A Proposal for the Estimation of Loss Time of Right-turn Traffic at. Signalized Intersections in Japan

Transcription

1 A Proposal for the Estimation of Loss Time of Right-turn Traffic at Signalized Intersections in Japan Keshuang Tang, Dr. -Eng JSPS Research Fellow Takeshi Ono Master Course Student Shinji Tanaka, Dr. -Eng Lecturer Masao Kuwahara, Ph. D Professor kuwahara@iis.u-tokyo.ac.jp Institute of Industrial Science The University of Tokyo Komaba, Meguro-ku, Tokyo Japan Tel: (81) , Fax: (81) Submitted for the presentation at the 89 th Annual Meeting of the Transportation Research Board (TRB) and publication in the Transportation Research Record Paper Length: 5,041 words in text 2,500 words in 10 tables and figures 7,541 words in total Tokyo, Japan November 15, 2009

2 ABSTRACT In the planning stage, loss time with the change of phases at signalized intersections is simply determined by the length of intergreen interval in the existing method in Japan. In addition, the drivers completing right turns (comparable to left-turns in the United Sates) during the effective red portion of intergreen interval are roughly considered to be 1~3 vehicles per cycle, dependent upon phase switching pattern and intersection scale. To better account for the unique features of signal phasing and driving behavior of right-turners in Japan, this paper proposes a new method particularly for the estimation of loss time of right-turn traffic. Start-up and clearance loss times under three conventional phasing plans, protected-only right-turn, permissive-only right-turn, and permissive-and-protected right-turn, were first theoretically analyzed, based on time-space diagram and shock-wave theory. Then, field data collected at 7 intersections was used for validation. Results showed that the existing method in Japan tends to provide improper estimation, and the proposed method is however capable of offering good accuracy. Finally, a series of case studies were conducted to demonstrate the application of the new method. Conclusions supported that the new method can more sophisticatedly assess loss time in terms of the length of waiting area and bring short cycle lengths when demand ratio is between 0.65 and Also, it is able to simplify signal timing procedure to certain extent by eliminating an iterative check of discharge flow rate of right-turn traffic and cycle length. KEY WORDS: Right-turn traffic, Left-turn traffic, Loss Time, Shock-wave, Time-space Diagram - 1 -

3 INTRODUCTION Tang, et al Loss Time with the Change of Phases To avoid traffic conflicts during the change of phases at signalized intersections, yellow and all-red times are designed to clear traffic movements released in the previous phase so as to give right of way to traffic movements released in the subsequent phase. Due to the clearing process, some portion of intergreen time is normally not used by traffic, leading to clearance loss time, L c, and the onset of green of conflicting streams in the next phase is delayed, leading to start-up loss time, L s. As depicted in Figure 1, L s is the sum of starting response time of the first vehicle in queue and the additional time it took the first several queued vehicles to discharge. L c refers to the part of intergreen time during which an intersection is not used by any traffic. L s and L c can be observed in the fully saturated situation and usually computed as follows according to Highway Capacity Manual 2000 (1). Rate of discharge of queue in fully saturated green period Start-up lost time, ls Saturation flow Effective green time Extension of effective green Clearance loss time, lc Time R G Y AR R Figure 1 Start-up loss time and clearance loss time - 2 -

