Supporting Material to NCHRP Report 674 (2011)

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APPENDIX I: Details on Simulation Analysis Framework This Appendix was previously published as conference proceedings at the 86th Annual Meeting of the Transportation Research Board, January 21-25, 2007. The citation for this work is: Schroeder, Bastian J. and Nagui M. Rouphail. A Framework for Evaluating Pedestrian-Vehicle Interactions at Unsignalized Crossing Facilities in a Microscopic Modeling Environment 86th Annual Meeting of the Transportation Research Board. 2007 131

Schroeder, Rouphail November 2006 Page 1 of 20 A Framework for Evaluating Pedestrian-Vehicle Interactions at Unsignalized Crossing Facilities in a Microscopic Modeling Environment By Bastian Jonathan Schroeder, E.I.* Graduate Research Assistant Institute of Transportation Research and Education (ITRE) North Carolina State University Centennial Campus, Box 8601 Raleigh, NC 27695-8601 Tel.: (919) 515-8565 Fax: (919) 515-8898 Email: Bastian_Schroeder@ncsu.edu Nagui M. Rouphail, Ph.D. Director, Institute for Transportation Research and Education (ITRE) Professor of Civil Engineering North Carolina State University Centennial Campus, Box 8601 Raleigh, NC 27695-8601 Tel.: (919) 515-1154 Fax: (919) 515-8898 Email: rouphail@eos.ncsu.edu November 2006 Submitted for presentation at the 86th Annual Meeting of the Transportation Research Board, January 21-25, 2007 Word Count: 5,982 text words plus 1,500 for figures/tables (6*250) = 7,482 total * Corresponding Author 132

Schroeder, Rouphail November 2006 Page 2 of 20 ABSTRACT This paper proposes a framework for evaluating the interaction of pedestrians and vehicles at pedestrian crossing facilities in a microscopic modeling environment. The paper discusses modeling parameters for the interaction of pedestrian and vehicle traffic that should be included in a microscopic simulation analysis of unsignalized pedestrian crossing facilities. The paper lists the requirements for stochastic input data in the model and discusses performance measures including pedestrian delay, vehicle delay and the likelihood of pedestrian-vehicle conflicts. The paper further describes how a calibrated microsimulation model can be used to simulate a range of pedestrian crossing treatments by modifying a limited number of input parameters. The analysis will include nuances of pedestrian-vehicle interaction that are frequently neglected in existing microsimulation software. The paper concludes by demonstrating the application of the framework for an unsignalized crosswalk example in the simulation model VISSIM. 133

Schroeder, Rouphail November 2006 Page 3 of 20 ACKNOWLEDGMENT The research leading up to this document was supported by the NCHRP 3-78 project, ‘Crossing Solutions at Roundabouts and Channelized Turn Lanes for Pedestrians with Visual Disabilities’. The authors would like to thank the National Academies for the opportunity to be involved in the project and for permission to share the proposed modeling framework with the Transportation Research Board Community. The authors would also like to thank the members of the project panel, who have provided continuous feedback to the research efforts and the proposed methodology. Finally, the authors would like to thank the other members of the project team, who have been invaluable in discussing the application of microsimulation models to the project. INTRODUCTION This paper proposes a framework for describing pedestrian-vehicle interaction at unsignalized pedestrian crossing facilities in a microscopic modeling environment. While some of the commercially available microsimulation packages are theoretically able to simulate pedestrians, the primary purpose of these models clearly lies in simulating motorized traffic. There is currently not a great amount of guidance in the literature on how to represent pedestrians in a microscopic environment and how to model their interaction with motorized traffic at pedestrian crossings. This paper attempts to summarize the characteristics that distinguish pedestrians from motorized traffic and discusses ways of implementing these pedestrian-specific attributes in microsimulation. BACKGROUND Microsimulation models are used frequently in transportation research applications due to their ability to evaluate a great range of geometric and operational configurations in a non-intrusive manner. They are also seeing increasing use in public and private traffic engineering practice to simulate complex geometries, intelligent transportation systems (ITS) solutions and for numerous other applications. The Next Generation Microsimulation (NGSIM) effort by the Federal Highway Administration (FHWA) has taken on the challenge of developing new and improved algorithms, working towards the goal of standardized application of microsimulation models in the US. With limited resources, the initial focus of the NGSIM effort is in areas with high degrees of applicability, such as the freeway lane selection algorithm and cooperative freeway merge behavior. The area of pedestrian simulation is much lower on the list of priorities on the national scale and won’t be addressed until these other ‘high-impact’ algorithms have been completed. Nonetheless, the field of microsimulation has a lot of potential applications in the area of pedestrian-vehicle interaction, especially in light of evaluating delay and safety impacts of different pedestrian crossing treatments. A lot of research in recent years has focused on proposing new and improved treatments for safe pedestrian crossings and most communities are including pedestrian-safety initiatives in transportation planning. While it is possible to a certain extent to conduct ‘before and after studies’ for testing pedestrian crossing treatments, there is clearly a benefit to performing some treatment evaluation in a microsimulation environment. 134

