Crossing Solutions at Roundabouts and Channelized Turn Lanes for Pedestrians with Vision Disabilities (2011)

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34 This chapter presents the analysis framework used in NCHRP Project 3-78A. It discusses performance character- istics of pedestrians that are used to quantify the availability of crossing opportunities in the traffic stream, as well as the pedestrians’ ability (or willingness) to successfully utilize these opportunities. This analysis framework was initially described in Schroeder and Rouphail (2007) and was later adopted in Schroeder et al. (2009), which are included in Appendices I and J, respectively. These characteristics are then tied to a set of accessibility criteria that were formulated in Schroeder et al. (2009). On the basis of these accessibility criteria, the chapter discusses analysis strategies for the collected field data, includ- ing definitions of pedestrian–vehicle events and variables used in the analysis. The results of the analysis are presented in Chapter 5. Crossing Performance Characteristics The analysis framework hypothesizes that the interaction of pedestrians and vehicles at unsignalized crosswalks can be described using principles of probability theory. Conceptu- ally, pedestrians encounter two types of crossing opportu- nities: (1) gaps in between vehicles of sufficient duration to allow for a safe crossing, and (2) drivers yielding the right of way to pedestrians. The likelihood of occurrence of these events is described by the following probabilities: • P(CG): the probability of encountering a crossable gap (CG) in the traffic stream and • P(Yield): the probability of encountering a yield in the traffic stream. The definitions for what constitutes a yield or a crossable gap are given later in this chapter. Given the complex auditory environment at roundabouts and CTLs and the lack of reliable cues to help identify these events, prior research (e.g., Guth et al. 2005, Ashmead et al. 2005, Schroeder et al. 2006) has established that pedestrians who are blind have difficulty dis- cerning either of these events reliably. As a result, it is expected that the rate of utilization of gap and yield crossing opportuni- ties is less than 100%, which is described mathematically by two additional probability terms: • P(GO|CG): the probability of utilizing an encountered cross- able gap and • P(GO|Y): the probability of utilizing an encountered yield. In the interpretation of these two probabilities, it is impor- tant to emphasize that it is often unclear from observational studies whether the crossing opportunities are missed (i.e., the pedestrian didn’t hear the yielding vehicle) or rejected vol- untarily (i.e., the pedestrian chose not to cross in front of the yielding vehicle). For observational studies, the objective description is that the opportunity was not utilized, which does not pass judgment about the reason for not crossing. This approach for describing pedestrian crossing behav- ior is initially based on unsignalized crossings but can also be applied to signalized crossings. At a signalized crossing, pedes- trians also encounter crossing opportunities in the form of gaps (no traffic) and yields (cars stopped at the signal), but with the caveat that these crossing opportunities tend to coin- cide with a particular phase in the signal cycle (i.e., the “Walk” phase). When applying this approach to a signalized crossing, the analyst should therefore make note of differences in these probability terms at different times in the cycle. Even at sig- nals, some drivers may not yield (e.g., may run a red light) and (blind) pedestrians may miss crossing opportunities, especially when no audible signal is provided. The probability terms described above therefore provide a universal evaluation framework of pedestrian–vehicle interaction at crosswalks that can be applied independently of the presence of a signal. Similarly, the above framework allows the analyst to quan- tify the impact of any other crossing treatments that are intended to facilitate pedestrian crossings but fall short of C H A P T E R 4 Analysis Framework