4 4 Tang, et al 4 (1) 4 Where, H i =time headway of the ith queued vehicle (s); n=total number of the queued vehicles. (2) Where, Y=yellow time (s); AR=all-red time (s); T e =entry time of the last cleared vehicle, regarding the start of intergreen as the beginning time (s). Properly estimating loss time with the change of phases is crucial for the determination of optimal cycle length as a small variation of loss time may cause a large change in cycle length according to Webster formula (2) shown below Where, C=optimal cycle length (s); L=loss time of one cycle (s); λ=demand ratio. (3) State of the Art of Loss Time Estimation in Japan As presented in Figure 2, there are generally three types of signal phasing plans in Japan, namely protected-only dual lagging right-turn (comparable to left-turn in US), permissive-only right-turn, and permissive-and-protected right-turn. In the first phasing plan, right turners wait before the stop-line for the onset of right-turn green arrow, while right-turners wait inside intersection to seek suitable gaps to cross and discharge after the opposite traffic completely clears in the latter two phasing plans. According to the current Japanese Manual on Traffic Signal Control (MTSC hereafter, (3)), loss time with the change of phases is roughly estimated by Eq. (4) in the planning stage. The fundamental assumption underlying the equation is that start-up lost time, L s, is equal to the extension of effective green, e. The compensation to loss time, n, is to account for the additional extension of effective green in the case of fairly long intergreen intervals. (4) Where, L=loss time of one cycle (s); Y=yellow time (s); AR=all-red time (s); j=a change of phases; n=number of the change of phases with Y 4s or (Y+AR) 5s

5 Phasing Plan Loss Time Estimation Note Protected-Only Dual lagging Right-turn Φ1 Φ2 Φ3 Φ4 Eq. (4) Permissive-Only Right-turn Φ1 Φ2 Eq. (4) (Sneakers:K=2 or 3 veh/cycle) D Permissive-and Φ1 Φ2 Φ3 Φ4 Eq. (4) -Protected Right-turn (Sneakers: K ER =1 or 2 veh/cycle) (D=waiting area length) Figure 2 Three types of right-turn phasing plans commonly adopted in Japan However, the basic assumption that L s is equal to e is very doubtable for right-turn traffic. The reason is that right-turners at signalized intersections in Japan are normally able to predict the onset of green from the previous signal displays, leading to small L s (Tang and Nakamura, (4)), and easily to run red light due to long all-red time, leading to large e (Tang and Nakamura, (5); Kimura et al. (6); Shikata et al. (7)). The combination of the above facts may result in a big difference between L s and e, which is not consistent with the assumption. In addition, instead of a time-based concept, a vehicle-based concept has been adopted in MTSC to account for the drivers completing right turns during the effective red portion of the clearance-and-change interval, sneakers according to HCM Provided an exclusive right-turn lane, 1 vehicle per cycle at small intersections and 2 vehicles per cycle at large intersections (i.e., K ER according to MTSC) are recommended for the permissive-and-protected right-turn phasing plan when permissive phases, i.e., Ф1 and Ф3, switch to protected phase, i.e., Ф2 and Ф4. 2 vehicles per cycle at small intersections and 3 vehicles per cycle at large intersections (i.e., K according to MTSC) are recommended for the permissive-only right-turn phasing plan when Ф1 changes to Ф2. In the current signal timing procedure presented in Figure 3, those sneakers are excluded from the total demand prior to the calculation of demand ratio (step (4) in Figure 3). In other words, such a part of demand is not directly considered in signal timing process. Due to that, a hypothesized cycle length has to be set before step (4). Afterwards, - 4 -

6 from Eq. (4) and the calculated demand ratio, an optimum cycle length is computed based on Eq.(3) (step (6) in Figure 3). Then, split ratios and green times are calculated based on that (step (7) in Figure 3). If all the right-turn traffic can be processed together with other traffics with a reasonable degree of saturation, e.g., less than 0.90, signal timing is completed. Otherwise, cycle length and/or signal phasing plan will be adjusted according to the result of step (6) to ensure minimum green time and discharge flow rate of turning traffic, and repeat the previous steps again till reaching the goal. Such an iterative calculation process is quite trivial and time-consuming. Redesign signal phasing plan if demand ratio is greater than 0.9 Choose the signal phasing plan with minimum demand ratio considering safety if multiple signal phasing plans are available (1) Determine design traffic volumes (2) Determine signal phasing plan (3) Estimate saturation flow rate (5) Determine yellow and all-red times A vehicle-based concept to estimate sneaker is introduced (4) Calculate demand ratio (8) Check discharge flow rate of turning traffic Eq. (4) is introduced When saturation flow rates of left-turning and right-tuning lanes are dependent upon cycle length and split (6) Calculate cycle length (7) Calculate split ratio Modify cycle length to ensure minimum green time (9) Examination of area control Figure 3 The current signal timing procedure recommended by MTSC To better account for the unique features of signal phasing and driving behavior of right-turners in Japan, this study thus intends to propose a new method for the estimation of loss time of right-turn traffic, based on time-space diagram and shock-wave theory. The rest of the paper is organized as follows. Section 2 reviews the existing research on loss time estimation