Schroeder, Rouphail November 2006 Page 4 of 20 The discussion that led to the development of this proposed framework originated in the NCHRP 3-78 research effort. Motivated by budget considerations and a very broad range of potential crossing treatments, the project team decided early-on to include microsimulation analysis in the process of screening and evaluating proposed treatments a priori to field implementation. Following the actual experiments in the field, calibrated microsimulation models will further be used to assess treatment effectiveness under a range of operational and geometric configurations. Due to authors’ involvement in NCHRP 3-78, most examples in this paper include behavioral comparisons between blind and sighted pedestrians. These are intended as illustrative examples and are easily transferable to other applications with varying driver and pedestrian populations. THE CROSSING TASK The movement of pedestrians is principally different from that of motorized traffic and therefore warrants a separate assessment of associated behavioral attributes. Blue and Adler (2001) compiled the following list of principal differences between pedestrian and vehicular traffic: • Pedestrians are not officially channelized • Pedestrians can vary their speed • Pedestrians can occupy any part of the walkway • Pedestrians can bump into each other • Pedestrians have almost instantaneous acceleration/deceleration profiles In this paper, the authors will transfer some of these pedestrian attributes to the pedestrian crossing task and discuss implications on the crossing performance at unsignalized crosswalks. The authors will define an ‘unsignalized’ crossing as one at which the crossing task is not explicitly regulated by a traffic signal. Assuming compliance and proper timing, a signalized crossing can be evaluated with existing capacity equations and theoretically does not pose risks to the pedestrians. The issue of non-compliance at signals and misunderstanding of signal indications will be deferred to future human factors research. At an unsignalized crossing the priority regulation is usually less rigid. Such crossings can also be outfitted with various pedestrian crossing treatments such as signage, flashing beacons or auditory pavement treatment. In fact, the principal purpose of this framework is the evaluation of such non-signal treatments in a microscopic environment. Conceptually, the process of pedestrians crossing at an unsignalized facility can be represented by a dual gap acceptance process: pedestrians accepting gaps in the vehicle stream, and vehicles accepting gaps in the pedestrian stream. Pedestrians waiting to cross the road screen the conflicting vehicle stream for crossable gaps or a yield situation. Drivers, in turn, observe the pedestrian crosswalk to decide whether to yield to a pedestrian. At the majority of unsignalized pedestrian crossings it is oftentimes not clearly defined, whether pedestrians or vehicles have the right-of-way. Legislative language commonly states that ‘drivers shall yield to pedestrians in the crosswalk’, but in observing any given crosswalk it quickly becomes evident that drivers are frequently non-compliant or over-compliant with this legislation; not stopping for pedestrians or yielding to pedestrians who have yet to arrive at the crosswalk. This apparent ambivalence makes any definition of this interaction challenging. 135

