**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

*Right-Turn-on-Red Operation at Signalized Intersections with Single and Dual Right-Turn Lanes: Evaluating Performance*. Washington, DC: The National Academies Press. doi: 10.17226/27264.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

*Right-Turn-on-Red Operation at Signalized Intersections with Single and Dual Right-Turn Lanes: Evaluating Performance*. Washington, DC: The National Academies Press. doi: 10.17226/27264.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

*Right-Turn-on-Red Operation at Signalized Intersections with Single and Dual Right-Turn Lanes: Evaluating Performance*. Washington, DC: The National Academies Press. doi: 10.17226/27264.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"2. Literature Review." National Academies of Sciences, Engineering, and Medicine. 2023.

Below is the uncorrected machine-read text of this chapter, intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text of each book. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

2. LITERATURE REVIEW This chapter presents an overview of relevant literature on the analysis of RTOR operation at signalized intersections. The review mainly focuses on the capacity analysis of RTOR operations and previous attempts to improve the handling of RTOR in the HCM signalized intersection methodology. This chapter is divided into sections according to types of approaches researchers have used in different studies and concludes with a tabular summary of the review. 2.1 Motivation for Right-Turn-on-Red Methodology Evaluation The HCM (TRB 2016) recommends using RTOR volume for capacity and LOS analyses but provides very limited guidance for predicting the volume in the absence of field data. The signalized intersection methodology in the HCM computes capacity using only the green portion of the cycle, ignoring the additional capacity that may result from allowing RTOR. This leads to an overestimation of delay and consequently a determination of LOS that is likely to appear worse than the actual performance. Therefore, it is essential to develop proper RTOR volume and capacity estimation models for correct estimation of LOS at signalized intersections. 2.2 History of Right-Turn-on-Red RTOR has been common in the United States for many years. New York City first adopted a permissive right-turn rule in 1924. However, local authorities replaced this with the prohibitive rule in 1937, and the city remains one of the few jurisdictions in North America where RTOR is completely prohibited. Also in 1937, the state of California adopted a permissive right-turn rule. In the following years, the western states gradually adopted the permissive rule following Californiaâs lead, and the rule became known as the âWestern rule.â Because the prohibitive right-turn rule was common in the eastern states, it was sometimes called the âEastern rule.â RTOR was often prohibited before the 1970s because of concerns about the safety of the maneuver (Jaleel 1984). The 1973 oil crisis and 1979 energy crisis saw significant increases in the prices of fuel, which encouraged the reduction of fuel consumption. Research sponsored by the Federal Highway Administration found that substantial reductions in delay (and, by extension, fuel consumption) were possible from allowing RTOR. Considering this potential for operational improvement and reduction in fuel consumption, Congress passed the Energy Policy and Conservation Act in 1975, which required states to permit RTOR to receive federal assistance. There was a change in the Uniform Vehicle Code following the act to allow RTOR in the absence of signs indicating RTOR prohibition. In current practice, allowance of RTOR is the default assumption by most drivers, with local prohibitions noted by use of the NO TURN ON RED sign, or by area-wide prohibitions in certain local jurisdictions. 14

2.3 Right-Turn-on-Red in the Highway Capacity Manual The HCMâs signalized intersection methodology defines the RTOR flow rate as the hourly rate at which vehicles turn right at an intersection during the red interval. Estimation of RTOR flow rate is a challenging task because it depends on many factors including lane configuration, total right-turn volume, sight distance, volume-to-capacity ratios for conflicting movements, right-turn arrival and service time distributions, conflicting left-turn phasing, and pedestrian conflicts. These factors can vary considerably from one intersection to another, making it difficult to predict RTOR flow rates. The HCM recommends that RTOR flow rate should be set to 0 veh/h in the absence of field data. When field data are available, the HCM suggests deducting the RTOR volume from the total right-turn volume (TRB 2016). Previously, the 2000 and 2010 editions of the HCM-recommended deducting the per-lane volume of shadowed left turns from the right-turn volume when an exclusive right-turn lane serves right turners and a protected left- turn phase exists on the cross street. This does not appear in the sixth edition of the HCM. Even where RTOR volumes are available from field data, practitioners performing tasks such as signal retiming or intersection redesign face challenges in applying the HCM recommendations: â¢ The observed RTOR volume is often less than the RTOR capacity, but standard traffic counting techniques do not determine how frequently the signal fully serves the RTOR demand or quantify the number of seconds when the RTOR movement is in starvation. â¢ Changes in signal phasing and timing may affect RTOR capacity. For example, the size of pedestrian groups crossing together is related to cycle length, so it is unclear whether there is a linear relationship between cycle length and the probability of RTOR-pedestrian conflicts. Although less critical from a purely theoretical perspective, another practitioner concern about the HCM methodology is its recommendation to analyze the effect of RTOR by deducting the number of RTOR vehicles from the right-turn flow rate. When analyzing a corridor, practitioners must remember to add this volume back to the downstream flows. 2.4 Studies on Right-Turn-on-Red Safety and Operational Guidelines Mamlouk et al. (1976) summarized the observations and findings from two research projects on RTOR in Indiana. The researchers measured several variables related to RTOR and concluded that allowing RTOR does not have significant adverse impacts on motorist or pedestrian safety. This study observed reductions in vehicular and pedestrian delay and noted that most drivers were pleased with RTOR. City size, number of subject approach lanes, and presence of an exclusive right-turn lane had significant effects on the RTOR maneuver. The researchers noted some problems with RTOR: drivers failing to come to a full stop before turning, driver confusion, and reluctance to use RTOR. The authors suggested warrants for prohibiting RTOR based on several factors such as minimum sight distance requirements, familiarity of signal phasing, number of intersection legs, duration of red interval, volumes of conflicting traffic and pedestrians, right-turn demand, and presence of school crossing route. 15