stopping traffic with a red signal indication. The framework therefore is sensitive to different treatment objectives, such as increasing the propensity of drivers to yield, P(Yield), or enhancing the ability of using crossing opportunities. Crosswalk Usability Criteria The crossing performance characteristics above provide a framework for quantifying pedestrian behavior from an observational study. For the purpose of establishing criteria for whether or not a crosswalk is accessible to and usable by a pedestrian who is blind, four accessibility criteria have been formulated. These criteria address different aspects of usability and together provide a comprehensive approach for quantify- ing crossing performance at a test location. The four crosswalk usability criteria, from Schroeder et al. 2009, are: 1. Crossing opportunity criterion – Are there sufficient crossing opportunities in the form of yields or crossable gaps? 2. Opportunity utilization criterion – Are the crossing opportunities utilized by the pedestrian? 3. Delay criterion – Is a crossing opportunity taken within a reasonable time? 4. Safety criterion – Do the crossing attempts involve a significant degree of collision risk? Each of the four criteria is discussed in more detail below. Crossing Opportunity Criterion Crossing opportunities may take the form of yields or gaps. A yield is defined as a driver reducing the speed of the vehicle or coming to a full stop to allow a pedestrian to cross the street. Legislation in most U.S. states requires drivers to yield to pedestrians in the crosswalk, but the laws (and driver under- standing of the law) vary in terms of the requirement to yield to pedestrians at the crosswalk. A nationwide survey of yield- ing practices at unsignalized crosswalks (Fitzpatrick et al. 2006) identified a wide range of yielding behaviors and fur- ther found varying levels of yield compliance for different pedestrian crossing treatments. Similar inconsistency was found for yielding behavior at roundabout crossings across the United States (Rodegerdts et al. 2007). For the purpose of this analysis framework, an increase in yielding directly affects the crossing opportunity criterion. When crossing opportunities are presented in the form of gaps between successive vehicles, a threshold needs to be intro- duced to define what constitutes a crossable gap. The threshold for separating crossable and non-crossable gaps is proportional to the crossing distance (longer distance requires more time to cross) and inversely proportional to the pedestrian walking speed (slower walkers require more time to cross). It is fur- ther reasonable to implement some additional buffer time to account for some lost time before a crossing is initiated and some safety clearance time after the crossing is completed. The U.S. Highway Capacity Manual (HCM) (TRB 2000) defines the critical gap for pedestrians as the crossing distance divided by the walking speed, plus a safety buffer. This same concept has been applied in other research on pedestrian behavior (Yang et al. 2006; Rouphail, Hughes, and Chae 2005). For the purpose of this analysis framework, an increase in the occur- rence of crossable gaps directly affects the crossing opportu- nity criterion. The remaining critical definition in this criterion is the term sufficient, which describes whether there are enough crossing opportunities in the traffic stream. The determination of how many crossing opportunities are enough depends on the rate of utilization of opportunities (criterion 2) and ultimately on acceptable levels of delay and risk (criteria 3 and 4). Opportunity Utilization Criterion The second criterion quantifies the level of pedestrian uti- lization of the available crossing opportunities. The utilization of crossable gaps is a function of the gap acceptance character- istics of the pedestrian. It may further be influenced by back- ground noise at the site. At roundabouts and channelized turn lanes in particular, the noise from background traffic may mask the auditory information at the crosswalk, affecting the ability of a blind pedestrian to identify a crossable gap or yield (Guth et al. 2005, Schroeder et al. 2006). Previous research has shown that pedestrians with vision impairments often do not cross in front of yielding vehicles because they either cannot hear the car or they are not confident that the cross- ing is safe despite the yield condition (Ashmead et al. 2005, Davis and Inman 2007). Multiple threat situations (FHWA 2004) at two-lane approaches, where a vehicle in the near lane visually and/or auditorily masks approaching vehicles in the far lane, further complicate yield utilization. It has been demonstrated in ongoing research funded by the NIH (2010) that sighted pedestrians can successfully iden- tify and utilize most (if not all) crossing opportunities they encounter. Clearly, individual differences remain, but with a relatively conservative definition of what constitutes a crossing opportunity (e.g., the crossable gap threshold), it is hypothe- sized that a yield and gap utilization rate of 100% represents a reasonable benchmark for what may constitute crossing behavior of a sighted pedestrian. While the first criterion is largely independent of the behavior (and any disability) of the pedestrian, this second criterion begins to distinguish between pedestrian groups with different travel skill levels. This dis- tinction includes the difference between blind and sighted 35

