**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." 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:**"4. Exploration of Right-Turn-On-Red Models." 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:**"4. Exploration of Right-Turn-On-Red Models." 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:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." National Academies of Sciences, Engineering, and Medicine. 2023.

**Suggested Citation:**"4. Exploration of Right-Turn-On-Red Models." 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.

4. EXPLORATION OF RIGHT-TURN-ON-RED MODELS The second chapter of this report presented a review of RTOR literature, including an exposition of models that were proposed by previous research. An objective of the present research was to develop operational models, striking a balance between accuracy and ease of use. Specifically, this required consideration of the ability of the models to reflect field conditions accurately under a variety of scenarios, and the required level of data input and potential for future implementation into the existing HCM methodology. In this chapter, the findings from the previous literature are synthesized, and their characteristics are evaluated in light of these objectives. 4.1 Previously Described Models for Right-Turn-on-Red Analysis The literature review identified several models for analyzing RTOR movements for four different basic site configurations: (1) exclusive right turns (single-lane), (2) dual-lane right turns, (3) shared through and right-turn lanes, and (4) shared through and right-turn lanes with an additional, short right-turn bay. The previous studies could be categorized according to their fundamental approach to RTOR analysis. Two basic approaches were seen in the literature: (1) the adjustment of the right-turn volumes through subtraction of RTOR and (2) the adjustment of total right-turn capacity to account for additional capacity available during the red interval. Several models were observed, including the use of gap acceptance, queuing theory, and regression. Table 7 presents an overview of those studies whose models were considered for further analysis in this chapter, along with a breakdown of the types of right-turn lane configuration scenarios considered in these studies and the types of adjustments and modeling approaches that were used. In the following sections, the models are discussed in further detail according to the right- turn lane configuration type. 43

Table 7. List of studies included for comparison of model outputs and implementation feasibility. Scenarios Considered Shared with Volume or Short Turn Capacity Study Exclusive Dual Shared Bay Adjustment Type of Model Luh and Lu 1990 ï¼ ï¼ Capacity Gap acceptance Stewart and Hodgson 1995 ï¼ Capacity Gap acceptance Liu 1995 ï¼ ï¼ Capacity Gap acceptance Abu-lebdeh et al. 1997 ï¼ Both Regression Virkler and Krishna 1998 ï¼ Capacity Gap acceptance Tarko 2001 ï¼ Capacity Gap acceptance Teply et al. 2008 (Canadian Capacity Guide) ï¼ Capacity Regression Hawley and Bruggeman 2009 (WisDOT) ï¼ ï¼ Volume Regression TRB 2010 (HCM) ï¼ Volume Other Creasey et al. 2011 ï¼ Both Gap acceptance Chen et al. 2012 ï¼ Capacity Gap acceptance Trafficware, LLC. 2017 (Synchro) ï¼ ï¼ Volume Gap acceptance 4.1.1 Exclusive Right-Turn Lane The most widely discussed scenario in the literature was the single exclusive right-turn lane. Ten different models were identified, including four that adjusted right-turn volumes and six that adjusted right-turn capacities. Among the volume-adjusting models were two studies based on regression as well as a method taken from the 2010 version of the HCM that uses a portion of the volume of the shadowed left-turn phase as a proxy for RTOR volume. Figure 14 shows an intersection diagram indicating several movements at a typical intersection that are likely to influence RTOR: â¢ V1, the conflicting through movement approaching from the left of the subject RTOR movement â¢ V2, the opposing left turn â¢ LT, the shadowed left-turn lane, which is typically considered compatible with RTOR â¢ V3, representing U-turns that might be executed from the shadowed left-turn lane, which are not compatible with RTOR â¢ P1, representing pedestrians crossing the RTOR movement, which are likely to be served concurrently with the green interval for V1 â¢ P2, representing pedestrians adjacent to the RTOR movement. At intersections employing a two-stage crossing with pedestrian overlaps, pedestrian intervals for P2 might be served concurrently with the shadowed left-turn phase. 44

V2 V3 V1 RTOR LT P1 P2 Figure 14. Volume and lane configuration used for modeling exclusive right-turn lanes. Nine models for RTOR traffic are compared (along with the existing HCM method) in Table 8. This table presents the forms of equations used for either the RTOR volume or RTOR capacity expressions, as well as a listing of which movements are considered in the analysis of each method. The mathematical notation has been adapted from the original formulas (as presented in Chapter 1) to combine common terms wherever possible. An explanation of the mathematical terms is presented in Table 9. 45