Schroeder, Rouphail November 2006 Page 5 of 20 The variability on the willingness of drivers to yield has been linked to vehicle speeds (Geruschat et al., 2005), the difference of entry and exit leg at roundabouts (Ashmead et al., 2005) and different roundabout geometries (Guth et al., 2005). Other research has identified relationships between yielding behavior and pedestrians attributes, including bright clothing and ‘assertiveness’ of pedestrians (Harrell, 2001), and the number of pedestrians waiting at the curb (Sun et al., 2002). The same researchers found that older drivers were more likely to yield than younger drivers. Research with blind pedestrians has further shown that it can be challenging for this group of pedestrians to successfully detect a yield. Due to auditory interference from background traffic, pedestrians with vision impairments oftentimes cannot distinguish if a vehicle has in fact yielded for them. Successful detection of driver yielding and the acceptance of such yield can also be complicated for older pedestrians, children and other individuals displaying extraordinary caution when crossing an unsignalized roadway. These findings suggest the need to link gap acceptance and yielding behavior in a generalized pedestrian crossing framework. GAP ACCEPTANCE APPROACHES In a review of gap acceptance approaches, most analytical software tools (including HCM2000 and aaSIDRA) and microsimulation models (VISSIM and others) use deterministic critical gap models when estimating unsignalized intersection capacity. The models use capacity equations that can be calibrated to local conditions by adjusting the ‘critical gap’ and ‘follow-up’ time parameters. By definition, the ‘critical gap’ is the gap time between two vehicles in the conflicting stream at which a pedestrian waiting to cross (or a vehicle waiting to merge) is equally likely to accept or reject that gap, i.e. enter the crosswalk or remain standing. In theory, any gap greater than the critical gap will be accepted, while shorter gaps will be rejected. The ‘follow-up time’ is the minimum additional time (beyond the initial critical gap for the first vehicle) needed for the next following vehicle to enter the conflict section within the same gap. Deterministic critical gap models assume constant values for critical gap and follow-up time, which are applied across the entire population of drivers. The use of deterministic gap acceptance parameters assumes that the driver population is both homogeneous and consistent. In a homogeneous driver population, all drivers have the same critical gap. Under consistency assumption, the same gap acceptance situation will always cause a driver to make the same (consistent) decision. Although these assumptions are not realistic, Troutbeck and Brilon (2002) justify their use because inconsistencies in driver behavior tend to increase capacity while a heterogeneous driver population will decrease capacity, thereby offsetting the previous effect. The HCM2000 pedestrian chapter offers a method for estimating a deterministic critical gap time for pedestrians as a function of crosswalk length, walking speed and a start-up time. Similarly, Rouphail et al (2005) described pedestrian gap acceptance using actual field observations to compare crossing attributes in a heterogeneous population of blind and sighted pedestrians. However, the HCM pedestrian methodology excludes ‘zebra-striped’ crossings, because pedestrians have the right-of-way and recommends applying the unsignalized intersection concepts in those cases. For any crossing with ambivalent priority regulations, arguably the 136

Schroeder, Rouphail November 2006 Page 6 of 20 majority of crossings, both methods fall short. For these conditions, microsimulation can provide a way to combine driver yielding and pedestrian gap acceptance characteristics. PEDESTRIAN CROSSING ATTRIBUTES A population of pedestrians in most applications is heterogeneous. At any given time or location, the pedestrian stream is made up of a mix of students, retirees, children, blind individuals, business people, wheelchair users, and parents with baby strollers. Building on the authors’ background in blind pedestrian research, people with vision impairments for example waited three times longer than sighted pedestrians when attempting to cross at a two-lane roundabout and also made 6% ‘risky’ decisions (Ashmead et al., 2005). Research by Sun et al. (2002) supports the notion of heterogeneity, showing that both the minimum and average accepted gaps at an unsignalized midblock crossing were longer for younger than for older pedestrians. Literature on pedestrian walking speeds in the Highway Capacity Manual (HCM, 2000) and in Bennett et al. (2001) further acknowledge that pedestrian attributes vary as a function of pedestrian age, and crosswalk location, respectively. Assuming consistency of pedestrians also doesn’t seem intuitive, because the nature of a walking trip ranges from exercising, to strolling, to shopping to rushing to a lecture. From a human factors perspective it appears intuitive that the same pedestrian will make very inconsistent crossing decisions in different situations. For modeling applications this suggests that a deterministic gap acceptance model may not be appropriate, because the distribution of pedestrian critical gap times is expected to have a much larger variance than for vehicle traffic. Pedestrians are also likely to become impatient and lower their critical gap time as a function of delay, which results in decaying critical gap times. Research at pedestrian mid-block crossings by Dunn and Pretty (1984) found that pedestrians tend to exhibit more risky behavior when waiting 30 or more seconds at a crossing. Accordingly, the HCM2000 predicts an increasing likelihood of non-compliance with pedestrian signals as pedestrian delay increases. On the other hand, Sun et al. (2002) actually found an increase in the average accepted gap as the waiting time of pedestrians increased. The authors explained this trend because pedestrians who still wait at the crosswalk after long waiting times tend to be careful in nature and therefore would never accept a short or risky gap; an argument in support of the heterogeneity discussion above. Inconsistent and impatient behavior eventually results in the occurrence of ‘forced gaps’ or ‘forced yields’. In a forced situation, a pedestrian’s accepting of a short gap in traffic, forces the oncoming motorist to decelerate or even come to a stop. The frequency of forced situations will intuitively vary across the pedestrian population and is likely to show significant differences as the degree of urbanization increases in a region. Ultimately, the range of pedestrian attributes and the variability of behavior call for a more sophisticated pedestrian crossing framework that relates these parameters to delay and risk performance measures for motorized and non- motorized modes. 137