pedestrians (the focus of this research), but can similarly be applied to represent other special pedestrian populations such as children, wheelchair users, or the elderly. Another caveat of the utilization measure is that it can be used to describe potentially risky behavior. For example, assum- ing that the defined threshold for a crossable gap is appropri- ate, any utilization of a non-crossable gap has the potential of increasing the rate of crossable gap utilization to something greater than 100%. This type of check also serves to validate that the crossable gap threshold was defined reasonably. Delay Criterion The first two criteria describe traffic conditions (gap avail- ability), driver behavior (yielding rate), and pedestrian behav- ior (utilization). However, they ignore the temporal aspect of the pedestrian–vehicle interaction. Assuming that a pedestrian eventually utilizes a crossing opportunity, the third criterion describes how much delay was experienced prior to that cross- ing initiation. The Highway Capacity Manual (TRB 2000) uses delay to define levels of service for pedestrian crossings. From an engineering perspective, it is thus intuitive that an inordi- nate amount of delay would make a crossing inaccessible. In the HCM, a (sighted) pedestrian delay over 45 s at an unsignal- ized intersection corresponds to level of service (LOS) F, which is the worst category on an A through F scale. At a signalized crossing the corresponding LOS F threshold is 60 s, acknowl- edging that pedestrians may be more willing to accept higher delays if they have confidence that the signal will eventually provide them with an opportunity to cross. The HCM further emphasizes that the likelihood of risk-taking behavior (by sighted pedestrians) is very high at these levels of delay. The usability of a crosswalk is improved with a reduction in criterion 3. It is expected that increasing levels in criteria 1 and 2 will result in an improvement (reduction) of pedestrian delay. Similarly, a low availability of crossing opportunities and/or a low utilization rate will increase delay. For pedes- trians who are blind, experience with increasingly high delay at a particular crossing may lead people to avoid the cross- ing altogether, making it, in effect, inaccessible. Similarly, it can be argued that high delays (caused by low levels in cri- teria 1 and 2) may lead to an increased propensity to make risky decisions, as is hypothesized in the HCM. In this research, the study trials were capped at a time duration of 2 min. Safety Criterion The fourth criterion describes pedestrian safety at a cross- walk. Even if pedestrians encounter crossing opportunities and utilize them within an acceptable amount of time, the site remains inaccessible if these crossings occur in dangerous situations. Research (Schroeder et al. 2006) found that blind pedestrians make significantly more risky decisions than sighted pedestrians at unsignalized crosswalks at channelized right- turn lanes. A study of blind pedestrians crossing at a two-lane roundabout (Ashmead et al. 2005) found that the experi- menter sometimes had to physically restrain the study partic- ipant from crossing to avoid a potential collision. The overall observed intervention rate was a clear indication of the risky nature of the studied two-lane roundabout crossing. The met- ric of intervention rates was also previously used at crossing studies at single-lane roundabouts (NIH 2010). Field Evaluation Approach The four crosswalk usability criteria were evaluated in con- trolled studies with blind volunteers as described in Chapter 3. The crossing trials were monitored by a field observer and were further videotaped for supplemental data extraction in the office. The analysis approach worked on the basis of time-stamped events that describe traffic conditions, driver behavior, and pedestrian behavior. The following section defines pedestrian–vehicle interaction events as used in this project, followed by a section of variable definitions and performance measures used in the analysis. Event Definitions The NCHRP Project 3-78A analysis used a performance evaluation framework that described the availability of cross- ing opportunities, the rate of utilization of these opportuni- ties, and the delay and risk associated with the crossings. For a single-lane crossing, the yield and gap events are uniquely defined by the vehicle state in the conflict lane. However, at a two-lane crossing the analysis needs to consider the vehicle state in both lanes. For a single conflicting lane, a pedestrian–vehicle event is defined