Later, Chadda and Schonfeld (1985) performed a review and analysis of pedestrian safety problems resulting from allowing RTOR and suggested a set of engineering, educational, and enforcement countermeasures to tackle the problem. The authors identified pedestrian and driver behavior-related problems causing pedestrian-RTOR vehicle conflicts. Likely causes of pedestrian-RTOR vehicle crashes mentioned in this study include creeping by motorists, inability to notice pedestrians due to barriers, driver mistakes during RTOR maneuvers, driver and pedestrian noncompliance, inadequate walk time for pedestrians, and insufficient law enforcement. Pedestrian crash countermeasure interventions that the authors suggested would be cost-effective include removal of unwarranted traffic signals, use of RTOR prohibition signs and angled stop bars, incorporation of RTOR regulations in driver education curriculum and driver licensing tests, and development and implementation of school safety education programs. Lord (2002) performed a study on the safety of RTOR in the United States and Canada. The purpose of this study was to collect crash data, review research documents on RTOR safety, and survey the opinions of transportation experts and researchers on this issue. The author concluded that RTOR in most cases does not pose any threat to motorists and pedestrians. According to the study outcomes, the proportion of crashes resulting from RTOR was usually very low and when a crash occurs the outcome was generally not severe. Cooner et al. (2011) proposed design and operational guidelines for dual right-turn lanes. They conducted a survey to collect information about the design and operation of dual right-turn lanes. Total right-turn volume, traffic and geometry of upstream and downstream intersections, turn bay length, design vehicle selection, intersection angle, sight distance, and intersection grade were the major factors influencing design and operation of dual right-turn lanes based on survey responses. One important finding of this study was that there is a potential risk involved in RTOR from the left lane of dual right-turn lanes when the number of receiving lanes is more than two, and from both lanes when the downstream location has an entrance ramp nearby. 2.5 Gap Acceptance and Probabilistic Approaches to Right-Turn-on-Red Luh and Lu (1990) proposed a method to calculate RTOR capacity using the HCM. Presence of an exclusive right-turn lane, proportion of right turns using a shared lane, duration of red interval, volume of conflicting traffic, and presence of pedestrians were the major factors affecting RTOR capacity. An experiment determined whether RTOR movement is analogous to a stop-sign-controlled right turn. Since RTOR traffic can only utilize the unsaturated green time of the conflicting traffic, the authors proposed the following modified capacity models: ï£«R ï£¶ Exclusive right-turn lane: ci = c p ï£¬ u ï£· f RT Equation 1 ï£C ï£¸ ï£« 3600 ï£¶ Shared right-turn lane: ci = min(cc , E ) ï£¬ ï£· ï£ C ï£¸ 16

Here, ci is the capacity of RTOR for phase i, c p is the HCM-based RTOR potential capacity for an exclusive right-turn lane, Ru is the unsaturated red time, f RT is the pedestrian adjustment factor, cc is the number of RTOR chances provided by gaps in the conflicting traffic, E is the expected number of leading right-turn vehicles in the shared lane, and C is the cycle length. Virkler et al. (Virkler and Maddela 1995; Virkler and Krishna 1998) proposed two approaches to analyze RTOR in the absence of field data. One of these is to use the capacity estimation procedure of right-turn movements at a two-way stop-controlled intersection, as previously proposed by Luh and Lu (1990). The second approach, called the âShadowing Procedure,â subtracts an RTOR volume equal to the per-lane volume of the shadowed left-turn movement. The authors applied the two approaches to 40 intersections. Both approaches demonstrated significant changes in the reported performance of the intersections. The authors concluded that use of either approach (or both) would be better than assuming an RTOR volume of zero in the absence of field data. Liu (1995) proposed methods for predicting RTOR capacity and evaluating RTOR operations under different traffic, signal, and geometric conditions. This study used computer simulation as the analytical approach for estimating RTOR capacity. Critical parameters influencing RTOR operations and performance included the RTOR arrival distribution, signal change interval, length of right-turn lane, discharging headway of conflicting traffic, turning headway, discharging time, and gap acceptance for RTOR vehicles. The author proposed an analytical RTOR capacity model using the probabilistic approach: exp ( âqc g min ) 3600 R â td QRTOR = Ã Ã Equation 2 1 â exp ( âqc ht ) hc C where: QRTOR = RTOR capacity of an exclusive right-turn lane qc = flow rate of the conflicting traffic g min = minimum gap required by an RTOR vehicle ht = average RTOR turning headway hc = average crossing headway of the conflicting traffic R = red interval duration td = total discharge time for conflicting queue at the beginning of green C = cycle length Because this mathematical model may not always result in realistic solutions, the author performed a regression analysis using simulation data and developed a piecewise linear function relation between RTOR capacity and conflicting traffic. If Vc represents the volume of the conflicting traffic in veh/h, then 17