Table 8. Comparison of models for analysis of RTOR from exclusive right-turn lanes. Movements considered RTOR volume expression RTOR capacity expression V1 V2 LT V3 P1 P2 TRB 2016 qRTOR = 0 , or use field (HCM) measurement None ï£«R ï£¶ Luh and Lu ci = c p ï£¬ u ï£· f RT 1990 None ï£C ï£¸ ï¼ ï¼ ï£«g ï£¶ ci = S RTOR ï£¬ CT ï£· Stewart and ï£ C ï£¸ Hodgson 1995 None S RTOR = 849.82 exp [ â0.00129v ] â 31 ï¼ ï¼ exp [ âqc tc ] 3600 R â td =ci â â Liu 1995 None 1 â exp [ âqc ht ] hc C ï¼ ï¼ g qRTOR 79.0 + 0.339VRT â 165 RT = C â0.0559Vc â 50.3Î´T g RT c = hc ï£® g ï£¹ Abu-lebdeh +0.108T â VRT + 143Î´T i â max ï£¯0,1 â RT S E â Vc ï£º et al. 1997 C ht ï£° C ï£» ï¼ ï¼ R 3600 ï£® V t ï£¹ 3600 ï£® VU ï£¹ ci =u â exp ï£¯ â c 0 ï£º â exp ï£¯ â c 0 ï£º C tf ï£° 3600 ï£» t f ï£° 3600 ï£» tf t0= tc â 2 Virkler and Krishna tf U= 0 Ru â 1998 None 2 ï¼ ï¼ Teply et al. 2008 (Canadian C ï£« qRT ï£¶ Capacity 850 â 0.35 ci = + qc ï£· Guide) None R ï£¬ï£ 2 ï£¸ ï¼ Hawley and Bruggeman 2009 (WisDOT) qRTOR = 0.50qRT None TRB 2010 (HCM) qRTOR = 0.50qSLT None ï¼ Trafficware, q R RTOR = min ( S RTOR , qRT ) LLC. 2017 C (Synchro) (additional details in Chapter 1) None ï¼ ï¼ ï¼ ï¼ 46

Table 9. Explanation of terms used in Table 8. Term Explanation ci Capacity of RTOR movement cp Potential right-turn capacity C Cycle length Indicator variable for type of conflict (0 if RTOR is conflicted by V1, 1 if conflicted by V1 and Î´T V2) fRT Right-turn adjustment factor gCT Green time of conflicting through movement gRT Green time of the right-turn movement ht Headway of turning traffic hc Headway of conflicting through traffic qc Flow rate of conflicting through traffic qRT Flow rate of the right-turn movement (including RTOR and non-RTOR) qRTOR Flow rate of RTOR movement qSLT Flow rate of shadowed left turn R Duration of red interval (for the right-turn movement) Ru Unsaturated red time (for the right-turn movement) SE Saturation flow rate of receiving (exit) lane SRTOR Saturation flow rate of RTOR movement tc Minimum/critical gap for RTOR movement td Queue clearance time for conflicting through traffic tf Follow-up time for RTOR movement Vc Volume of conflicting traffic As Table 8 shows, a variety of expressions with numerous forms have been used for both volume and capacity adjustments; these tend to rely on similar concepts. For example, fractions of cycle time relative to red or green intervals are common, and some models employ the critical headway and follow-up time concepts employed in analysis of two-way stop control. Most of the models have considered both V1 and V2, while few have directly included the LT or P1 movements and none have directly considered V3 or P2. Because the models varied in their application of adjustments to both right-turn volume and capacity, to perform a sensitivity analysis of the results, the resulting v/c ratio of the right-turn movement could illustrate results for all of the models simultaneously with respect to different conflicting volumes. To carry out this analysis, a spreadsheet was created wherein each of the models was implemented using a common set of site characteristics (number of lanes, volumes, signal timing, etc.). A base model used the following characteristics: each approach was comprised of a left-turn lane, two through lanes, and a right-turn lane; volumes of 150, 250, and 150 veh/h/ln were used for the left, through, and right-turn movements on each approach (with the exception of the subject right turn); an eight-phase signal timing plan was assumed with protected left-turn phases; and, for simplicity, a simple timing plan was assumed, using green times of 20 seconds for each phase, 5 seconds in total of change and clearance time on each phase, and a total cycle length of 100 seconds. For this analysis, pedestrian volumes were not considered. The volumes of the V1, V2, and LT movements (Figure 14) were varied on top of these base conditions. 47