Schroeder, Rouphail November 2006 Page 7 of 20 TOWARDS A PEDESTRIAN CROSSING MODEL Troutbeck and Brilon (2002) suggest that vehicle gap acceptance involves the two basic elements of gap acceptance and gap distribution (a function of the arrival patterns of major stream traffic). In the case of pedestrian gap acceptance, it can be argued from above literature that two additional factors are of importance: The willingness of drivers to yield to a pedestrian (or accepting a gap in the pedestrian stream) and the possibility of the pedestrian to detect that yield. The process of pedestrians crossing the road then becomes a function of four behavioral probability parameters: P[G] – the probability of a crossable gap occurring in the traffic stream, or gap distribution (exclusive of yields), P[Gap] P[GD] – the probability that a pedestrian detects a crossable gap, P[Gap Detection] P[Y] – the probability of drivers yielding to a pedestrian at the crosswalk, P[Yield] P[YD] – the probability that a pedestrian detects a yield, P[Yield Detection] In the case of a yielding vehicle, it needs to be determined what fraction of drivers yield when a pedestrian is present, and what fraction of those yields are detected by different types of pedestrians. In the absence of such potential yielders, the crossing task becomes a pure gap acceptance process, dependent on headway characteristics of the traffic stream and the attributes of the waiting pedestrian. While actual parameters for these probabilities need to be estimated directly from field observations, it is possible to make certain assumptions to allow for a preliminary sensitivity analysis. Pedestrian Delay Mathematically, the probability of crossing in a yield= P[Y]*P[YD]. One can reasonably assume that P[YD] =1.0 for the majority of pedestrians, but is expectedly less than 1.0 for blind and maybe others. In the case of a crossable gap, methods from traffic flow theory and empirical observations can be used to relate the conflicting traffic volume with the probability of safe crossable gaps P[G]. The particular duration of a “safe” crossable gap is based on the crossing distance and an assumed “safe” crossing speed, accounting for the clearance time between completing the crossing and the arrival of the next vehicle. Following above discussion, the correct detection of a crossable gap, P[GD] follows a probabilistic distribution for a heterogeneous population, may differ across situations (inconsistency) and may change as a function of waiting time (decay). The probability of a pedestrian incurring delay upon arrival, P[pd] at the crossing can then be estimated as a function of the four parameters. Equation 1: Probability of Pedestrian Delay at Unsignalized Crosswalk ])}[*][*])[1(][*][{1][ YDPYPGPGDPGPpdP −+−= As an illustrative example, if 55% of the drivers yielded, but only 20% of those yields are detected by the pedestrian and the traffic flow is such that it contains 40% crossable gaps, 80% 138

Schroeder, Rouphail November 2006 Page 8 of 20 of which are detected, then P[pd]= 1- [0.40*0.8+0.60*0.55*.20]= 0.614. So, there is a ~ 39% chance of crossing immediately, and a 61% chance of waiting for a yield or a crossable gap. It should be noted that these 4 probabilities are not necessarily independent. As traffic volume increases, one would expect that P[G] decreases, as would possibly be the case for P[GD] and P[YD] for blind pedestrians – due to increased ambient noise. On the other hand, heavier traffic will result in lower overall speeds, and probably higher P[Y]. Thus, there is a tradeoff between the frequency of crossable gaps and the amount of driver yielding. This points to a non-linear relationship between variables - indicating that intermediate volumes may be more challenging than either the high or low volume cases. A chart depicting the effect of yield and gap detection percentages on the probability of pedestrian delay at various volume levels is shown below (Figure 1). The two curves can be viewed as reflecting the abilities of sighted (solid curve) and blind (dashed curve) pedestrians, respectively to initiate an immediate crossing. In this diagram, a crossable gap of 5 sec is assumed, average speed is assumed to be decreasing with traffic volume, P[Y] is assumed to be inversely correlated with speed, and the P[G > 5sec] assumes a volume-based exponential distribution of gaps in traffic. Figure 1: Possible Relationship Between Pedestrian Delay and Conflicting Vehicle Volumes Probability of a Pedestrian Delayed Crossing vs Conflicting Traffic Volume for Selected Yield and Gap Detection Probabilities 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% 0 100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400 1500 1600 1700 Volume (vph) Pr (D el ay ed C ro ss in g) P[YD]=20%, P[GD]=50% P[YD]=90%, P[GD]=90% 'Equal Access' Line Blind Pedestrians Sighted Pedestrians While these relationships need calibration, the integration of the concepts of yield and gap detection directly into a model of crossing performance is crucial. It is evident that poor gap judgment will have a strong influence on pedestrian delay, both at high and low volumes. It is also clear that training or technological treatments intended to increase the yield and gap detection capabilities for blind or low vision pedestrians could simplify the crossing process. An interesting sidebar of the curves is the ability to define traffic volumes that provide ‘Equal 139

