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78 Table 17. Input parameters for simulation scenarios. Run-Specific Attributes Treatment Functionality Pedestrians Drivers (Assume 100% Yield 50 Sighted Pedestrians per 50 Blind Pedestrians per 300 Vehicles Detection) Hour Hour per Hour P(C) P(A) P(R) P(C) P(A) P(R) P(Y) NC No Information n/a n/a n/a n/a n/a n/a 0% UA Unassisted Crossing 5 90 5 10 70 20 20% YS Yield Sign for Drivers 5 90 5 10 70 20 50% Vehicle Detect for VD 5 90 5 0 90 10 20% Pedestrians Yield Sign and YSVD 5 90 5 0 90 10 50% Vehicle Detect Perfect Information, PI 0 100 0 0 100 0 100% Everybody Yields P(C) Probability of conservative pedestrian crossing behavior. Pedestrian will accept gaps of 12 s or more. P(A) Probability of average pedestrian crossing behavior. Pedestrian will accept gaps of 6 s or more. P(R) Probability of risky pedestrian crossing behavior. Pedestrian will accept gaps of 3 s or more. P(Y) Probability of drivers yielding to pedestrians (percentage of potential yielders). attributes (Table 17). For illustrative purposes the implemen- gests challenges to estimating the required model input of tation was tested and executed in the VISSIM simulation potential yielders [P(Y)] from field observations of actual package (PTV 2005), but the approach should be applicable yielders. to other simulation tools as well. This sample analysis shows that it is possible to use micro- It is assumed that the typical pedestrian has a critical lag of simulation models to extract conflict and delay data for 6 s, which is considered safe compared to the actual crossing pedestrianvehicle interaction as a function of run-specific time of about 5 s at a walking speed of 4 ft/s. Accordingly, con- attributes of the two groups. The approach describes the inter- servative pedestrians are assigned a longer critical lag value action of the two modes in terms of four probability param- (12 s) and risky pedestrians have a short critical lag of only eters: the likelihood of crossable gap occurrence [P(G)], the 3 s. The resulting delay and risk measures of effectiveness likelihood of gap detection [P(GD)], the likelihood of driver (MOEs) from 10 simulation replications per scenario are yielding [P(Y)], and the likelihood of yield detection [P(YD)]. shown in Table 18. From a preliminary analysis, it appears that the delay and The tables suggest that an increased likelihood of drivers conflict estimates produced by the model in fact follow expec- yielding (case YS) decreases the percentage of conflicts. Improv- tations. For further information the reader is referred to the ing VD for pedestrians appears to slightly increase observed paper included in Appendix I. conflicts compared to the unassisted case. Looking at the large standard deviations of the risk estimates, it cannot be stated Simulation-Based Analysis if this is a real effect at the given sample size. This suggests the of Signalized Crosswalks need for large sample sizes in the model repetitions to show significant effects when evaluating actual treatments. The aforementioned approach for describing pedestrian In comparison, the delay MOEs suggest that as drivers vehicle interaction in a microsimulation environment applies yield more, delay for pedestrians decreases while driver delay to all unsignalized crosswalks, where the interaction is gov- increases. The table also indicates that the percent of actual erned by the four assumed probability parameters. For sig- driver yields is considerably less than the specified percent of nalized crossings, simulation tools already incorporate algo- theoretical yielders. This finding is expected at low pedes- rithms to replicate the way real-world traffic signals function trian volumes since the majority of drivers do not encounter and operate. Consequently, these built-in algorithms should a pedestrian waiting at the crosswalk. This observation sug- be used when a signalized crosswalk is to be evaluated.

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79 Table 18. Measures of effectiveness from simulation. Measures of Effectiveness (Average of 10 VISSIM Runs) Treatment Functionality (Assume Actual Driver Pedestrian Risk Pedestrian Risk Pedestrian Vehicle Delay 100% Yield Detection) Yield % Yield Lead, % Lag, % Delay (s) (s) Avg. Std. Avg. Std. Avg. Std. Avg. Std. Avg. Std. Dev. Dev. Dev. Dev. Dev. 0.0% 0.00% 27.0% 5.20% 19.3% 2.40% 0.0 0.00 2.4 NC No Control Unassisted 3.8% 0.99% 2.1% 0.70% 0.5% 0.70% 4.4 0.28 3.1 0.32 UA Crossing Yield Sign for 9.3% 1.16% 1.0% 0.80% 0.2% 0.70% 4.1 0.20 4.2 0.29 YS Drivers Vehicle 3.7% 0.84% 2.7% 1.40% 0.2% 0.70% 4.3 0.37 3.1 0.27 VD Detect for Pedestrians Yield Sign 9.0% 1.33% 1.0% 1.00% 0.2% 0.70% 3.9 0.27 4.2 0.31 YSVD and Vehicle Detect Perfect 15.0% 2.00% 0.0% 0.00% 0.0% 0.00% 3.5 0.30 5.4 0.41 Information, PI Everybody Yields Depending on the specific signal strategy (i.e., a conven- With these considerations in mind, simulation tools can tional signal versus a pedestrian hybrid beacon), it may be nec- readily be used to estimate the effect of signals on pedestrian essary to customize the signal control logic to some extent. and vehicle delay. Even without fully capturing the behav- The analyst should have a thorough understanding of how the ioral aspects related to the signal, a simulation-based analy- signal is or will be implemented in the field before attempting sis is a great tool for a relative comparison of different signal to represent it in simulation. Particular attention should be strategies. paid to whether the signal operates in "free" operation or whether it is in some way coordinated with other pedestrian Pedestrian Signals at Roundabouts signals (two-stage crossing) or with the vehicle signal at the main intersection (for channelized turn lanes). This section summarizes a detailed sensitivity analysis of The analyst should further consider whether actual driver pedestrian signalization options for modern roundabouts and pedestrian behavior is consistent with the way it is intended performed in