Figure 15 shows the influence of volume V1 on the v/c ratio of the subject right turn under two conditions: a high total right-turn volume (275 veh/h), and a low total right-turn volume (100 veh/h). The HCM 2016 analysis, shown by the uppermost horizontal line, shows that the base v/c ratio is 91% or 33%, respectively, for the high and low subject right-turn volumes. The other models show values less than this, representing a reduction in v/c ratio because of the additional capacity provided by RTOR. Some of the models converge to the HCM 2010 v/c ratio at higher volumes, representing the loss of capacity as volume V1 occupies most of the potential time when RTOR could be served. In some cases, these converge to a slightly lower value because the opposing left-turn phase is still available for RTOR; however, some models use the total conflicting volume rather than separating V1 and V2. Lastly, a few models (HCM 2010, WisDOT, and Synchro) use relatively static volumes that do not converge as V1 increases. HCM 2016 HCM 2010 WisDOT Abu-lebdeh Synchro Luh Stewart Virkler SSA Virkler ASSA Canadian Liu 1 0.4 0.9 Volume-to-Capacity Ratio Volume-to-Capacity Ratio 0.8 0.3 0.7 0.6 0.5 0.2 0.4 0.3 0.1 0.2 0.1 0 0 0 300 600 900 1200 1500 1800 0 300 600 900 1200 1500 1800 Conflicting Through Movement Volume (veh/h/ln) Conflicting Through Movement Volume (veh/h/ln) (a) High right-turn volume scenario. (b) Low right-turn volume scenario. Figure 15. Influence of conflicting through movement volume V1 on right-turn v/c ratio. Figure 16 shows an analysis that examines the influence of V2. Similar to the previous analysis, the HCM 2010 value shows the largest v/c ratio, while the other models have lower values, reflecting the availability of RTOR capacity. Many of the models show convergence to a flat-line value early in the analysis, representing the loss of all available RTOR capacity on the left-turn movement; the remaining RTOR capacity is attributable to the through movement at a volume of 250 veh/h/ln. 48

HCM 2016 HCM 2010 WisDOT Abu-lebdeh Synchro Luh Stewart Virkler SSA Virkler ASSA Canadian Liu 1 0.4 0.9 Volume-to-Capacity Ratio Volume-to-Capacity Ratio 0.8 0.3 0.7 0.6 0.5 0.2 0.4 0.3 0.1 0.2 0.1 0 0 0 300 600 900 1200 1500 1800 0 300 600 900 1200 1500 1800 Opposing Left Turn Volume (veh/h/ln) Opposing Left Turn Volume (veh/h/ln) (a) High right-turn volume scenario. (b) Low right-turn volume scenario. Figure 16. Influence of opposing left-turn volume V2 on right-turn v/c ratio. Lastly, Figure 17 shows the outcomes for the HCM 2010 model, which considers the shadowed left-turn volume to be a proxy for the RTOR volume. Here, results for the subject right-turn are shown for total right-turn volumes of 500 and 150 veh/h/ln. The two lines represent the v/c ratios as a function of the left-turn volume. As can be seen, the larger the left-turn volume, the smaller the v/c ratio; when the left-turn volume reaches twice the subject right-turn volume, the v/c reaches zero. 49

V=500 V=150 1 0.9 0.8 Volume-to-Capacity Ratio 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800 Shadowed Left Turn Volume (veh/h/ln) Figure 17. Relationship between shadowed left-turn volume and right-turn v/c ratio under the HCM 2010 model, for different total right-turn volumes. The Synchro model, as described in its user guide (Trafficware 2017), contains an adjustment that considers the conflicting pedestrian volume P1. This is combined with other potential RTOR intervals for which a weighted average is taken to establish an RTOR saturation flow rate. This rate is only employed when it falls beneath another base rate for RTOR that depends only on the total right-turn volume. With the presence of the shadowed left turn, this overall RTOR saturation flow rate achieves an overall high value. The influence of P1 is only seen if the shadowed left-turn phase is removed from the analysis. There is a great deal of variety in these overall results; as seen in Figure 15 and Figure 16, for the same conditions, the v/c ratio might vary as much as 50% from the highest to the lowest model values in some cases for high right-turn volumes. Several of the models appear to converge as V1 or V2 volumes are increased; some models do not appear to explicitly consider V1 and V2 as separate contributors to the availability of RTOR. For example, in Figure 15a, three of the models converge to the HCM v/c ratio at high levels of V1, while there should still be available time for RTOR when the opposing left (V2) is being served. None of the models explicitly considered the shadowed left turn, other than the HCM 2010 technique, which does not do so in a very realistic way, and the Synchro model, which considers the green time of that movement (although it is overshadowed by other dynamics). The RTOR volume would not be able to serve all of the right-turn volume because not all of the right-turn arrivals at the intersection will occur during that interval. At a minimum, the right-turn volume 50