7 Section 3 introduces the proposed method for the estimation of loss time of right-turn traffic. Section 4 validates the proposed method by the use of field data. Section 5 presents several case studies to demonstrate the application of the proposed method. Conclusions and future studies are highlighted in Section 6. Acknowledgements to those people who have contributed to this work are given in Section 7. LITERATURE REVIEW For the operation stage, a few empirical studies have investigated the influence of signal display sequence, phasing and timing on loss time. Bonneson and McCoy (8) evaluated driver s starting response time, a part of start-up loss time, to the leading left-turn indication. No significant difference among five PPLT (protected-permitted or permitted-protected left turn) signal displays was found. Chris Sheffer et al. (9) compared start-up lost time between lead and lag protected-only phasing. It was found to be smaller for the locations with lag phasing than with lead phasing. No difference in start-up lost time was found due to the type of PPLT signal display by Noyce et al. (10). Other studies by Tang and Nakamura ((4), (5), and (11)) showed that signal display sequence has significant effect on starting response time, and signal timing significantly affects clearance lost time as well. There is also some research done in Japan that particularly looked at loss time of right-turn traffic under various phasing plans. Shikata et al. (7) compared start-up loss time under permissive-and-protected and protected-only right-turn phases, and found that it goes up by 0.5 s with the increase of one vehicle waiting inside intersection. Also, the whole yellow is often completely used, and part of all-red is sometimes used. Ono et al. (12) focused on loss time under protected-only right-turn phase, and found that the observed total loss time is quite smaller than the estimated value based on Eq. (4). For the planning stage, the method to estimate loss time varies across the world due to distinct traffic circumstance. According to (1), (3), and (13)~(15), an assumption is often made in USA, Japan, Germany and Australia that the extension of effective green is equal to start-up loss time, averagely 2s. Thus, the total loss time, L, is approximated as the sum of intergreen times, I, i.e., L=I. However, some modifications have also been suggested. For instance, an extra 1 or 2s for a change of phases may be added in USA if yellow is not the legal go time, i.e., L=(I+1) or (I+2). As introduced earlier, 1s is substituted when Y 4s or (Y+AR) 5s in Japan, i.e., L=(I-1). Those treatments are to account for the change of driver s stop-line crossing behavior due to the definition of yellow signal and the length of intergreen interval. Unlike the other countries, the sum of start-up loss time and the unused yellow is often assumed as 2s in UK according to (2) and (16), which leads to a total loss time of (I-1) as Y is standardized at 3s. It is likely because a - 6 -

