S1 and L C1.In addition, the occurrence of gap acceptance was not considered in the case studies. Further analysis thus needs to be carried out to examine the differences in signal timing parameters with the presence of gap acceptance. ACKNOWLEDGEMENTS This study was financially supported by a research grant of the Japan Society for the Promotion of Science (JSPS, no. P08396). The authors also convey their sincere appreciation to Prof. Takashi Oguchi of The University of Tokyo, Prof. Hideki Nakamura of Nagoya University, and Prof. Edward Chung of Queensland University of Technology for their insightful inputs to this study. REFERENCES 1. Webster FV. Traffic signal settings. Road Research Technical Paper No. 39, Road Research Laboratory, Her Majesty Stationary Office, London, UK, ITE. Traffic Signal Timing Manual. Institute of Traffic Engineers: Washington, D.C., JSTE. Revised Edition of Manual on Traffic Signal Control. Japan Society of Traffic Engineers: Tokyo, FGSV. Handbuch fuer die Bemessung von Strassenverkehrsanlagen (Highway Capacity Manual). Forschungsgesellschaft fuer Strassen- und Verkehrswesen: Cologne, ARRB. Traffic Signals: Capacity and Timing Analysis. Research Report. Australian Road Research Board: Victoria, UK Department of Transport. Traffic Advisory Leaflet: General Principles of Traffic Control by Light Signals. UK Department of Transport: London, Tang K, Nakamura H. A comparative study on traffic characteristics and driver behavior at signalized intersections in Germany and Japan. Journal of the Eastern Asia Society for Transportation Studies 2007; 7: Ngoduy D. Multiclass first-order traffic model using stochastic fundamental diagrams. Transportmetrica 2011; 7(2): Fang C, Elefteriadou L. Modeling and simulation of vehicle projection arrival discharge process in adaptive traffic signal controls. Journal of Advanced Transportation 2010; 44(3): Bonneson JA, McCoy PT. Driver understanding of protected and permitted left-turn signal displays. Transportation Research Record 1994; 1464: Sheffer C, Janson BN. Accident and capacity comparisons of leading and lagging left-turn signal phasings. Transportation Research Record 1999; 1678: Noyce DA, Fambro DB, Kacir KC. Traffic characteristics of protected/permitted left-turn signal displays. Transportation Research Record 2000; 1708: Noyce DA, Kacir KC. Driver understanding of simultaneous traffic signal indications in protected left turns. Transportation Research Record 2002; 1801: Brehmer CL, Kacir KC, Noyce DA, Manser MP. Evaluation of traffic signal displays for protected/permissive left-turn control. NCHRP Report 493, Transportation Research Board, Washington, D.C., Knodler MA, Noyce DA, Kacir KC, Brehmer CL. Evaluation of traffic signal displays for protected permissive leftturn control using driving simulator technology. Journal of Transportation Engineering 2005; 131(4): Tang K, Nakamura H. Operational performance of group-based signal control policy under various traffic conditions. Proceedings of the 10th International Conference on Applications of Advanced Technologies in Transportation, Athens, 2008 (CD-ROM). 17. Tang K, Nakamura H. Safety evaluation for intergreen intervals at signalized intersections based on probabilistic method. Transportation Research Record 2009; 2128: Shikata S, Katakura M, Oguchi T, Murai N. An analysis on lost time with the change of right-turn phases. Proceeding of Traffic Engineering Meeting 2003; 23:57 60.

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