served during green would be proportionate to the g/C ratio of the through and right-turn movement, assuming random arrivals. 4.1.2 Dual Right-Turn Lane Dual right-turn lanes were considered in two previous studies: the WisDOT model, which used a fixed value of 30% of the total right-turn volume, and Chen et al. (2012), which presented a more involved analysis including a separate calculation of capacities for each lane that considers the conflicting through and opposing left-turn movements. The green time of the shadowed left-turn is also considered. Figure 18 shows an intersection layout that shows various volumes relative to the RTOR movement; the same basic volumes are present as in Figure 14, but there are now two right-turn lanes. V2 P2 V3 RTOR V1 RTOR LT P1 Figure 18. Volume and lane configuration used for modeling dual right-turn lanes. An analysis was carried out for this scenario using the same geometry and volumes per lane as for the exclusive right-turn lane analysis described earlier. Results are presented in Figure 19. The HCM 2016 v/c ratio is 0.91, while the adjustment suggested in the WisDOT report gives a v/c ratio of 0.64. The results from Chen et al. (2012) are shown for two different volumes of the opposing left (V2): the base value of 150 veh/h/ln and a higher value of 450 veh/h/ln. These respectively yield v/c ratios of 0.44 and 1.32 for the opposing left-turn movement, and so a wide range of variation with respect to V2 is represented. Results are also shown both with and without the shadowed left turn. Chen et al. (2012) predicts v/c ratios of about 0.20 to 0.50 depending on the values of V1 and V2 and the presence of the shadowed left turn. 51

Chen (V2 = 150 veh/h/ln; with shadowed LT) Chen (V2 = 450 veh/h/ln, with shadowed LT) Chen (V2 = 150 veh/h/ln; without shadowed LT) Chen (V2 = 450 veh/h/ln, without shadowed LT) WisDOT HCM 2016 1 0.9 0.8 Volume-to-Capacity Ratio 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0 0 150 300 450 600 750 900 1050 1200 1350 1500 1650 1800 Conflicting Through Movement Volume (veh/h/ln) Figure 19. Influence of conflicting through movement volume on right-turn v/c ratio for different models of dual-lane right turns. 4.1.3 Shared Through and Right-Turn Lane Several models of shared through and right-turn lanes were identified in the literature. Figure 20 illustrates this scenario. In addition to the volumes identified in the previous scenarios (Figure 14, Figure 18), a fourth conflicting volume (V4) is added: the amount of through traffic in the shared through and right-turn lane. For shared through and right-turn lanes, this volume (or rather, its proportion of the total volume in the shared lane) constrains the ability for the RTOR maneuver to be executed more strongly than the other volumes, since even a relatively small proportion of through traffic to total lane volume will block the movement for right-turning vehicles. Table 10 summarizes the mathematical forms of the models found in the literature for shared through and right-turn lanes, while Table 11 lists the terms used in these models. 52

V4 V2 V3 V1 RTOR LT P1 P2 Figure 20. Volume and lane configuration used for modeling shared through and right-turn lanes. 53

Table 10. Comparison of models for analysis of RTOR from shared through and right-turn lanes. Movements considered RTOR volume expression RTOR capacity expression V1 V2 LT V3 P1 P2 V4 TRB 2016 qRTOR = 0 , or use field (HCM) measurement None Luh and Lu 3600 ci = min ( cc , E ) 1990 None C ï¼ ï¼ ï¼ Probabilistic approach contingent on the likelihood of lane blockage; see Chapter 1 Liu 1995 None for details ï¼ ï¼ ï¼ c c A + cB = ï£« vt C ï£¶ v exp ï£¬ â i c ï£· ï£« vp ï£¶ i ï£ 3600 f i ï£¸ ï£¬1 â cA = ï£·â ï£ 2100 ï£¸ 1 â exp ï£« â vi t f C ï£¶ ï£¬ ï£· ï£ 3600 f i ï£¸ 3600 R cB = â tf C Tarko 2001 qRTOR = min ( q0 , ci ) Used in the volume adjustment ï¼ ï¼ ï¼ ï¼ ï£« 1 â p ï£¶ 3600 c1 + PRTOR ( c2 + c3 ) ci = min ( X r ,1.0 ) ï£¬ ï£· ï£ p ï£¸ C 1 â p 3600 1 PRTOR = â â qTh p C qTh + qRT Creasey et p= al. 2011 qTh + qRT (additional details in Chapter 1) ï¼ ï¼ ï¼ R qRTOR = min ( S RTOR , qRT ) C Trafficware, qRT 3600 LLC. 2017 = S RTOR ( k + 1) (Synchro) qTh R None ï¼ ï¼ ï¼ ï¼ ï¼ 54