ï£±206 â 0.22Vc for 0 â¤ Vc â¤ 300 QRTOR = ï£² Equation 3 ï£³183 â 0.18Vc for 300 â¤ Vc â¤ 650 It was found that the effect of cycle length on RTOR capacity is insignificant and that a negative correlation exists between split and RTOR capacity. For shared through and right-turn lanes, because there exists a chance of lane blockage, the author proposed a different equation for RTOR capacity using a probabilistic approach: 3600 â Shared QRTOR = â yP( y) C y =0 Equation 4 where: y = the number of RTOR occurrences during a signal cycle P(y) = probability of y RTOR occurrences during a signal cycle = (1 â PRT ) PRT y PRT = proportion of right turners in the shared lane On further analysis, the study found that for both shared and exclusive right-turn lanes, the actual number of RTOR occurrences and the right-turn demand during the red interval are positively correlated. Virkler and Maddela (1995) compared the field capacity for right turns into gaps with predicted capacities from the Stop Sign Analogy (SSA) and Adjusted Stop Sign Analogy (ASSA) procedures. They pointed out that the SSA procedure may overestimate right-turn capacity by ignoring the effect of short phase duration. Because only the unsaturated green time of the conflicting traffic is usable by RTOR vehicles, the authors proposed the following adjusted capacity model: 3600 ï£« Vct0 ï£¶ 3600 ï£« VcU 0 ï£¶ cA = exp ï£¬ â ï£·â exp ï£¬ â ï£· Equation 5 tf ï£ 3600 ï£¸ tf ï£ 3600 ï£¸ where: c A = adjusted RTOR capacity (pcph of unsaturated red) Vc = conflicting traffic volume (veh/h) tf = follow-up time (s) t g = critical gap (s) t0 = tg â t f 2 18

U = unsaturated red time (s) U0 = U â t f 2 The following adjustment gives the RTOR capacity of the interval: ï£«R ï£¶ c = cA ï£¬ u ï£· Equation 6 ï£C ï£¸ Here, Ru is the unsaturated red time and C is the cycle length, both in seconds. This study also found that the shadowed left-turn procedure in the HCM may provide an inaccurate estimate of RTOR volume when either the shadowing left-turn demand or the right- turn demand at the subject approach is less than capacity. Tarko (2001) proposed analytical models for predicting RTOR volume and capacity at signalized intersections. The study considered total right-turn volume during red phase, blockage by same- approach vehicles, and blockage by conflicting traffic, and the model used the following equation for the average number of unblocked right-turning vehicles during a particular red interval: ï£± pâ k ï£¼ =b min ï£² , p â tï£½ Equation 7 ï£³1 â p ï£¾ where: k = maximum number of vehicles in the right-turn bay t = total number of vehicles arriving during red = an n + ar p = right-turn proportion in the rightmost lane = ar t ar = expected right turners arriving during red = vr â ( C â R p â f r ) 3600 an = expected non-right-turners arriving during red vr = right-turn flow rate (veh/h) C = cycle length (s) Rp = platoon ratio corresponding to right-turn arrivals fr = phase duration for right turns (s) n = number of lanes in the lane group Tarko (2001) expressed the RTOR capacity as the summation of capacities under conditions where conflicting traffic impedes the RTOR vehicles and when there is no traffic to impede it. The HCM capacity equation for unsignalized intersections was modified to derive an expression for capacity when RTOR vehicles must yield to cross street flow. The equation is 19

ï£« v â t â C ï£¶ vi â exp ï£¬ â i 0 ï£· ï£« vp ï£¶ ï£ 3600 â fi ï£¸ C= 1 ï£¬1 â ï£·. Equation 8 ï£ 2100 ï£¸ 1 â exp ï£« â vi â t f â C ï£¶ ï£¬ ï£· ï£ 3600 â fi ï£¸ where: v p = pedestrian volume across the subject approach (ped/h) vi = volume of conflicting through traffic in the rightmost lane (veh/h) C = expected signal cycle (s) t0 = critical gap for right turns (6.9 s) tf = follow-up time (3.3 s) and fi = green duration for conflicting flow (s) The following capacity equation applies when there is no impeding traffic: 3600 C â f r â fi C2 = . Equation 9 tf C where the terms are as defined earlier. Finally, the following RTOR volume estimation model was suggested considering the possibility of some right turners being unable to clear the intersection during the red interval: VRTOR = min ( v0 , c ) Equation 10 where: VRTOR = RTOR volume (veh/h) v0 = Total right-turn volume arriving during red (veh/h) = b â m m = expected number of cycles per hour c = total RTOR capacity = C1 + C2 The study evaluated the models using the CORSIM simulation program. The evaluation analysis produced unbiased results when there was no impedance from the conflicting traffic but showed limited bias when the flows on the cross street were critical for the RTOR volumes. Because RTOR is likely to increase the capacity of an intersection, Creasey et al. (2011) developed deterministic RTOR volume estimation and incremental capacity models by 20