simulation. The discussion is based on work by the signal. For example, it was observed at the PHB installa- published in Schroeder et al. (2008), which is included in tion in this project that some pedestrians crossed before the Appendix L for quick reference. "Walk" phase came on while others waited until the "Flashing The objective of this sensitivity analysis is to explore the Don't Walk" before they felt comfortable crossing. In other pedestrian-induced impacts of different signalization strategies words, pedestrians used the signal as a crossing aid, but by no at modern roundabouts in a simulation environment. The means as the sole means of determination for stepping into the analysis focuses on six analysis dimensions: roadway. Similarly, some drivers were observed to proceed despite a red signal indication. For modeling the vehicular 1. Roundabout geometry: The analysis includes a single- impact of the PHB signal, it is of particular importance to ade- lane and a two-lane roundabout. quately represent driver behavior. That signalization strategy is 2. Crosswalk location: The analysis includes three alterna- intended to result in more efficient vehicle operations by allow- tive crosswalk geometries. The proximal crossing is the stan- ing drivers to proceed during the "Flashing Red" phase if no dard crosswalk location set back from the circulating lane pedestrian is in the crosswalk. Clearly, the estimated vehicle by one vehicle length (20 ft). The zigzag configuration delay for this strategy is principally tied to the level of under- moves the exit portion of the crosswalk to a distance of standing of and compliance with this phasing scheme. three vehicle lengths (60 ft) from the circulating lane to

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80 Table 19. Test matrix of treatment combinations The table demonstrates that some of the combinations (source: Schroeder et al. 2008). were not tested because they were considered impractical. For example, a two-stage crossing at a single-lane roundabout Crosswalk Crosswalk Single-Lane Two-Lane Location Staging Roundabout Roundabout proximal crosswalk is expected to result in low compliance Proximal One stage Yes Yes and therefore wasn't tested. Similarly, a one-stage crossing was Crossing Two stage No Yes not tested for the zigzag configuration since the elongated Zigzag One stage No No splitter island provides a natural separation between the two Crossing Two stage Yes Yes stages of the crossing. For each of the checked cells, the analysis Distal One stage Yes No considered all combinations of the remaining three dimen- Crossing Two stage No Yes sions (signalization strategy, vehicle volumes, and pedestrian volumes). In addition, the analysis included an additional vol- ume sensitivity that was intended to capture the effect of even provide additional queue storage on the exit leg. The distal higher pedestrian flows of up to 300 pedestrians/hour. The crossing location moves the entire crosswalk to a distance analysis used the average results from 10 simulation replica- of five vehicle lengths (100 ft) from the circulating lane. tions in each scenario. All runs evaluated the effect of one sig- 3. Signal staging: The analysis includes single-stage and two- nalized crosswalk being installed at the busiest approach to the stage phasing schemes as appropriate. roundabout. 4. Signalization strategy: The analysis includes a conven- The analysis results provide a quantitative comparison of tional pedestrian signal and a pedestrian hybrid beacon (i.e., different signalization options for pedestrian crossings at HAWK signal). The analysis assumes full understanding one-lane and two-lane roundabouts, all of which intended to of and compliance with the signal phases, which is reason- improve access for blind pedestrians. Table 20 highlights a able for a relative comparison. For an absolute assessment subset of the results for the case of 50 pedestrians/hour cross- of the delay impact, some variation in behavior should be ing at the signalized two-lane roundabout crosswalk. Results considered. are shown for below-capacity and at-capacity vehicle vol- 5. Vehicle volumes: The analysis considers a range of vehi- umes. These two-lane roundabout scenarios were selected cle volumes, categorized as below capacity, at capacity, because they directly relate to the most likely application of and slightly above capacity. roundabout pedestrian signals. Additional results are pro- 6. Pedestrian volumes: The analysis considers two levels of vided in Appendix L. pedestrian volumes (10 and 50 pedestrians per hour) rel- The results indicate that innovative signalization treat- ative to the baseline of no pedestrians. ments, including the PHB and two-stage crossings, can sig- nificantly decrease vehicle delay. With 50 pedestrians/hour at Appendix L provides a more detailed description of the dif- the two-lane roundabout, a proximal single-stage pedestrian- ferent model scenarios. Table 19 summarizes the tested com- actuated signal resulted in pedestrian-induced vehicle delays binations of the dimensions of roundabout geometry, cross- of 14.2 s per vehicle in the below-capacity scenario and 68.4 s walk location, and signal staging. for the at-capacity case. The use of a PHB at the same location Table 20. Sample results of roundabout signalization sensitivity analysis. Two-lane Roundabout, 50 peds/hour Below Capacity At Capacity Crosswalk Signal Signal Delay per % Change Delay per % Change Location Staging Strategy Vehicle (s) over Base Vehicle (s) over Base Single Ped. signal 14.2 Base 68.4 Base stage PHB 6.3 56% 39.4 42% Proximal Two Ped. signal 4.1 71% 24.4 64% stage PHB 1.5 89% 5.5 92% Two Ped. signal 3.9 73% 23.4 66% Zigzag stage PHB 1.3 91% 7.0 90% Two Ped. signal 2.8 80% 5.9 91% Distal stage PHB 1.2 92% 0.0* 100% * This scenario actually resulted in a net decrease of the total roundabout delay, explained by the fact that the signal was metering demand on a busy approach. Number was limited to a positive range for this table.