Table 11. Explanation of terms used in Table 10. Term Explanation cc number of opportunities for RTOR provided by gaps in conflicting traffic ci capacity of the RTOR movement c1 HCM-based approach capacity during green c2 approach capacity when intersecting through and opposing left turns receive an exclusive green c3 approach capacity when shadowed left turns receive an exclusive green E expected number of leading right-turn vehicles in the shared lane k storage length of turn bay (passenger cars) qRT total right-turn flow rate qTh total through flow rate R duration of red for the right-turn movement tc critical headway for right-turn movement tf follow-up time for right-turn movement vi volume of conflicting traffic departing from the rightmost lane vp conflicting pedestrian volume (across the approach; P1) Xr volume-to-capacity ratio of the shared through and right-turn lane For the model analysis, the same base volumes were used as for the exclusive right-turn lane analysis. The analysis included four models that provided specific procedures for shared through and right-turn lanes. In addition, the model presented by Tarko (2001) for shared through and right-turn lanes with short turn bays was included. In the latter case, the model results are presented for a very short turn bay with a capacity of a single vehicle. (The use of zero vehicles would yield an RTOR volume of zero, and thus the results would be the same as the existing HCM model.) Figure 21a shows results from the models for a scenario with a high right-turn volume (275 veh/h) while Figure 21b shows the results for a low right-turn volume (100 veh/h), with varying right-turn volumes. The total v/c ratio of the through and right-turn lane group is presented as a function of the amount of through volume in the shared lane. Equal distribution of volume in the two through lanes was assumed; thus, the total volume on the approach for any given variation of the scenario would be equal to twice the value shown on the x-axis plus the right-turn volume. The ratio of right-turn volume to the total lane group volume is also shown as the secondary horizontal axis in the charts. 55

HCM Tarko Synchro Luh Creasey Liu Ratio of Right-Turn Volume to Total Volume Ratio of Right-Turn Volume to Total Volume 1.00 0.89 0.77 0.66 0.54 0.43 0.31 1.00 0.89 0.77 0.66 0.54 0.43 0.31 1.2 1 0.9 Volume-to-Capacity Ratio Volume-to-Capacity Ratio 1 0.8 0.8 0.7 0.6 0.6 0.5 0.4 0.4 0.3 0.2 0.2 0.1 0 0 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Through Volume in Shared Lane (veh/h) Through Volume in Shared Lane (veh/h) (a) High right-turn volume scenario. (b) Low right-turn volume scenario. Figure 21. Influence of right-turn movement volume on right-turn v/c ratio from shared through and right-turn lanes. In contrast with previous analyses, the models are largely in agreement with each other and only differ from the base HCM analyses by small amounts that cannot be seen in the diagram. This is especially true at higher amounts of through volume (lower ratios of right-turn volume to total lane group volume). The Synchro, Tarko, and Creasey et al. models show some lower v/c ratios at low amounts of through volume, which converge to the other solutions as the volume increases. The linear change is largely a result of the total lane group volume reaching the capacity provided for the two lanes by the green indication. The added capacity of the RTOR movement provides a little additional capacity, and thus a slightly lower v/c ratio, when the right-turn volume is a high proportion of the total traffic. However, this disappears quite rapidly. Even when the ratio is at 80% (meaning that the through traffic is only 20%), most of the RTOR capacity is lost and the v/c ratio is almost the same as that of the base HCM model. 4.1.4 Shared Through and Right-Turn Lane with Short Turn Bay A further variation of the shared through and right-turn model was presented by Tarko (2001), wherein the situation of a short turn bay of varying length was considered. Figure 22 illustrates this scenario. The storage length of the turn bay, k, is one of the key parameters of the model; the V1, V2, and P1 volumes are also considered. The probability that the right-turn bay is blocked by through traffic is explicitly handled in this model. Chapter 1 presents additional detail. 56

V4 V2 V3 V1 RTOR LT P1 P2 k Figure 22. Volume and lane configuration used for modeling shared through and right-turn lanes with short right-turn bays. Model analysis was carried out using the same input parameters as for the shared through and right-turn analysis presented earlier. Results are shown in Figure 23, again for a high right-turn volume (275 veh/h) and a low right-turn volume (100 veh/h). Results are shown for k = 2 and k = 5. The dashed line representing the HCM analysis reflects the scenario of a shared through and right-turn lane with no storage area for right-turning vehicles. Thus, the results of the two models with lower v/c ratios for the lane group illustrate the influence of RTOR in decreasing the total volume used in the calculation of the v/c ratio. As would be expected, the effect is smaller for the shorter storage length (k = 2), since those lanes are more likely to be blocked as the through volume increases. Conversely, the effect is stronger for the longer storage length (k = 5), since the lane is less likely to be blocked. 57