Schroeder, Rouphail November 2006 Page 9 of 20 Access’. For example, a horizontal line drawn at 60% shows that a blind pedestrian negotiating a facility with conflicting volumes of 180 vehicles per hour (vph) is exposed to the same likelihood of delay as a sighted pedestrian negotiating the same facility at a much higher flow rate of 890 vph. While above graphic and discussion deal with the issue of pedestrian delay, similar thought processes may be applied to derive relationships between the four interaction parameters and vehicle delay, as well as, the likelihood of pedestrian-vehicle conflicts. Evaluating Conflicts The discussion above ignores the challenge of assessing the risk posed by a pedestrian making an incorrect decision, such as incorrectly assuming that a crossable gap or a vehicle yield has occurred (false positives). For the purpose of discussion, we will assume that upon arrival at the crossing location, the pedestrian is exposed to two types of gaps, safe or unsafe. Safe gaps can be thought of as a combination of large gaps in moving traffic as well as gaps due to yielding drivers. The pedestrian then makes a decision to accept or reject the gap. For the following discussion it will be assumed that all pedestrians can accurately detect a yielding vehicle, as not to deal with too many parameters at once. It will further be assumed that a pedestrian’s crossing decision can be described as a function of the pedestrian’s critical lag time. A ‘lag’ will be defined as the time between a pedestrian’s arrival at the crosswalk (or the point he/she makes a decision to cross or not) and the arrival of the next conflicting vehicle. The pedestrian will cross if the lag time to the next vehicle arrival is greater or equal to the critical lag time, where the vehicle arrival time is a function of that vehicle’s speed and distance to the crosswalk. It can be reasoned that the average pedestrian will have a ‘safe’ critical lag time; one that allows a sufficient safety margin to the next vehicle arrival. However, there are also cases where pedestrians will make ‘risky’ decisions, or ‘conservative decisions’, which will be represented by shorter and longer critical lag values, respectively. Conceptually, a conflict will occur when a ‘risky’ pedestrian decision coincides with a vehicle arrival; especially if that particular vehicle happens to move fast or has slow reaction time parameters. The section on model implementation below will discuss this in more detail. THE ROLE OF TREATMENTS The NCHRP 3-78 research effort is principally interested in identifying treatments that will assist blind pedestrians to cross at certain facility types safely and efficiently. Based on the framework described above, the purpose of these or any other pedestrian crossing treatment is to enhance or minimize delay and risk for pedestrians, without unduly impacting traffic flow. This can be done in one of four ways: • Increasing the probability of driver yielding, P[Y]: Previous research implies that slower speeds, increased driver awareness and education/enforcement may be able to achieve that. Some natural speed reduction also occurs at high flows. Treatments addressing P[Y] could include warning signs, flashing lights, or raised crosswalks. 140