8 two-second of yellow-and-red signal is applied before the onset of green, which could significantly reduce start-up loss time implied by (11). Moreover, a practical minimum value is imposed on left-turn adjustment factor, f m, to account for sneakers in HCM 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, e.g., it becomes 2 vehicles per cycle given an exclusive left-turn lane correspondent to P L =1. Assuming an approximate average headway of 2 s per vehicle in an exclusive lane on a protected phase, the practical minimum value of 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 enter and depart the intersection during the yellow or red intervals (1). In summary, despite empirical studies have discovered several factors influencing loss time, they haven t been taken into consideration when estimating loss time in the planning stage. Loss time is still solely determined by the length of intergreen interval so far. Furthermore, the vehicles completing right turns (or left turns in the case of right hand traffic) during the effective red portion of intergreen interval are not sophisticatedly and straightforwardly considered in the loss time estimation as well as in the signal timing procedure. Therefore, the purpose of this study is to develop a new method for the estimation of right-turn traffic in order to overcome the aforementioned drawbacks. THE PROPOSED METHOD FOR THE ESTIMATION OF LOSS TIME OF RIGHT-TURN TRAFFIC IN JAPAN In the following part, time-apace diagram and shack-wave theory are adopted to reproduce vehicle trajectory of right-turn traffic under three conventional phasing plans in Japan. Based on that, loss times of right-turn phases are analyzed theoretically. For simplification, arrival pattern of traffic is assumed to be uniform, and acceleration and deceleration times of vehicles are assumed to be zero in the time-space diagram. Protected-only Dual Lagging Right-turn Phasing In the phasing plan of protected-only dual lagging right-turn, right-turners are able to predict the start of right-turn green arrow (3) via the previous yellow for through and left-turn traffics (2), and thus very likely start to move before the onset of right-turn green arrow, as illustrated in Figure 4. Therefore, start-up lost time of right-turn traffic movement, L s1 (i.e., start-up loss time of the protected right-turn phase) is possible to be very small. Moreover, it has been reported in literature that quite a lot of right-turners enter intersection even after the start of red as mentioned - 7 -

9 earlier, which leads to a large extension of effective green, e 1 ( i.e., the extension of effective green of the protected right-turn phase). Distance Stop bar Ls1 e1 ➊ ➋ ➌ ➍ AR ➎ Time Figure 4 Time-space diagram of protected-only right-turning traffic Thus, L s1 is supposed to be influenced by intergreen times before the right-turn green arrow (2), usually yellow only but including all-red in some cases. e 1 should be dependent upon intergreen times after the right-turn green arrow (45). Permissive-only Right-turn Phasing In the permissive-only right-turn phasing plan, although right-turners can enter the intersection at the beginning of the permissive right-turn phase, they are normally unable to cross the intersection because of the presence of the opposing flow and have to wait inside the intersection, as illustrated in Figure 5. They seek suitable gaps of the opposing flow to cross within the phase (1), or pass the intersection after the opposing traffic flow completely clears at the end of the phase and intergreen time interval behind the phase (23). Thus, start-up loss time of the priority through and left-turn traffics can be regarded as that of the permissive right-turn phase. At the end of the phase, a certain part of intergreen time interval is usually used by through and left-turn traffics to clear, e TL, i.e., the extension of effective green. Afterwards, another part of intergreen time interval is used by the right-turners - 8 -

10 inside the waiting area to discharge. Based on the time-space diagram, the time necessary for clearing all the right-turners inside the waiting area, e 2, can be computed by Eq. (5). As a result, clearance loss time of the permissive right-turn phase, L c2, may be calculated by Eq. (6). (5) Where, D=the length of waiting area, refer to Figure 2, km; u=shock-wave speed of discharge flow of right-turn traffic, km/h, which can be derived by Eq. (7) as explained in the figure. (6) Where, e TL is normally assumed as 2s (3s if Y 4s or (Y+AR) 5s in the existing method) / Where, S r =saturation flow rate of right-turn traffic, veh//h; k j =jam density, veh/km; v=free flow speed, km/h. (7) Distance Stop bar D ➊ ➋ ➌ e2 q s r u AR Time v u k j Relationship between traffic volume and density Figure 5 Time-space diagram of permissive-only right-turning traffic k - 9 -

11 Permissive-and-Protected Right-turn Phasing Tang, et al In the permissive-and-protected right-turn phasing plan, right-turners can enter the intersection after the start of the permissive right-turn phase, and however they usually cannot cross the intersection right away due to existence of the opposing flow as discussed previously. They either find acceptable gaps to pass during the permissive right-turn phase, or discharge after the opposing flow clears, which includes the last part of permissive right-turn green phase (1) without the opposing flow, intergreen interval before the right-turn green arrow (2), the following protected right-turn phase(3), and intergreen interval after that (4), as illustrated in Figure 6. In the latter case, right-turning vehicles are legal to move right after the clearance of the last opposite through vehicle, without the need to wait for the onset of right-turn green arrow. Therefore, similar to the previous case, start-up loss time of the permissive right-turn phase can be treated as that of through and left-turn traffics. Meanwhile, start-up loss time of right-turn traffic movement at the beginning of the protected right-turn phase, L s2, could be significantly lower than that of protected-only right-turn phasing plan, L s1, owing to the first right-turner s start-up position. Based on the time-space diagram depicted in Figure 6, the relationship between L s1 and L s2, can be expressed by Eq. (8). In addition, the extension of effective green at the end of the protected right-turn phase can be considered same as the previous case, clearance loss time as well. (8) Where, D=the length of waiting area, km; v=free flow speed of right-turn traffic, km/h