HCM Tarko (k=2) Tarko (k=5) Ratio of Right-Turn Volume to Total Volume Ratio of Right-Turn Volume to Total Volume 1.00 0.89 0.77 0.66 0.54 0.43 0.31 1.11 1.00 0.89 0.77 0.66 0.54 0.43 0.31 1.2 1 0.9 Volume-to-Capacity Ratio Volume-to-Capacity Ratio 1 0.8 0.8 0.7 0.6 0.6 0.5 0.4 0.4 0.3 0.2 0.2 0.1 0 0 0 100 200 300 400 500 600 0 100 200 300 400 500 600 Through Volume in Shared Lane (veh/h) Through Volume in Shared Lane (veh/h) (a) High right-turn volume scenario. (b) Low right-turn volume scenario. Figure 23. Influence of right-turn movement volume on right-turn v/c ratio from shared through and right-turn lanes with short turn bays (k = storage length of the bay in number of passenger cars). 4.2 Model Inputs and Feasibility of Implementation The feasibility of implementation in the HCM is an important consideration in the development of models for RTOR volume. To assess this, each of the models in the study was investigated to identify the parameters each requires to carry out its analysis. This section presents those results. All of the models required basic information about the site characteristics and common parameters reflecting the traffic scenario, which are already included in the existing HCM. Site characteristics include the following: â¢ Lane configuration (number of lanes, shared/exclusive/dual, presence of bicycle lanes, etc.) â¢ Lane width â¢ Storage length â¢ Approach grade â¢ Parking maneuver rate adjacent to a lane group â¢ Bus stopping rate on each approach â¢ Area type â¢ Presence/absence of work zone â¢ Downstream lane closure â¢ Spillback from downstream intersection Another set of common parameters, already used in the HCM and most of which would be available to users of a model for volume or capacity estimation, include the following: 58

â¢ Demand volumes â¢ Pedestrian volumes â¢ Bicycle volumes â¢ Percentage of heavy vehicles â¢ Signal timing parameters â¢ Platoon ratio â¢ Progression factor â¢ Incremental delay factor â¢ Upstream filtering factor For existing locations, most of the above should be known because these are the basic data for performing a signalized intersection LOS analysis. For planning use cases, signal timing data may not be available, so it may be desirable to develop models that exclude such data to obtain estimated RTOR volumes, although the signal timing is needed to go further into an LOS analysis. Alternatively, a plausible signal timing plan could be developed based on the volumes. The inclusion of additional parameters beyond those listed above would make implementation more difficult, since new terms would have to be estimated to conduct the analysis. The studies identified from the literature review were examined to determine how many included additional parameters; the results are presented in Table 12. Four of the methods found in previous studies do not include any additional parameters: the HCM 2010 technique, which uses the shadowed left-turn volume; the WisDOT method, which uses a fixed proportion of the total right-turn volume (Hawley and Bruggeman 2009); the method in the Canadian Capacity Guide for Signalized Intersections (Teply et al. 2008); and the Synchro method (Trafficware, LLC. 2017). The methods found in the other studies do include some additional parameters. The following are definitions of the parameters seen in various previous studies: â¢ Critical gap. This is the minimum gap required for an RTOR vehicle to proceed beyond the stop line. This is similar to the critical gap used for two-way stop control analysis. â¢ Follow-up time. This is the amount of time needed after a gap is accepted for the next vehicle to move forward to the stop line. This is similar to the follow-up time used in two-way stop control analysis. â¢ Saturation flow rate of receiving lane. This is the maximum flow rate into the receiving lanes. Although not currently used for the HCM signalized intersection LOS methodology, it could probably be estimated using a similar process as the estimation of saturation flow rates for through lanes. â¢ Saturation headway of intersecting through traffic. The saturation flow rates of the through movement are already used in HCM analysis; these could be restated in terms of headways. â¢ Saturation headway of RTOR traffic. One previous study specified a saturation flow rate for RTOR traffic in particular. This quantity is related to the follow-up time and critical gap for the RTOR movement. â¢ Unsaturated red time. This refers to the amount of red time that is available for the RTOR movement. Any model for RTOR would likely need to address the amount of red time when the RTOR movement is feasible. An upper bound would be the total amount of red time available, which could be determined from the signal timing. 59