considering the probabilistic nature of RTORs occurring from shared lane approaches (Creasey et al. 2011). The following volume estimation model considers a continuous demand on the subject approach and availability of gaps in the conflicting traffic: ï£« 1 â p ï£¶ 3600 N RTOR = min( X r ,1.0) ï£¬ ï£· Equation 11 ï£ p ï£¸ C Here, N RTOR is the expected RTOR volume in veh/h, X r is the demand volume-to-capacity ratio for the shared lane of the subject approach, p is the ratio of through vehicles to the total volume in the shared lane (veh/h), and C is the average cycle length during the analysis period in seconds. The following RTOR incremental capacity model applies when RTORs are permitted from a shared lane approach: c1 + PRTOR ( c2 + c3 ) c= Equation 12 where: c = total approach capacity for a shared lane (veh/h) c1 = HCM-based approach capacity during green (veh/h) c2 = approach capacity when intersecting through and opposing left turns receive an exclusive green (veh/h) c3 = approach capacity when shadowed left turns receive an exclusive green (veh/h) PRTOR = probability of RTOR occurrence from a shared lane, given by 1 (1 â p ) 3600 PRTOR = Equation 13 VSL p C In the above, VSL is the total shared lane volume (veh/h). The c2 term originates from applying the same principles used in the HCM for two-way stop- controlled unsignalized approaches: ï£« Vt ï£¶ exp ï£¬ â c c ï£· c2 = Vc ï£ 3600 ï£¸ g c â g q Equation 14 ï£« Vt ï£¶ C 1 â exp ï£¬ â c f ï£· ï£ 3600 ï£¸ 21

where: Vc = total conflicting flow rate (veh/h) tc = critical gap (s) t f = follow-up time (s) g c = effective green time for the conflicting traffic (s) g q = portion of effective green used for clearance of conflicting queue (s) C = average cycle length (s) The capacity associated with shadowed left turns is a function of signal interval of the shadowed left turn and the follow-up time: g SHLT 3600 c3 = Equation 15 C tf where g SHLT is the effective green duration for the shadowed protected left-turn phase and t f is the follow-up time, both expressed in seconds. The researchers used CORSIM to validate the volume estimation model and found that the estimated RTOR volumes were within the confidence intervals of the simulated RTOR volumes 75% of the time. The analysis also showed that the estimated capacities using the incremental capacity model were always greater than the HCM-based capacities. Gao (2011) proposed a probabilistic model for delay estimation at signalized intersections considering short right-turn lanes and RTOR. The proposed model takes into account the effect of blockage at short lanes with different lengths to overcome a limitation of the HCM in which the analysis treats short right-turn lanes as exclusive full lanes, ignoring blockage. Gao validated the model using simulation and found that the estimated delay decreased with the increase of storage length, which matched the output of the simulation. Chen et al. (2012) proposed analytical models for predicting lane-specific RTOR capacities of dual right-turn lanes for two RTOR maneuver regimes. The authors defined regime A as an occurrence of RTOR under acceptable gaps in conflicting traffic from a left-hand cross street or an opposing left-turn movement, whereas regime B indicated RTOR movements during shadowing left-turn movements from the right-hand cross street. For regime A, the authors proposed capacity models considering three possible gap acceptance patterns. The capacity of the left-side right-turn lane during regime A is as follows: 22

ï£® ï£« qtc2 ï£¶ ï£« qt f1 ï£¶ ï£¯ exp ï£¬ â ï£· 1 â exp ï£¬ â ï£· ï£¯ ï£ 3600 ï£¸ q1 â q2 ï£« q (tc2 + t f2 ) ï£¶ ï£ 3600 ï£¸ cleft A =Î» â ï£¯ q2 â + exp ï£¬ â ï£·â qt q 3600 ï£¸ ï£« 2 ï£¯ 1 â exp ï£¬ï£« â f2 ï£·ï£¶ ï£ ï£« qt f2 ï£¶ ï£¶ ï£¯ ï£ 3600 ï£¸ ï£¬ï£¬1 â exp ï£¬ â 3600 ï£· ï£·ï£· ï£° ï£ ï£ ï£¸ï£¸ Equation 16 ï£« qtc1 ï£¶ ï£¹ exp ï£¬â ï£· ï£º q12 ï£ 3600 ï£¸ ï£º + â q ï£« qt f1 ï£¶ ï£º 1 â exp ï£¬ â ï£·ï£º ï£ 3600 ï£¸ ï£ºï£» where: q1 = conflicting volume in the rightmost lane (veh/h) q2 = conflicting volume in the left lane (veh/h) q = total conflicting volume (veh/h) = q1 + q2 tc1 = RTOR critical gap when gap closed by vehicles in the rightmost lane (s) tc2 = RTOR critical gap when gap closed by vehicles in the left lane (s) t f1 = RTOR follow-up time when gap closed by vehicles in the rightmost lane (s) t f2 = RTOR follow-up time when gap closed by vehicles in the left lane (s) Î» = cycle split for regime A (percent) Vehicles departing from the curb lane usually turn into the rightmost lane of the right-hand cross street. The capacity of a curb lane during regime A is as follows: ï£® ï£« qtc1 ï£¶ ï£« qt f2 ï£¶ ï£¯ exp ï£¬ â ï£· 1 â exp ï£¬ â ï£· c Acurb ï£¯ =Î» â ï£¯ q1 â ï£ 3600 ï£¸ + q1 â q2 exp ï£« â q (tc1 + t f1 ) ï£¶ â ï£ 3600 ï£¸ ï£¬ ï£· qt q 3600 ï£¸ ï£« 2 ï£¯ 1 â exp ï£¬ï£« â f1 ï£·ï£¶ ï£ ï£« qt f1 ï£¶ ï£¶ ï£¯ ï£¬ï£¬ 1 â exp ï£¬ â ï£· ï£·ï£· ï£° ï£ 3600 ï£¸ ï£ ï£ 3600 ï£¸ ï£¸ Equation 17 ï£« qtc2 ï£¶ ï£¹ exp ï£¬ â ï£· ï£º q 2 ï£ 3600 ï£¸ ï£º + â 2 q ï£« qt f2 ï£¶ ï£º 1 â exp ï£¬ â ï£·ï£º ï£ 3600 ï£¸ ï£»ï£º During regime B, there is no conflicting traffic, and a simpler capacity estimation model was proposed: 23