as the interaction of one pedestrian and one vehicle. For each participant, the total number of events is therefore equiv- alent to the number of vehicles encountered during the cross- ing attempt(s). For a two-lane crossing, a pedestrian–vehicle event will be defined as the interaction of one pedestrian and one vehicle in the lane nearest to where the pedestrian is waiting. The vehicle state in the far lane is considered and will be discussed in more detail below. For all types of crossings, a pedestrian–vehicle event has one of five outcomes: 1. Rolling yield (RY): Pedestrian encounters a driver who has slowed down for the pedestrian, but has not come to a full stop. 2. Stopped yield (STY): Pedestrian encounters a driver who has come to a stop, defined as moving at a speed less than approximately 3 mph. 36

3. Forced yield (FY): Pedestrians initiates crossing before the vehicle initiated the yield, forcing the driver to slow down by entering the crosswalk. 4. Crossable gap (CG): Pedestrian encounters a gap large enough to safely cross the street without the need for a driver yield. A crossable gap is defined as the time needed to cross at an assumed walking speed plus a safety buffer. 5. Non-crossable gap (non-CG): Pedestrian encounters a gap between vehicles shorter than the crossable gap threshold. For event categories 1–3, the event is associated with the vehicle (driver) executing the yielding maneuver. For event categories 4 and 5, the event is associated with the second of the two vehicles that define the gap (the vehicle that “closes” the gap). Conceptually, event type 5 also represents a vehi- cle that did not yield to the pedestrian. The sum of event types 1 through 5 corresponds to the total number of vehicles encountered by the pedestrian. The five event categories are used to define the operational variables below. Performance Measures Using the five event outcomes defined above, the NCHRP Project 3-78A analysis framework defines performance mea- sures to describe the four accessibility criteria: crossing oppor- tunity, opportunity utilization, delay, and safety. The first analysis component describes the availability and utilization of yields. Initially, all three yield types (rolling, stopped, and forced) are combined, but they can also be broken out for a more detailed assessment. Three performance mea- sures related to yielding are defined, although only the latter two are used in the analysis: • P(Yield): The probability of a driver yielding, defined as the number of yields divided by the total number of drivers that could have yielded. • P(Y_ENC): The probability of encountering a yield event, defined as the number of yields divided by the total of all pedestrian–vehicle events encountered by the pedestrian until he/she completes the crossing. • P(GO|Y): The probability of yield utilization, defined as the number of crossings in a yield divided by the total number of yields encountered by the pedestrian. The P(Y_ENC) performance measure is different from the traditionally used probability of yielding, P(Yield), since it is calculated on the basis of all pedestrian–vehicle events and not just potential yielders. Figure 14 and the associated dis- cussion provide an example that illustrates the distinction between the two measures. The analysis next considers the availability and utilization of crossable gaps. For the purpose of this analysis, a crossable gap is defined as the time needed to cross the width of the crosswalk at a walking speed of 3.5 ft/s while allowing for a 2-s safety buffer. This 2-s buffer allows for some pedestrian reaction time before initiating the crossing as well as the safety buffer between a completed crossing and the next vehicle arrival. Similar to the yield statistics, three gap-related parameters are defined, but only the last two are used in the analysis: • P(CG): The probability of a gap being crossable, defined as the number of crossable gaps divided by the number of crossable and non-crossable gaps encountered. • P(CG_ENC): The probability of encountering a CG event, defined as the number of crossable gaps divided by the total of all pedestrian–vehicle events encountered by the pedestrian. • P(GO|CG): The probability of crossable gap utilization, defined as the number of crossings in a CG divided by the total number of CGs encountered by the pedestrian. The gap utilization concept is related to other traffic engineer- ing studies that evaluate the numbers of accepted and rejected gaps. A walking speed of 3.5 ft/s in the determination of the cross- able gap threshold is based on the proposed walking speed in the latest release of the MUTCD (FHWA 2009). This estimate represents the 15th percentile walking speed of the general pedestrian