â¢ Queue clearance time of conflicting traffic. This refers to the amount of time needed for standing queues in the source lanes of conflicting traffic to be cleared. This would represent the end of saturation flow in those lanes and thus the beginning of those portions of time where RTOR is possible and the gaps in traffic become dependent on the random-arrival process. Such times could potentially be estimated using a simple queuing analysis of the source movements of the conflicting traffic. Altogether, despite the specification of several new parameters, none of the parameters included in the models examined here present especially onerous requirements for new analysis in the HCM methodology (i.e., none of them would necessarily require new field data collection). Two possible exceptions are the critical gap and follow-up time, which are not used in the HCM signalized intersection LOS analysis. However, values for these parameters are included in two- way stop control intersection LOS analysis. Table 12. Observable items needed in each model. Key parameters (excluding common parameters and Lane configuration Model site characteristics) TRB 2010 (HCM) â Critical gap Luh and Lu 1990 Follow-up time Hawley and Bruggeman 2009 (WisDOT) â Stewart and Hodgson 1995 â Saturation flow rate of receiving lane Saturation headway of intersecting through traffic Abu-Lebdeh et al. 1997 Saturation headway of RTOR traffic Critical gap Virkler et al. 1998 (SSA Follow-up time and ASSA) Unsaturated red time Teply et al. 2008 (Canadian Capacity Guide) â Trafficware, LLC. 2017 (Synchro) â Exclusive Liu 1995 Average crossing headway of conflicting traffic Expected number of cycles per hour (can typically be Tarko 2001 derived from signal timing data) Shared and shared with Critical gap right-turn bay Creasey et al. 2011 Follow-up time Critical gap Follow-up time Dual Chen et al. 2012 Queue clearance time of conflicting traffic 4.3 A Framework for Modeling Right-Turn-on-Red Volume and Capacity The preceding exposition of RTOR volume and capacity models from the literature shows a variety of approaches with a wide range of variation in the outcomes, particularly in the case of an exclusive right-turn lane, which is the most widely studied scenario. Most of the models surveyed in the literature used the entirety of the red duration. A limitation of this approach is 60

that the conflicting volumes control the availability of time for the RTOR movement within separate intervals inside of the total red time. That is, there are different flow regimes occurring within the red interval. Depending on the type of modeling approach used, these dynamics may be important or unimportant. Use of statistical modeling with volume inputs may be able to achieve a good estimation of the RTOR volume without the need to dissect the overall red time into its constituent parts. However, the development of physical models for capacity will probably need to examine the intervals separately to arrive at reasonable results. Figure 24 shows a ring diagram that corresponds to the intersection diagram shown in Figure 14; the phase numbering is a typical eight-phase configuration commonly used at intersections in the United States, in this case featuring left-turn phases on every approach. In this example, the right turn served by phase 2 is the subject right turn, while the conflicting left (phase 1), conflicting through (phase 4), and shadowed left turn (phase 3) are served under three different phases. The entire cycle can be divided among these phases into the green interval (phase 2) and three separate opportunities for RTOR (phases 1, 3, and 4). A similar analysis could be done for the other three right turns. If any of the phases were omitted (e.g., if one of the left turns did not have a separate phase), then the corresponding interval would not exist. 1 2 3 4 Protected Permitted Pedestrian Subject RT 5 6 7 8 Conflicts Shadowed Figure 24. Analysis of typical eight-phase control scheme showing an example subject right- turn movement and when other conflicting movements are scheduled. Figure 25 shows the intervals for a generic right-turn phase in more detail. Following the definitions of effective red and effective green in the existing HCM methodology, a similar distinction can be drawn between the displayed intervals and the effective times for each interval. In the HCM, a start-up lost time of 2 seconds and an âencroachmentâ time of 2 seconds are used to define the effective green time. The intervals affecting the right-turn movement could be similarly adjusted. The four intervals are displayed in Figure 25 along with the relevant flow rates (as defined in Figure 14 and Figure 20 in the case of shared through and right-turn movements). Details regarding these intervals are as follows: â¢ RTOR Interval 1 occurs with the shadowed left-turn phase, which is generally available for RTOR movement unless there is a large number of U-turns (V3). If pedestrian overlaps are in use, movement P2 could have an active Walk indication during this interval and therefore 61