Schroeder, Rouphail November 2006 Page 10 of 20 • Increasing the occurrence of crossable gaps, P[G]: It is unclear if there are treatments whose sole purpose is an increase in P[G], but a number of situations will have an impact, including upstream signals or more conservative driver behavior. • Increasing the probability of yield detection, P[YD]: This is particularly important for blind pedestrians, but others may benefit from such treatments. Pavement sound strips, surface treatments or automated yield detection tools can be applied. • Increasing the occurrence of gap detection, P[GD]: There may be treatments that enable pedestrians to perform better gap judgment, as to decrease the frequency of risky, as well as, overly conservative decisions. Examples include improved lighting conditions or automated gap detection technology. Testing Treatment Functionality For purpose of exploring these concepts, the authors used the VISSIM (PTV, 2005) simulation package to define a modeling test-bed. Other models such as AIMSUN or Paramics may have similar capabilities, but were beyond the scope of this preliminary evaluation. For a comparison of these software tools, refer to the referenced NGSIM document (Cambridge Systematics, 2004). In the default vehicle-pedestrian interaction model in VISSIM, no information is imparted by either vehicles or pedestrians! Barring the use of ‘priority rules’, vehicles and pedestrian will flow perpendicular to each other at the crosswalk with no consideration of potential conflicts. This will be referred to as the ‘No Control’ (NC) case. By tracking ‘risky’ vehicle-pedestrian events, we can measure the frequency of pedestrian-vehicle conflicts for random arrivals of both classes and across a range of traffic and pedestrian volumes. Interestingly enough, ‘delay’ to pedestrians and pedestrian-induced delay to vehicles in this case is zero, independent of conflicting volumes (vehicles may still experience some delay due to car-following algorithms and site geometry). This scenario represents the ‘base’ maximum conflicts condition that behavioral parameters, and ultimately treatments, are intended to remedy. Conceptually, as pedestrian-vehicle interaction ‘improves’, the number of conflicts tend to decrease, while driver and pedestrian delay tend to increase. On the other extreme, if ‘Perfect Information (PI)’ is imparted, as in the case of all drivers yielding to pedestrians and pedestrians accepting only safe gaps or yields, conflicts are eliminated at the expense of added delay to both pedestrian and vehicles. It is clear that there are trade-offs between risk and delay. Not every wrong decision (by pedestrians or drivers) will result in a conflict, but as vehicle and pedestrian volumes increase, both delay and conflicts are likely to increase in some fashion. Figure 2 shows a conceptual schematic of the conflict-delay tradeoff from the pedestrian perspective. 141

Schroeder, Rouphail November 2006 Page 11 of 20 Figure 2: Conceptual Relationship between Traffic Volume and Pedestrian Delay/Conflicts Traffic Volume Pedestrian Delay/Risk Risk - No Control (NC) Risk - Perfect Information (PI) Delay - No COntrol (NC) Delay - Perfect Information (PI) Risk - NC Risk - PI Delay - NC Delay - PI The relationship in the figure suggests that pedestrian delay for the NC case (black lines) will remain zero as traffic volume increases, because there is no interaction between modes. The likelihood of conflicts is expected to increase exponentially as a function of random arrivals at the crosswalk. In the PI case (gray lines), there won’t ever be any conflicts as a result of the strictly controlled interaction between modes. In this case it is the pedestrian delay that will increase in a non-linear fashion as a function of traffic volume. In reality, most operating scenarios will lie somewhere between the two extremes defined above, which will include some combination of risk and delay. The implementation of pedestrian crossing treatments will change model input parameters (more yielding, less risky decisions …) and will impact risk, as well as, pedestrian and driver delay in some fashion. MODEL IMPLEMENTATION In a microscopic implementation of pedestrian-vehicle interaction, the modeler has to account for the driver and pedestrian behavioral attributes that are captured by these four parameters. Deterministic models assume driver consistency and driver homogeneity, within each vehicle class. By defining multiple vehicle classes and estimating separate critical gaps for each, the homogeneity assumption can be partly overcome. In the following, this approach will be referred to as a quasi-heterogeneous driver population, because the homogeneity assumption still holds within each vehicle class. Gap acceptance in VISSIM is achieved through ‘priority rules’, which define where a minor movement has to screen conflicting traffic for certain conditions before continuing. By applying 142