population, which is a conservative estimate. As a result, the crossable gap threshold used in this project is also conservative. It is expected that most sighted pedestrians would likely accept gaps that are shorter than this calculated threshold, and this may also be observed for some of the blind study participants. The calculated crossable gap threshold may therefore introduce a potential analysis bias: The probability of encountering a crossable gap, P(CG_ENC), may be lower than what would be perceived by a pedestrian who readily walks at a faster speed and therefore utilizes shorter gaps. Sim- ilarly, the probability of utilizing a crossable gap is expected to be high, given that the threshold for what is considered cross- able is high for 85% of the general pedestrian population. Nonetheless, the chosen walking speed is considered a reason- able assumption in light of national policy documents like the MUTCD, and in light of the fact that the threshold is consis- tently applied to all sites to allow for a relative comparison. The same crossable gap definition is also proposed in Chap- ter 6, which talks about extension of the research results. The combined effect of gap and yield availability and uti- lization is reflected in the delay experienced by pedestrians. Three delay performance measures are defined in the analysis: • Observed Delay per Leg (s): The pedestrian delay in sec- onds, defined as the time difference between when the trial started and when the pedestrian initiated the crossing. 37

1 2 3 4 62 4 5 7 7 8 8 109 Cross Yield Cross Cross Cross Cross Cross Cross Cross Cross CrossYield Yield Yield = 10 Vehicles GO = 1 Crossing NY Y YNY NY NY Y Y NY = 4/(4+5) = 4/9 = 44.4% non-CG CG non-CG CG non-CG = 3/(3+3) = 3/6 = 50.0% YY Y Y = 4/10 = 40.0% CG CG = 3/10 = 30.0% Rej. Y Rej. Y Rej. Y Rej. Y = 0/4 = 0.0% Rej. CG Rej. CG = 1/3 = 33.3% First Opportunity = (4/10)*0% + (3/10)*33.3% = P(Y_ENC)*P(GO|Yield) + P(CG_ENC)*P(GO|CG) P(Crossing) = 70% = 4/10 + 3/10 = 7/10 = P(Y_ENC) + P(CG_ENC) P(Crossing Opportunity) Delay>Min (sec.) Delay>Min. = t(crossing) - t(first opportunity) = 10% P(GO|Yield) Yield Utilization (n=4) Utlz. CG P(GO|CG) CG Utilization (n=4) Delay Delay (sec.) = t(crossing) - t(start trial) CG Encounters (n=10) CG P(CG_ENC) MEASURES # of Events # of Crossings Veh. # Yield Encounters (n=10) P(Yield) P(CG) P(Y_ENC) Start of Trial Vehicle Events (n=10) Pedestrian Events (n=1) Yield Events (n=9) Gap Events (n=6) CG This figure shows an illustrative example of how pedestrian–vehicle events are determined in the NCHRP Project 3-78A analysis framework. The figure shows the hypothetical interaction of one pedestrian and 10 vehicles and translates the different yield and gap events into the performance measures discussed in this chapter. This process is described in detail in the text. Figure 14. Graphical illustration of variable definitions with example (source: Schroeder and Rouphail 2010).

• Minimum Delay (s): The minimum theoretical pedestrian delay in seconds, defined as the time difference between when the trial started and when the first yield or crossable gap was encountered by the pedestrian. • Delay>Min (s): The delay beyond the first opportunity, defined as the time difference between first yield or crossable gap encountered by the pedestrian and the actual crossing initiation. The analysis further investigates two parameters that are intended to describe the efficiency with which a crossing oppor- tunity is utilized for both gaps and yields: • Latency (s): The latency is defined as the time between when the last vehicle went through the crosswalk and the time the pedestrian initiated the crossing. • Yield Lost Time (s): The yield lost time (YLT) is defined as the time between when a driver first yields and the time the crossing is initiated. Note that in some cases, pedestri- ans may prefer to cross only after a car has come to a full stop (stopped yield), and so some inherent yield utilization time is expected. Finally, the analysis uses the rate of O&M interventions that represent a measure of pedestrian safety during the crossings. The study participants were at all times accompanied by a certified O&M specialist who was directed to stop the partic- ipants if the crossing decision would have resulted in undue risk to pedestrian and/or driver. The resulting rate of O&M interventions is defined as follows: • Intervention rate (%): The number of times the O&M specialist intervened for a particular participant divided by the total number of lanes crossed for a particular condi- tion. For example, one intervention over a set of eight lane crossings at the roundabout entry corresponds to an inter- vention rate of 12.5%. Most of the performance measures above