c= B sOL â tOL Equation 18 Here, tOL is the green duration for the shadowed left-turn phase and sOL is the flow rate at which stop-and-go RTORs can cross the stop line. The reciprocal of the follow-up time can substitute for field data when there is none. The above equations assume exclusive right-turn lanes. When the left lane of the subject approach is a shared through and right-turn lane, the authors proposed the following adjusted capacity expression: ï£« 3600 â Ï left left ï£¶ =cshared min ï£¬ , c A + cB ï£· Equation 19 ï£ C ï£¸ Here, Ï is the average number of unblocked RTOR vehicles per cycle, C is the cycle length in seconds, and cBleft is the RTOR capacity for left-side shared lane during regime B in veh/h, from Equation 17. The following equations were previously derived by Tarko (2001) and Creasey et al. (2011) for calculating Ï : p Shared lanes without islands: Ï = Equation 20 1â p pâ k Shared lanes with islands: Ï = 1â p Here, p represents the proportion of right turners in the shared lane and k is the maximum number of vehicles stored in the right-turn bay. Australia is a left-hand drive country, but its road design practices are strongly influenced by U.S. practice. Report ARR 123 published by the Australian Road Research Board (AkÃ§elik 1981) has had a strong influence on the current HCM signalized intersection methodology. This report included methods to estimate saturation flow rates for permissive turning movements for single exclusive and shared lanes. In a left-hand drive country, the corresponding movement would be a left turn on red (LTOR), and the analysis would be mirrored. The term âopposed turnâ can be used to collectively describe LTOR or RTOR for both left-hand and right-hand drive countries. The method presented in ARR 123 for opposed turns used a base saturation flow rate, sb , and a few adjustment factors to calculate the saturation flow rate, including an adjustment for the presence of heavy vehicles (HVs): 24

ï£« fw fg ï£¶ sshared = ï£¬ ï£· sb Equation 21 ï£ fc ï£¸ The opposed turn saturation flow rate is given by qc exp(âÎ±qc ) su = Equation 22 1 â exp(â Î²qc ) The unsaturated portion of opposing movement green, gu, is as follows: sc g c â qc c gu = Equation 23 sc â qc For exclusive lanes, the opposed turn saturation flow rate is 1800 sexcl = Equation 24 e0 The opposed turn equivalent is given by ï£± 0.5 g ï£´s g + n for cars ï£´ u u f e0 = ï£² Equation 25 ï£´ 0.5 g + 1 for heavy vehicles ï£´ï£³ su gu + n f In the above equations, the terms are as follows: sshared = saturation flow rate of shared lane (veh/h) sexcl = saturation flow rate of exclusive lane (veh/h) fw = lane width adjustment factor fg = adjustment factor for gradient fc = traffic composition adjustment factor = Î£ ei qi Î£qi qi = movement flow for vehicle and turn type i (veh/h) ei = through car equivalent for vehicle and turn type i e0 = opposed turn equivalent g = effective green time for the opposed turn (s) gc = effective green time for the opposing movement (s) 25

gu = unsaturated portion of g c (s) su = opposed turn saturation flow rate (veh/s) during gu sc = opposed turn saturation flow rate qc = opposing movement flow rate (veh/s) Î± = critical gap (s) Î² = minimum opposed turn departure headway (s) nf = number of vehicles departing after the end of green 2.6 Empirical Studies of Right-Turn-on-Red Stewart and Hodgson (1995) used two different approaches for estimation of RTOR saturation flow rates. A microscopic approach modeled gap acceptance behavior and arrival probability distribution of conflicting through traffic streams. Major factors affecting gap acceptance behavior included the time of day, number of conflicting lanes, and turning radius. A formula for RTOR saturation flow rate was expressed as follows: ï£« âVt ï£¶ =s V â P (h= â¥ t ) V â exp ï£¬ ï£· Equation 26 ï£ 3600 ï£¸ where: s = RTOR saturation flow rate V = flow rate of conflicting traffic h = individual time headway of conflicting traffic tc = RTOR critical gap tf = RTOR follow-up time t = selected time interval = tc , tc + t f , tc + 2t f , etc. The second approach was a macroscopic model that used the following linear equation to estimate RTOR saturation flow rate: ln( s + Î³) = ln c + dv0 Equation 27 where: C = cycle length v0 = total opposing flow v0â² = converted conflicting flow = v0C g g = effective green time Î³, c, d = calibration parameters 26