could reduce the RTOR capacity. In such a scenario, it is very likely that RTOR would be prohibited, but it is not absolutely required. â¢ RTOR Interval 2 coincides with the conflicting through phase. Movements V1 and P1 conflict with the right-turn movement during this interval. If U-turns are permitted from the opposing left-turn lane during this interval, these may also act to reduce the RTOR capacity. â¢ RTOR Interval 3 represents the time when the opposing left turn is served, which is likely to conflict with RTOR vehicles unless there is some reason to anticipate that the two movements would be received by different lanes. The main conflicting movement is V2. â¢ The number of RTOR vehicles might be increased if the right-turn capacity is reduced during green, as may occur if movement P2 has a heavy pedestrian volume. If the opposing left (V2) is permitted, this could potentially affect the right-turn flow rate served, especially during clearance intervals. â¢ In the case where the subject right turn is served by a shared lane, the total through flow rate in the shared lane (V4) will limit the number of RTOR vehicles that can be served. â¢ A further consideration is the storage length of the right-turn lane and the possibility that it may be blocked by significant queues in the through lane. Conflicting Display RT Green Shadowed LT Conflicting Left Through Phase Effective Effective RT RTOR Interval 1 RTOR Interval 2 RTOR Interval 3 Timings Green â¢ V2 â¢ LT â¢ V1 â¢ V2 Volumes â¢ P2 â¢ V3 â¢ P1 â¢ V4 (shared) Involved â¢ V4 (shared) â¢ P2 (ped overlap) â¢ V3 (permitted) â¢ P1 (ped overlap) â¢ V4 (shared) â¢ V4 (shared) Figure 25. Breakdown of a typical cycle with phases in ordinary sequence into intervals where RTOR is possible. Taking these matters into consideration, it is possible to formulate a generic framework for either the flow rate (or volume) or capacity adjustment: = f1 ( qLT , qV 3 , qP1 , qP 2 , qV 4 ) + f 2 ( qV 1 , qP1 , qV 3 , qV 4 ) + f3 ( qV 2 , qV 4 ) cRTOR Equation 46 qRTOR min ï£®ï£°cRTOR , qRT â qg + f X ( qV 2 , qP 2 , qV 4 ) ï£¹ï£» = Equation 47 c cg + cRTOR = Equation 48 ï£® sgN ï£¹ =cg max ï£¯0, â f X ( qV 2 , qP 2 , qV 4 ) ï£º Equation 49 ï£° C ï£» Equation 46 represents the total RTOR capacity, which includes three terms ( f1 , f 2 , and f3 ) that correspond to the three RTOR intervals. If any of those intervals does not exist, the corresponding term would be eliminated. 62

Equation 47 represents the actual RTOR flow rate, which is the lesser of (1) the RTOR capacity or (2) the total right-turn flow rate ( qRT ) minus the amount potentially served by green ( qg ) plus the leftover demand that could not be served in green ( f X ). By definition, the flow rate cannot exceed the capacity, so the use of the minimum function avoids the possibility of the second term yielding a value that exceeds cRTOR . In Equation 48, the total right-turn capacity c is a sum of the capacity under green ( cg ) and the RTOR movement ( cRTOR ). The capacity during green (Equation 49) could be calculated using the right-turn saturation flow s, green time g, number of lanes N, and cycle length C. An adjustment is made for a potential reduction in capacity due to conflicts during green due to V2, P2, and V4. However, the capacity cannot be less than zero (hence the use of the maximum function). In the current HCM, this is modeled as a reduction of the saturation flow rate by use of the pedestrian and bicycle adjustment factor for right-turn groups, which may be appropriate to retain rather than treat the capacity loss as a separate term. The above framework provides a starting point for bringing together the various pieces under a unified model for analyzing right turns at signalized intersections. The mathematical forms of volumes or capacities are investigated in Chapter 6. 4.4 Conclusion This chapter presented an exploration of various models for estimating the impacts of RTOR on the capacity of signalized intersections through a sensitivity analysis with respect to some of the key volume characteristics of the intersections. Four different scenarios were identified: (1) exclusive right-turn lane, (2) dual right-turn lane, (3) shared through and right-turn lane, and (4) shared through and right-turn lane with a short turn bay. Each of these was presented in turn, including a breakdown and comparison of the models and some of their mathematical forms, along with the different volumes at the intersection that were taken into account. It was observed that many of the models in the literature did not consider all of the different movements affecting the RTOR movement. While most considered the conflicting through and left-turn movements, few acknowledged pedestrians and none considered U-turns. The outcomes of the models were then analyzed with respect to variations in some of the volumes influencing the RTOR performance, as well as other parameters as appropriate. The v/c ratio of the subject movement was employed to illustrate these differences, since some models adjusted the volume while others adjusted the capacity, and the v/c ratio combines both quantities. For the dual right-turn lane and shared through and right-turn lane with a short turn bay, there were only a limited number of studies, making it difficult to compare various models. For the exclusive right-turn lane scenario, there were several different models; many of these had similar results, but among all models considered there was a lot of variation in the outcomes. There was more agreement for the shared through and right-turn lane scenario, although some of the models included for analysis did not differ substantially from the existing HCM method. 63

Finally, the parameters needed for the models from the literature were considered in light of the need for eventual implementation into the HCM. Several new parameters were discovered through this analysis; however, each of these is likely to be estimable from existing quantities used in the HCM methodology. Further research is needed to validate this. The chapter concluded by presenting a framework for further development of RTOR models that uses the notion of relevant signal intervals as the starting point and identifies places where effects would be implemented within the models. Given that none of the models from the literature considers all of the different volumes potentially affecting the RTOR, it is unlikely that any of the existing models will satisfy the desired outcomes of this research, which is to incorporate such effects. However, the components of these models show potential ways that some individual effects can be modeled. Chapter 6 presents the models developed for this study, which includes models of RTOR volume using a statistical modeling approach, and models of RTOR capacity including one model based on a synthesis of the literature and another model based on observations from simulation. 64