are expressed as percentages, which could also be interpreted as a probability of a certain event taking place or a rate of occurrence of that event. For all percentage measures, the level of aggregation is on the level of the individual participant for all crossings by that participant at a particular location. For example, a pedes- trian who crosses the entry leg of a roundabout four times will have an average rate of yield encounters calculated from those four crossing attempts. The same pedestrian will have a dif- ferent rate of yield encounters for the exit leg crossing and also different entry and exit leg percentages for any additional approaches at the roundabout included in the study. The aggregation to the leg per participant level is necessary to ensure that the data point includes at least one of each event type (i.e., a crossable gap and a yield) and a range of outcomes (utilized and non-utilized). Data for a single crossing attempt are often characterized by scarce data, where only certain events are represented. Once the data are combined for all participants, the analysis reports the average, minimum, maximum, and standard deviation of performance at each crossing location. The delay performance measures are measured in a tempo- ral dimension (in seconds). For those measures, aggregation is again to the level of the single participant at one crossing location. But in addition to the average, minimum, maxi- mum, and standard deviation, the analysis further reports the 85th percentile of the estimate. This is common practice for the analysis of continuous variables in traffic engineering applications such as delay studies (Institute for Transporta- tion Engineers 1994). Performance Measure Example This section presents an illustrative example of the dif- ferent performance measures used in the analysis, which was previously published in Schroeder and Rouphail (2010). The example in Figure 14 assumes a crossing attempt by a single pedestrian who encounters 10 different vehicles at a single-lane crossing. Figure 14 shows a time line of a pedestrian encountering 10 hypothetical vehicle events. The time line proceeds from left to right, from the start of the trial until the last vehicle that interacted with the pedestrian crossed the plane of the crosswalk. Of the 10 vehicles, vehicles 2, 4, 7, and 8 yielded to the pedestrian, but none of these yields were utilized. Vehicles 1, 3, 5, 6, 8, and 9 didn’t yield even though a pedes- trian was waiting at the crosswalk. No yield information is available for vehicle 10 since the pedestrian had already walked across by the time it crossed the plane of the crosswalk. Con- sequently, the variable P(Yield) is calculated from 4 yields divided by a total of 9 drivers that could have yielded and equals 44.4%. On the contrary, the variable P(Y_ENC) = 40% is calculated by dividing 4 yields by a total of 10 vehicles encountered in the trial. The temporal separation between vehicles 2–3, 5–6, and 9–10 constitute 3 crossable gaps, the last of which was utilized by the pedestrians. The gap from the start of the trial to vehi- cle 1 and the gaps between vehicles 4–5 and 8–9 were below the crossable gap threshold. The measure P(CG) = 50.0% is calcu- lated by dividing 3 crossable gaps by 6 total gaps encountered. P(CG_ENC) = 30.0% is calculated by dividing 3 crossable gaps by a total of 10 events. The advantage of the P(Y_ENC) and P(CG_ENC) mea- sures is that they have the same denominator (total number of encounters) and are thus additive. This ensures a consistent and objective definition of events. In the NCHRP Project 3-78A 39

analysis, these two variables are preferred and are used instead of P(Yield) and P(CG). The common denominator is further critical in the extension work described in Chapter 6. The rates of yield and crossable gap utilization are calcu- lated at P(GO|Y) = 0.0% and P(GO|CG) = 33.3%, respectively. Delay is defined as the temporal duration from the time the trial starts until the pedestrian initiates the crossing. The min- imum delay is less, calculated as the time spent waiting until the first crossing opportunity, which in this case is the yield by vehicle 2. Consequently, the Delay>Min is defined as the dif- ference between delay and minimum delay. Adapting the Framework to Two-Lane Crossings The above framework was initially developed for single- lane approaches. For any crossing situation where the pedes- trian only faces one conflicting lane, crossing opportunities are uniquely defined by the vehicle state in that lane (yield, crossable gap, or non-crossable gap). However, at a two-lane crossing, the analysis needs to consider the vehicle state in both lanes. The analysis of two-lane crossings therefore distin- guishes