The authors undertook regression analysis with measured field data to obtain the values of the calibration parameters and finally obtained the following simple equation for RTOR saturation flow rate. The coefficients were found to be statistically significant at the 95% confidence level. =S 849.82e â0.00129 v â 31 Equation 28 Abu-Lebdeh et al. (1997) developed a linear regression model for RTOR volume estimation after analyzing the data obtained from 11 intersections in Urbana, Illinois. The authors showed that ignoring RTOR volumes can result in significant differences in the estimation of delays and that this difference increases with an increase in right-turn volume. They proposed a linear model for RTOR volume: G RTOR p= 79.0 + 0.339VRT â 165 â â 0.0559Vc â 50.3T C Equation 29 G + 0.108T â VRT + 143T â C where: RTOR p = potential RTOR volume (veh/h) VRT = total right-turn volume (veh/h) G = green duration (s) C = cycle length (s) Vc = volume of conflicting traffic (veh/h) T = type of conflict variable (T = 0 if conflict from the intersecting approach only; T = 1 if conflict from both intersecting and opposite approaches) The authors mention that the potential RTOR volume may be reduced by practical constraints and present a modified equation for the expected RTOR volume: RTORexp = min( RTORP , RTORCap ) Equation 30 where RTORexp is the expected RTOR volume (veh/h) and RTORCap is the RTOR capacity, given by ï£´ï£± ï£®ï£« ï£« G ï£¶ ï£¶ ï£¹ ï£¼ï£´ RTOR = Cap Î± ï£²max ï£¯ï£¬ ï£¬1 â ï£· Ã S â Vc ï£· , 0 ï£º ï£½ Equation 31 ï£³ï£´ ï£°ï£ ï£ C ï£¸ ï£¸ ï£» ï£¾ï£´ The value Î± is the ratio of the saturation headway of conflicting through vehicles and the saturation headway of RTOR vehicles. Finally, S is the saturation flow rate of the receiving lane (veh/h). 27

The RTOR capacity determined the expected RTOR volume at high volumes of conflicting traffic and the type of conflict played a major role in estimating the expected RTOR volume. A study by the Wisconsin Department of Transportation (WisDOT) led to the development of empirical RTOR volume estimation models for intersections and interchanges with different lane configurations (Hawley and Bruggeman 2009). Previously, WisDOT calculated RTOR volumes by utilizing the lesser of two possible values. The first potential value is based on an assumption that the signal serves two RTOR vehicles in each cycle, while the second potential value assumes that half the total right-turn volume is served as RTOR. Therefore, the RTOR volume using this previous methodology would be the following: ï£® 3600 ï£¹ VRTOR min ï£¯ = Ã 2 , 0.5VR ï£º Equation 32 ï£° C ï£» where VR is the total right-turn volume. Another method for RTOR volume estimation mentioned in the Wisconsin study is the Synchro RTOR Reduction Method. To evaluate existing methods and to propose new methodology for RTOR volume estimation, in 2009 researchers collected turning movement and RTOR counts at several interchange ramp terminal locations and suburban intersections in the Milwaukee area. The existing methods yielded rather different results from the field data, so the authors developed a new methodology that used statistical tests to evaluate the effects of traffic volume, geometry, and signal timing on RTOR volumes. The RTOR volume was highly correlated with total right-turn volume in all cases except for interchanges with dual right-turn lanes, where there was significant dispersion of the data and a strong chance of overestimating the RTOR. To limit the risk of overestimation, the study team recommended two manually adjusted hybrid equations for RTOR volume estimation: Single right-turn lanes: VRTOR = 0.50VRT Equation 33 Dual right-turn lanes: VRTOR = 0.30VRT Based on the results of a 2015 study (TranSmart Technologies, Inc. 2015) that included additional areas of the state, WisDOT adjusted its models as follows: Single Right-Turn Lanes at Intersections: VRTOR = 0.38VRT Equation 34 Single Right-Turn Lanes at Interchanges: VRTOR = 0.66VRT Dual Right-Turn Lanes (any location): VRTOR = 0.30VRT Most Canadian jurisdictions allow RTOR. In the absence of conflicting traffic, research has estimated the capacity of RTOR movements as 700 to 900 pcu/h. The Canadian Capacity Guide for Signalized Intersections suggests a set of equations for estimation of RTOR capacity for exclusive right-turn lanes in terms of effective conflicting flow at the intersection (Teply et al. 2008): 28

= 850 â 0.35qmâ² qRTOR Equation 35 Here, qmâ² is the effective conflicting flow rate during the red interval of the subject approach in pcu/h, which is again a function of adjusted right-turn flow rate, qmR â² , and adjusted through flow rate, qmâ² 1 , from the curb lane of the conflicting approach, both expressed in pcu/h. â² qmR qmâ² = + qmâ² 1 Equation 36 2 where: C C â² = qmR qmR â² = qmR = qmR r r C C qmâ² 1 = qm1 = qmâ² 1 = qm1 r r qmR = conflicting right-turn flow rate from the curb lane during red phase of the subject approach (pcu/h) qm1 = conflicting through flow rate from the curb lane during red phase of the subject approach (pcu/h) C = cycle length (s) r = red interval when RTOR can occur (s) This method may underestimate the capacity when there is a separate island for the right-turn lane and the movement is yield-controlled. Also, the RTOR capacity may be lower when there are large pedestrian volumes crossing the subject approach. 2.7 Right-Turn-on-Red Studies Using Queuing Theory Diegel (1994) represented the RTOR maneuver as a queuing system and measured the inter- arrival and service time probability distributions of RTOR by observation of sample intersections. The author recorded vehicle arrivals at two intersections in Michigan with and without an exclusive right-turn lane. After analyzing the data, Diegel (1994) classified the RTOR movement as an M/M/1 process and found that the distribution of inter-arrival times had a good fit with a negative exponential model, while the service time distribution had a good fit with a shifted negative exponential model. Qureshi and Han (2001) proposed uniform delay models based on queuing theory. The authors considered four different signal phasing schemes based on the potential sequences of one green interval and three red intervals. They developed a queue accumulation polygon (QAP) for each of these schemes. The study results suggest that the HCM procedure overestimates right-turn delay by removing RTOR from the analysis. 29