12 Distance Ls1 Stop bar v ➊ ➋ ➌ ➍ ➎ AR Ls2 e1 D Time Figure 6 Time-space diagram of Permissive-and-Protected right-turning traffic VALIDATION OF THE PROPOSED METHOD Data Collection and Reduction In order for the validation of the proposed method, video surveys were conducted at 7 intersections located in urban area, 3 in Tokyo and 4 in Nagoya. The subject intersections are all typical four-leg intersections and have exclusive right-turning lanes at all approaches. Out of them, Hibiya (HY) and Sakurayama (SY) are protected-only right-turn phasing (Pro.), Tokyo-Kokusai-Forum-Nishi (TN) is permissive-only right-turn phasing (Per.), and Kawana (KN), Aoyama-Ichome (AI), Suemori-Tori (ST), and Sunadabashi (SB) are permissive-and-protected right-turn phasing (Per.-Pro.). Moreover, the vast majority of vehicles consist of passenger cars and small trucks, and pedestrian volumes were quite small at the selected intersections. Thus, the effects of heavy vehicles on discharge headway as well as the influence of pedestrians on right-turning vehicles behavior during the change of phases can be neglected in this study. Table 1 outlines the relative information on the subject intersections. Surveys were undertaken mostly during saturated time period and in good weather conditions. In addition to signal timing parameters, traffic volumes and basic geometric

13 parameters, data collection is mainly to observe crossing time of right-turning vehicles at the stop-line as well as the stopping bar of waiting area. Data reduction was done by a lab-developed image processing software with a 1/30 second resolution. Based on the acquired data, speed, the extension of effective green, saturation flow rate, and start-up and clearance loss times of right-turn traffic were calculated cycle by cycle. Among them, start-up and clearance loss times were measured by following Eq. (1) and (2) respectively. Validation Table 2 presents the measured and estimated parameters as well as loss times at the subject intersections

14 Tang, et al Table 1 Outline of the subject intersections and right-turn movements Inter. App. Phasing Time # of lanes Size (m) D (m) Y b (s) AR b (s) Y a (s) AR a (s) C (s) HY NB 7:00-9: ~144 Pro. SY NB 7:20-8: ~158 TN NB Per. 7:00-10: ~146 KN NB 7:20-8: AI SB 7:00-10: ~153 Per.-Pro. ST SB 9:00-10: SB NB 17:00-19: (Size=the distance between the opposite stop-lines; Y b, AR b =yellow and all-red before the onset of right-turn green arrow (cycle green in case of Per.); Y a, AR a =yellow and all-red time after the right-turn green arrow (cycle green in case of Per.); C=cycle length) Table 2 Observed and estimated parameters as well as loss times at the subject intersections Inter. Phasing M(L s1 ) M(L s2 ) M(e 1 ) E(e 2 ) 1 D v E(Ls 2 ) 2 M(L s2 ) -E(L s2 ) Y a +AR a e 1 /( Y a +AR a ) (s) (s) (s) (s) (m) (m/s) (s) (s) (s) (s) HY (21) (24) Pro. SY 0.08 (18) (16) TN Per KN (15) 2.70 (30) AI (15) 2.13 (21) Per.-Pro. ST (31) 2.67 (34) SB (28) 2.83 (31) (M()=measured; E()=estimated; 1=estimated by Eq. (5); 2=estimated by Eq. (8); (#)=number of valid sample cycles)