between driver behavior in the near lane (the closest lane relative to the position of the pedestrian) and the far lane. Depending on the crossing location (entry/exit and curb/ island), the near lane can be the inside or outside lane of the two-lane approach. The analysis defines the vehicle state in the near lane in the same five event categories defined previously: rolling yield (RY), stopped yield (STY), forced yield (FY), crossable gap (CG), and non-crossable gap (non-CG). The vehicle state in the far lane will then be defined relative to the near-lane con- dition in the same five principal categories (RY, STY, FY, CG, and non-CG). Initially, this results in 25 possible combina- tions of the near/far-lane vehicle state. Further, the near-lane events typically have some temporal dimension. For example, a crossable gap lasts a certain amount of time. Similarly, a yield has some duration associated with it that is related to driver patience and the responsiveness of the pedestrian. To adequately recognize this temporal dimen- sion, a separate far-side category is introduced: multiple events. This category indicates that more than one event took place in the far lane during one near-lane event. For example, sev- eral cars could have passed the plane of the crosswalk in the far lane during one large gap in the near lane. For purpose of analysis, it is assumed that the last event in the multiple-event sequence governs the interaction. In total, the two-lane round- about analysis thus considers five near-lane event categories and 10 far-lane categories (five single-event and five multiple- event categories) for a theoretical 50 possible event combina- tions (see Figure 15). Since this high number of event classifications becomes unmanageable, the results in the main portion of the report combine all near-lane events in three categories (yield, cross- able gap, and non-crossable gap) and do the same for far- lane events, thus simplifying the distinction between a single event or multiple events in the far lane substantially. With this aggregation, the number of near–far lane event combi- nations is reduced to nine (Figure 16). The results for the full event matrix are discussed in detail in Appendix A. The nine event outcomes in Figure 16 can further be put into three categories that are themselves represented as probabilities: • PA_Dual: The likelihood of encountering a crossing oppor- tunity in both lanes, including yield–yield, yield–CG, CG– yield, and CG–CG events, divided by the total of all events. • PA_Half: The likelihood of encountering a crossing oppor- tunity in only one lane, including yield–non-CG, CG–non- CG, non-CG–Yield, and non-CG–CG events, divided by the total of all events. • PA_None: The likelihood of encountering a crossing oppor- tunity in neither lane, including non-CG–non-CG events, divided by the total of all events This stratification becomes important in light of identifying crossing opportunities and interpreting pedestrian utilization of these opportunities. Clearly, a crossing opportunity in both lanes corresponds to a valid crossing strategy. Similarly, if neither lane exhibits a crossing opportunity, the event clearly is non-crossable. If only one of the lanes exhibits a crossing opportunity, a conservative pedestrian would be expected to wait. A more assertive pedestrian may seize the crosswalk in hope of eliciting a driver response in, for example, the far lane. The utilization parameters associated with PA_Dual, PA_Half, and PA_None are denoted as PU_Dual, PU_Half, and PU_None, respectively. Definitions of the utilization mea- sures are consistent with the single-lane analysis framework. For the purpose of this analysis, it is assumed that only events with a crossing opportunity (either a yield or crossable gap) in both lanes represent valid overall crossing opportunities. Consequently, only those events will be included in the dis- cussion of rates of encounter of crossing opportunities and their utilization. The definitions for delay and safety perfor- mance measures are the same as for single-lane crossings. Research Hypotheses The analysis framework hypothesizes that the perform- ance measures above describe the most pertinent aspects of pedestrian–vehicle interaction at the test sites. The mea- sures will be used in this research to quantify the operational differences between test sites and to contrast various cross- ings at the same site (for example, entry versus exit leg). More 40