Gao (2011) proposed a model for uniform delay estimation that used QAPs for through and right-turn movements at approaches with short storage lengths with consideration of RTOR. The model takes into account various vehicle arrival and departure patterns, the possibility of blockage and conflicts, and different signal timing plans. The author validated the model with a simulation model developed in SimTraffic using real-world volume data and found that there was little difference in the resulting simulation delays and the estimated delays using the proposed model. The QAP model provided better estimation of uniform delay than the HCM model. 2.8 Right-Turn-on-Red in Commercial Software Packages Synchro is a commercial software package that is used to optimize traffic signal timing and is bundled with a companion simulation model. Synchro models RTOR by calculating an RTOR saturation flow rate using the signal timing, volumes of the subject approach, and volumes of the conflicting movements (Trafficware 2017). The method uses different saturation flow rates for different red intervals to account for the type of movements causing the conflict. The formula, based on gap-acceptance theory, is as follows: ï£« vx â 6.2 ï£¶ vxi â exp ï£¬ â i ï£· ï£ 3600 ï£¸ sRTORi = Equation 37 ï£« vx â 3.3 ï£¶ 1 â exp ï£¬ â i ï£· ï£ 3600 ï£¸ where: sRTORi = saturation flow rate (veh/h) during the ith interval = 1091 veh/h when vxi = 0 Ri = duration of the ith interval (sec) C = cycle length (sec) vx â sxi â C vxi = merging volume (veh/h) during the ith interval = â(s xi â Ri ) vx = total volume of the conflicting movement (veh/h) sxi = saturation flow rate (veh/h) of movement x during the ith interval The Synchro method obtains the final RTOR saturation flow rate for an exclusive right-turn lane by taking a time-weighted average of saturation flow rates during each interval when RTOR can occur: sRTOR = â(s â R ) RTORi i Equation 38 âR i 30

For exclusive right-turn lanes with a defined storage length, and for shared right-turn lanes, Synchro calculates the RTOR saturation flow rate by considering the possibility of blockage by through vehicles: vR 3600 sRTOR = â (k + 1) â Equation 39 vTh R Here, vR is the total right-turn volume in veh/h, vTh is the volume of non-right turns in veh/h, k is the storage length in vehicles, and R is the duration of the red interval in seconds. The non- right-turn volumes for the two cases are as follows: vT Exclusive right-turn lane with storage: vTh = Equation 40 N â f LU vT Shared right-turn lane: v= Th â vR when vTh â¥ (vT â vR ) Ã 0.2 N â f LU Here, vT is the total lane group volume in veh/h, N is the number of lanes in the lane group, and f LU is the lane utilization factor. When the RTOR saturation flow rate sRTOR is known, Synchro calculates the RTOR volume as follows: r =vRTOR min( sRTOR , v) â Equation 41 C Here, v is the adjusted lane group volume in veh/h and r is the effective red duration in seconds. One major difference between the HCM and the Synchro RTOR methodology is that Synchro considers the incremental capacity achieved by allowing RTORs whereas the HCM recommends a reduction in the total right-turn volume. Sidra Intersection is another commercial traffic evaluation software package marketed in both right-hand drive and left-hand drive countries. The developers define an opposed turn as any turning movement that must yield and look for adequate gaps in conflicting vehicle or pedestrian traffic (AkÃ§elik and Associates 2011). Permitted left turns in the United States, permitted right turns in Australia, and RTOR in the United States are examples of opposed turns. Sidra Intersection uses a direct method for determining opposed turn capacity by calculating the opposed turn saturation flow rate using gap-acceptance theory. In this method, the following formula calculates the filter turn saturation flow rate during the unsaturated portion of green by taking into account all the opposing movements that may cause conflicts: 31

ï£« 3600 ï£¶ ï£¬ t ï£·ï£· ( â 1 â â 0 q0 + 0.5t f Ï0 q0 ) â e ( c 0 ) â Î» t ââ =su ï£¬ Equation 42 ï£ f ï£¸ where: su = saturation flow rate of opposed turn (veh/h) tc = critical gap (s) t f = follow-up time (s) q0 = total opposing flow rate (pcu/s) â0 = minimum headway in opposing traffic (s) Ï0 = proportion of free vehicles in opposing traffic Î» = a parameter, given by ï£± Ï0 q0 0.98 ï£´ 1â â q when q0 â¤ ï£´ 0 0 â0 Î»= ï£² Equation 43 ï£´ 0.98Ï0 when q0 > 0.98 ï£³ï£´ â 0 (1 â â 0 q0 ) â0 Before using the above formula, the maximum filter turn saturation flow rate, sumax, is compared to the unopposed saturation flow rate, sLV , for light vehicles, where sbâ² sLV = Equation 44 eLV Here, sbâ² denotes the adjusted lane saturation flow rate and eLV denotes the turn equivalent for light vehicles, which is equal to 1.05 through car units per vehicle (TCU/veh) for normal right turns and 1.25 TCU/veh for restricted right turns according to the Sidra Intersection standard. When sLV < sumax , the follow-up time t f is determined from 3600 tf = Equation 45 sLV According to the Oregon DOT Analysis Procedures Manual (Oregon DOT 2019), the PTV Vistro traffic signal timing software does not take RTOR into consideration. Oregon therefore recommends the use of the formulas developed by Creasey et al. (2011), as described previously. 32