15 Protected-only Right-turn Phasing Intersections HY and SY were observed to validate the proposal for loss time estimation in the case of protected-only right-turn phasing. The observed start-up loss times, L s1, -0.40s and 0.08s, are much lower than the extensions of effective green, e 1, 1.73s and 2.62s at the two intersections, as shown in the table. It implies that the existing method tends to provide overestimation for loss time of right-turn traffic. Possible explanations have been given before that long intergreen times before the start of right-turn green arrow may induce hurry start behavior of right-turners. It is worthy of mentioning that the observed L s1 at HY is slightly smaller than that at SY. The reason could be that there is no all-red between the yellow for through and left-turn traffics and the right-turn green arrow so that right-turners may feel easier or safer to enter the intersection. Slightly longer yellow time at HY may have somehow contributed to such a difference as well. It was also found that e 1 at HY is almost 1s smaller than that at SY. It is perhaps due to the longer intergreen time after the right-turn green arrow at SY, 2s, which may have induced more aggressive stop-line crossing behavior. Permissive-only Right-turn Phasing Plan Intersection TN was observed to validate the proposal for loss time estimation in the case of permissive-only right-turn phasing plan. When estimating the necessary time of clearing right-turners inside waiting area, e 2, a saturation flow rate of 1800 veh/h, a vehicle length of 4.5m and a stopping space of 1.5m are assumed based on MTSC. Also, free flow speed of right-turning vehicles was measured to be 28km/h and the length of waiting area to be 20m at TN. Propagation speed of shock-wave, u, was thus calculated to be 4.87m/s by Eq. (7), and e 2 to be 4.11s by Eq. (5), which are essential to estimate clearance loss time, L c2. If the existing method was adopted, the estimated number of sneakers at intersection TN would be 2 or 3 vehicles per cycle according to its size. Considering a 2s of average saturation headway, the estimated e 2 value by the proposed method, 4.11s, is very close to the result by the existing method if 2 veh/cycle was applied. However, the existing method may produce an evident overestimation for the ability to process sneakers if 3 veh/cycle was applied, considering a 7s of intergreen interval at the intersection. It suggests that the proposed method is capable of offering a more sophisticated and accurate estimation of loss time as compared with the existing method. Permissive-and-Protected Right-turn Phasing Plan Intersections KN, AI, ST, and SB, were observed to validate the proposal for loss time

16 estimation in the case of permissive-and-protected right-turn phasing plan. The measured L s1 at HY, -0.40, was used to estimate L s2 at the four intersections by Eq. (8) as yellow and all-red times before the onset of right-turn green arrow at the four intersections are quite close to those at HY. In addition, the measured free flow speeds of right-turn traffic and lengths of waiting area at the four intersections were used as well. It was found that the difference between the measured and estimated L s2 ranges from 0.39 to 1.19s. In essence, no error should take place if all the parameters were correctly measured. Thus, such errors can be attributed to two factors, v and L s1. First, the observation of v may not be very accurate due to the limited sample size as well as complex speed change of turning maneuver. Second, the measured L s1 at HY may not be exactly same as those at the four intersections. A possible explanation is that, in the former case most of right-turners would start to move earlier than the onset of right-turn green arrow if the opposing flow has cleared, but a small part of them may still comply signals, i.e., start to move after the onset of right-turn green arrow. However, in the latter case, right-turners would immediately move as soon as the opposing flow clears, without the need to wait for the onset of right-turn green arrow. Due to such a difference, start-up loss time may become varied as well. On the other hand, the measured e 1 at the four intersections was found to be very close to one and another, in spite of a slightly lower value at AI perhaps due to its shorter Y a and AR a shown in Table 1. The measured values are almost identical as that at SY with a 7s of (Y a +AR a ), but a little bit higher than that at HY, 5s. This result can be well interpreted by the length of (Y a +AR a ), as discussed before. APPLICATION OF THE PROPOSED METHOD To demonstrate the application of the proposed method, this part presents a series of case studies which design signal parameters based on the current signal timing procedure introduced in Figure 3 and the modified procedure by replacing the current loss time estimation method with the proposed one. The only difference between them is that, instead of Eq. (4) (step (6) in Figure 3) and a vehicle-based concept to estimate sneakers (step (4) in Figure 3), the proposed loss time estimation method is adopted before the calculation of cycle length in step (6). Assumed Basic Conditions for Case Studies Table 3 presents the assumed conditions for case studies, including design traffic volumes, design speeds, signal phasing plans, intersection sizes, and basic intersection configurations. In order to eliminate the complex calculation of capacity of right-turn traffic at the presence of gap-acceptance, design traffic volumes of through traffics were maintained over 1,000 veh/h