41 This figure shows a diagram of all possible pedestrian–vehicle interaction events at a two-lane crossing. The figure shows five possible event states for the lane nearest the pedestrian: rolling yield, stopped yield, forced yield, crossable gap, and non-crossable gap. Each of these five event states can be associated with the same five event outcomes in the far lane. The far lane can further feature multiple event outcomes, which in turn are classified by the five categories. In total, the figure shows 50 possible event combinations. This figure shows a diagram of the condensed matrix of pedestrian–vehicle interaction events at a two-lane crossing. The figure shows three possible event states for the lane nearest to the pedestrian: yield, crossable gap, and non-crossable gap. Each of these three event states can be associated with the same three event outcomes in the far lane for a total of nine event combinations. Figure 15. Full matrix of near-lane and far-lane event combinations. Figure 16. Condensed matrix of near-lane and far-lane event combinations. importantly, it is hypothesized that the performance measures are sensitive to the installation of pedestrian crossing treatments (Schroeder and Rouphail 2007). Each treatment is intended to improve one or more of the performance measures. In particular, a treatment that is primarily geared toward improving driver awareness of the crosswalk and the presence of the pedestrian is expected to increase the likelihood of encountering a yield, P(Y_ENC). Yielding behavior is likely also affected by the speed of the vehicle (Geruschat and Hassan 2005), and consequently any traffic calming treatment is likely to increase yielding behavior. The rate of yielding or stop- ping for pedestrians is expected to increase to very high levels for any treatment that shows a solid red indication to drivers (Fitzpatrick et al. 2006), which includes the PHB or HAWK signal. The availability of crossable gaps is primarily a function of traffic volume, where higher volumes will decrease the availabil- ity of crossable gaps. Any upstream metering of traffic through, for example, a signal will also increase the availability of cross- able gaps as it bunches traffic in platoons. The downside of

vehicle platooning is that it has been linked to a lower propensity to yield (Schroeder 2008). The ability or willingness to utilize yields, P(GO|Y), may be improved by lower ambient sound levels or an amplification of the noise of the approaching vehicle. The sound-strip treat- ment attempts to do the latter in that it auditorily distinguishes the conflicting traffic stream from the general background traf- fic (Inman et al. 2005). The willingness to utilize a yield may further be affected by any treatment that gives the pedestrian confirmation in the form of an audible message (APS device or other audible information device) or that slows traffic down to make the pedestrian more comfortable interacting with traffic. The ability or willingness to utilize crossable gaps, P(GO|CG), is also expected to be correlated with the rela- tive noise of conflicting traffic to the overall level of ambi- ent noise. Again, the sound-strip treatment is hypothesized to help in this regard in that the absence of sound cues cor- responds to a potentially crossable gap. An upstream signal that meters overall traffic on the approach may generate “all- quiet” periods during which a blind pedestrian can more reliably identify a crossable gap. For the treatments tested, the following hypotheses are made: • Flashing beacon: Increase P(Yield) and P(GO|Y), • Sound strips: Increase P(GO|Y) and P(GO|CG), • Raised crosswalk: Increase P(Yield) and P(GO|Y), and • Pedestrian hybrid beacon: Increase P(Yield) and P(GO|Y). Further, the occurrence of crossable gaps, P(CG), is likely to vary across sites and study participants depending on traf- fic volumes and the time of day of the study. Ultimately, the four probability terms are hypothesized to affect the delay experienced by the pedestrians. An increase in one or more of the probability terms is expected to decrease the experi- enced delay as more crossing opportunities are available and/ or utilized. The hypothesized impact on pedestrian safety is more dif- ficult to define. For example, one would generally expect that a PHB would create more frequent and safe crossing opportu- nities. However, experience at pedestrian signals (Fitzpatrick et al. 2006) shows that driver compliance may be less than 100%. Consequently, reliance on the audible device message from the signal may contribute to additional risk. In this study, participants were generally instructed to not solely rely on the APS message but to always use their own judgment and audi- ble perception of the traffic environment. In principle, the research hypothesizes that any of the treatments will con- tribute to reducing pedestrian delay and enhancing safety. However, it is recognized that the safety performance evalua- tion may deliver mixed results. 42