2.9 Conclusion Research on RTOR operations at signalized intersections spans several decades. Previous studies on RTOR have primarily focused on safety and capacity analyses of RTOR movements. Studies on RTOR safety have also contributed to operational guidelines such as the prohibition of RTOR in locations with high pedestrian volumes. Table 6 provides a summary of the literature covered in the previous discussion, including a brief synopsis and an indication of whether the modeling approaches, right-turn lane configurations, and models of capacity or volume were included. Table 6. Summary of literature review. Reference Synopsis Outcomes Modeling Right-Turn Capacity RTOR Approach Lane Volume Configuration Mamlouk et al. Observational study of Recommendations on N/A N/A N/A N/A 1976 RTOR safety and factors whether RTOR should be influencing RTOR in permitted or prohibited by Indiana rule AkÃ§elik 1981 Capacity analysis for Opposed turn saturation Gap Exclusive and ï¼ N/A opposed turns at flow rates for shared and acceptance shared signalized intersections exclusive lanes Chadda and Evaluation of pedestrian A set of countermeasures for N/A N/A N/A N/A Schonfeld 1985 safety with RTOR ensuring pedestrian safety when RTOR is allowed Luh and Lu Computation of RTOR A method to calculate Gap Exclusive and ï¼ N/A 1990 capacity using the HCM RTOR capacity by acceptance shared modifying the HCM-based capacity computation procedure for stop-sign controlled right turns Diegel 1994 Queuing theory-based Service time distribution and Queuing N/A N/A N/A approach to RTOR RTOR process classification theory operations using queuing theory Stewart and RTOR saturation flow Gap size requirements for Gap Exclusive ï¼ N/A Hodgson 1995 rate estimation using gap- RTOR maneuver and acceptance acceptance theory regression equation for estimating RTOR saturation flow rates Virkler and Evaluation of HCM SSA Changes in v/c ratios and N/A N/A N/A N/A Maddela 1995 and shadowing procedures LOS using left-turn for RTOR capacity shadowing and HCM SSA computation procedures Liu 1995 Simulation study on Models for estimating Gap Exclusive and ï¼ N/A RTOR characteristics and RTOR capacity using acceptance, shared capacity probability and regression- probabilistic based approaches and regression Abu-lebdeh et Estimation of RTOR Percent error in delay Regression Exclusive N/A ï¼ al. 1997 volume and its impacts on computation from ignoring intersection delay RTOR and linear regression model for RTOR volume estimation Virkler and Comparison of SSA and Pros and cons of the two Gap Exclusive ï¼ N/A Krishna 1998 ASSA procedures for approaches in estimating acceptance RTOR capacity estimation RTOR capacity 33

Reference Synopsis Outcomes Modeling Right-Turn Capacity RTOR Approach Lane Volume Configuration Tarko 2001 Analytical procedure for RTOR volume estimation Probabilistic Shared with ï¼ ï¼ predicting RTOR volume model producing unbiased and gap short right- and capacity prediction under low acceptance turn bay impedance and limited bias under high impedance from conflicting traffic Qureshi and Delay study of right-turn Uniform delay models using Queuing N/A N/A N/A Han 2001 movements with uniform QAPs indicating that the theory arrivals and RTOR HCM overestimates right- turn delay by ignoring RTOR Lord 2002 Study on the safety of No severe safety impact N/A N/A N/A N/A RTOR in the United resulting from allowing States and Canada RTOR Teply et al. Estimation of RTOR flow A set of equations for Regression Exclusive ï¼ N/A 2008 (Canadian rate based on previous estimation of RTOR Capacity Guide) research capacity for exclusive right- turn lanes considering presence of conflicting traffic Hawley and Field study to estimate Two manually adjusted Regression Both single N/A ï¼ Bruggeman RTOR volume using hybrid equations for RTOR and dual 2009(WisDOT) regression analysis volume estimation using total right-turn volume Creasey et al. Study on prediction of Deterministic RTOR volume Probabilistic Shared ï¼ ï¼ 2011 RTOR volume and and incremental capacity and gap incremental capacity for models demonstrating acceptance shared lane approaches greater capacity compared to the HCM method Gao 2011 Delay estimation Probabilistic and queue Probabilistic Shared with N/A N/A considering short right- accumulation polygon and queuing short right- turn lanes and RTOR models for uniform delay theory turn bay estimation Cooner et al. Design and operational Recommendations on N/A N/A N/A N/A 2011 guidelines for dual right- whether to allow RTOR for turn lanes dual right-turn lanes Chen et al. 2012 RTOR capacity estimation A gap-acceptance model Probabilistic Dual ï¼ N/A for dual right-turn lanes with an improved ability to and gap predict RTOR capacity for acceptance dual right-turn lanes Trafficware, Estimation of RTOR RTOR volume estimation Gap Exclusive and ï¼ ï¼ LLC. 2017 volume and incremental model through computation acceptance shared (Synchro) capacity resulting from of RTOR saturation flow allowing RTOR rate AkÃ§elik and Calculation of opposed Saturation flow rate model Gap Exclusive ï¼ N/A Associates 2011 turn capacity using a for opposed turns acceptance (SIDRA) direct method To summarize the literature review, four different approaches to RTOR capacity modeling were found in the literature. Probabilistic and gap-acceptance approaches to modeling were the most common. Other studies used regression models, especially for modeling RTOR volume. Queuing theory-based approaches focused on modeling of delay for right-turn movements with RTOR. This review provides insights on the previous work that informed the development of new models as part of this study. 34

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