17 according to MTSC. Demand ratios between 0.65 and 0.8 were included in the analysis. To investigate the sensitivity of loss time as well as signal timing parameters to the length of waiting area, various intersection sizes were assumed, indicated by A, B and C. Intersection configurations were considered to be complete symmetrical to reduce computation efforts. In addition, K and K ER were determined as 2 veh/cycle according to intersection sizes when adopting the current procedure. The lengths of waiting area were derived based on the assumed intersection size by assuming a distance between the opposite stop-bars of waiting area of 10 m. Basic saturation flow rates were assumed to be 1800 veh/h/l for the exclusive right-turning lanes and 2000 veh/h/l for the other lanes. Adjustment factors for lane width, grade, and heavy vehicle were 1.00, 1.00, and 0.97 respectively. Signal Timing Results of Case Studies Given basic inputs in Table 3, yellow and all-red times are first determined for each type of phasing plan from intersection size and design speed, and saturation flow rate for each traffic movement was estimated in accordance with MTSC. Note that there was no all-red time inserted between the yellow for through and left-turn traffics and right-turn green arrow in the case of permissive-and-protected right-turn phasing plan. Then, loss times of right-turn traffic were estimated by following the current method and the proposed method separately. However, 2s was assumed for start-up loss time and 2s or 3s for the extension of effective green of through and left-turn traffics according to intergreen time lengths, when applying the modified procedure. Subsequently, the optimum cycle length calculated by Eq. (3), or the closest value to it, was used to calculate split ratios and green times. In the idealized case, L s1 and e 1 should be modeled Y b, AR b, Y a, and AR a, and the result should be applied in the signal timing procedure. However, modeling L s1 and L c1 was not realistic in this study due to the shortage of observations. Therefore, the observed value of L s1 at HY intersection, -0.40s, and the average ratio of e 1 to (Y a +AR a ) observed at the subject intersections (except TN), 0.39 shown in Table 2, were used to estimate L s2 and L c1. Table 4 presents signal timing results under protected-only, permissive-only and permissive-and-protected right-turn phasing plans respectively

18 Pro. Per. Per. -Pro. Tang, et al Table 3 Assumed traffic conditions for case studies Design Traffic Volumes (veh/h) Intersection EB SB WB NB Size (m) L T R L T R L T R L T R 1-A B C A B C A B C Intersection Configuration EB SB V=60km/h NB Protected-only (Pro.) WB EB SB V=40km/h NB Permissive-only (Per.) WB EB SB V=60km/h WB NB Permissive-and-protected (Per.-Pro.)

19 Pro. Per. Per. - Pro. 1-A 1-B 1-C 2-A 2-B 2-C 3-A 3-B 3-C Existing Proposed Existing Proposed Existing Proposed Existing Proposed Existing Proposed Existing Proposed Existing Proposed Existing Proposed Existing Proposed Tang, et al Table 4 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 (Y+AR) λ 1 L s +L c λ 2 L s +L c λ 3 L s +L c λ 4 L s +L c λ (L s +L c )

20 In the case of protected-only right-turn phasing plan, no significant difference between the total loss times estimated by two methods was found due to intersection size indicated by A, B and C. The values estimated by the proposed method are just slightly lower than those estimated by the existing method. The reason is that the estimated loss times of through and left-turn traffics (Φ1 Φ2 and Φ3 Φ4) by the proposed method are a little bit higher than those by the existing method, although the estimated loss times of right-turn traffic (Φ2 Φ3 and Φ4 Φ1) by the proposed method are considerably smaller than those by the existing method. As demand ratio is same in the two procedures, cycle lengths as well as green times are also pretty close. For the other two phasing plans, loss times estimated by the proposed method are significantly lower than those by the existing method. On the other hand, demand ratios calculated by the proposed procedure are relatively large since a part of right-turn traffic demand was excluded in the existing procedure. Such a tradeoff leads to a result that cycle lengths by the proposed procedure are 26%, 10%, and 15% shorter than those by the existing method respectively for different intersection sizes, 2-A, 2-B and 2-C. Cycle lengths became closer for 3-A, 10% and 23% reductions for 3-B and 3-C. In addition, the difference between loss times estimated by two methods arises as the increase of intersection size, since the proposed method quite relies on the length of waiting area, D, while the existing method is not very sensitive to it. In summary, given demand ratios between 0.65 and 0.80, loss times by the proposed method are slightly lower comparing with the existing method in the case of protected-only right-turn phase, and significantly lower in the other two cases. Large difference in control parameters didn t appear at the protected-only right-turn phase. However, in the other two phasing plans, cycle lengths can be remarkably shorter by applying the proposed method due to smaller loss times, though different ways of calculating demand ratio of right-turn traffic have somehow narrowed down the gap. Moreover, intersection size is positively related to the difference between the cycle lengths estimated by two methods. CONCLUSIONS AND FUTURE STUDIES This paper proposed a new method based on time-space diagram and shock-wave theory for the estimation of loss time of right-turn traffic under three conventional phasing plans in Japan, protected-only right-turn, permissive-only right-turn, and permissive-and-protected right-turn. It was validated by the use of field data, and validation results showed that the existing method in Japan tends to provide improper estimation and the proposed method is however capable of offering good accuracy. Based on that, control parameters designed by the current signal timing procedure and the modified procedure, incorporating the proposed loss time estimation method

21 into the current procedure, were compared in case studies. It was found that, under a demand ratio between 0.65 and 0.80, large difference in signal control parameters didn t come up in the case of protected-only right-turn phasing plan due to close total loss times estimated by two methods. Also, intersection size seems to have less effect on the difference in signal timing parameters in the above case. However, cycle lengths as well as green times can be remarkably shorter in the other two phasing plans when applying the proposed method, due to smaller loss times. Furthermore, such difference arises as the increase of intersection size, since the proposed method relies on the length of waiting area, while the existing method is not very sensitive to it. Future works are still necessary to improve the proposed method. Firstly, more observations should be conducted to reinforce the conclusions, such as start-up loss time of the protected-only right-turn phase, L s1. Secondly, the proposed method could be more sophisticated if start-up and clearance loss times of the protected right-turn phase, L s1 and L c1, could be modeled based on widespread observations. Thirdly, gap-acceptance occurrence was not considered in the case studies. Further analysis thus needs to be done to investigate the difference in control parameters at the presence of gap-acceptance. ACKNOWLEDGEMENT The authors would like to convey their sincere appreciations to Japan Society for the Promotion of Science (JSPS) for its financial support, and to Prof. Takashi Oguchi of Tokyo Metropolitan University, Prof. Hideki Nakamura of Nagoya University, and Prof. Edward Chung of Queensland University of Technology, for their insightful comments on this study. The authors are also very thankful for Mr. Kazufumi Suzuki of Nagoya University for kindly providing data processing software for this research. REFERENCES 1. Transportation Research Board (TRB). Highway Capacity Manual National Research Council, Washington, D.C., Webster, F.V.. Traffic Signal Settings. Road Research Technical Paper No. 39, Road Research Laboratory, Her Majesty Stationary Office, London, UK, JSTE Japan Society of Traffic Engineers. Revised Edition of Manual on Traffic Signal Control. JSTE, Tokyo

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