Schroeder, Rouphail November 2006 Page 12 of 20 different ‘priority rules’ to different entities and at different geometries, VISSIM can model quasi-heterogeneous populations of drivers and pedestrians. This allows the user to code a certain percentage of drivers as ‘potential yielders’ P[Y]. The gap distribution, P[G], is automatically determined from the headway distribution of traffic upon entering the system. It is important to note that the authors worked with existing modules in the software and did not employ any external code. Conflicts To extract conflict data from the model, we will define a spatial boundary for the pedestrian path and track the crossing times of all vehicles and pedestrians at that boundary within a prescribed time window. For example, we could identify the passage time of all vehicles that occur at a lead time of X seconds before and a lag time of Y seconds after the pedestrian appears at that boundary. Hence, a simulated (one-way, one stage) pedestrian crossing would be defined as “risky”, if one or more vehicles appear at the spatial boundary within the (X, Y) time window. Thus, the percentage of risky crossings would be the number of crossings defined as risky divided by the total number of crossings. The values for X and Y to define the cut-offs for critical leads and lags can be user-defined. The spatial boundary in this example takes the form of two overlapping data collection points; one on the vehicle link and one on the pedestrian link. The two data collection points can be configured to output raw data of pedestrian and vehicle arrival and departure events at the defined location. Using Visual Basic script, this data can be formatted as necessary to calculate the lead time since the last vehicle (rear bumper) and the lag time to the next vehicle (front bumper) for each pedestrian arriving at the conflict point. A spreadsheet was configured to compare each lead and lag time to user-defined critical values and to keep track of all risky leads and risky lags. The pedestrian-vehicle conflict approach presented is similar to the method discussed in a recent FHWA publication on using microsimulation for conflict analysis (FHWA, 2003). That document describes two measures of effectiveness, Post Encroachment Time (PET) and Time to Collision (TTC), which are similar in concept to the lead and lag terminology used in this document. The FHWA document also points to the big potential advantage of performing conflict analyses in microsimulation, because a range of treatments and traffic intensity can be tested. The document does not go into detail on modeling pedestrian-vehicle conflicts. Modeling Example To illustrate the use of multiple vehicle and pedestrian classes, the two populations are divided into several groups. Vehicles are categorized as either Yielding or Non-Yielding Drivers, P[Y]. Pedestrians are divided into blind and sighted pedestrians and within those groups in categories with different gap acceptance parameters; risky, typical and conservative – where critical lag times are increasing in that order. It will generally be assumed that most sighted pedestrians will make ‘typical’ decisions, while blind pedestrians will be more strongly represented at either extreme. As crossing treatments are 143

Schroeder, Rouphail November 2006 Page 13 of 20 implemented at a facility, more pedestrians will shift away from ‘risky’ and ‘conservative’ decisions, thereby reducing conflicts and delay, respectively. In the following, we will assess the operational impacts of six treatment functionalities: • No Control, NC: This configuration represents the default interaction in the VISSIM model without any interaction between modes. Delay is a function of car-following parameters only and risk is the result of random arrivals at the conflict point • Unassisted Crossing, UA: Pedestrian and drivers are assigned 'priority rules', which govern the interaction. Pedestrians have different gap acceptance parameters and some drivers will yield if encountering a pedestrian. No further treatments are implemented. • Yield Sign for Drivers, YS: The likelihood of drivers yielding is increased through treatments such as a raised crosswalk, warning signs, pedestrian flashers, enforcement, or education measures. It is assumed that the treatment has no effect on pedestrian behavior. • Vehicle Detection, VD: Some treatments will help blind pedestrians to more effectively detect the arrival of a vehicle. The assumption is that this will enable them to make better (safer and more efficient) crossing decisions. Examples include a gap-detection system, or noise-generating rumble strips. It is assumed that driver behavior is not affected. • Yield Sign and Vehicle Detect, YSVD: This treatment category combines YS and VD treatments to increase driver yielding and improve vehicle detection capabilities of blind pedestrians. Examples include a combination of automated vehicle detection with a pedestrian flasher or rumble strips in the approach of a raised crosswalk. • Perfect Information, PI: This configuration represents perfect unsignalized crossing conditions from a pedestrian perspective. 100% of Vehicles yield to pedestrians, thereby minimizing pedestrian delay and risk. This form of driver behavior might represent a strictly enforced right-of-way law. The six treatment scenarios are implemented in VISSIM at a one-way, one-lane pedestrian crossing, using assumed run-specific pedestrian and driver attributes (Table 1). Table 1: VISSIM Input Parameters for Simulation Scenarios P(C) P(T) P(R) P(C) P(T) P(R) P(C) P(T) P(R) P(Y) 50 Blind 'Pedestrians' per hour 70 70 90 90 Perfect Information, Everybody Yields 0 300 Vehicles per hour P(Y) 0% 20% 50% Drivers No Information n/a n/a 5 5Yield Sign and Vehicle Detect 90 90 5 5 0 0 10 0 0100 100 90 50% 100% Probability of Conservative Pedestrian Crossing Behavior. Pedestrian will accept gaps of 12 seconds or more. Yield Sign for Drivers Vehicle Detect for Pedestrians 5 20%5 5 0 1090 Probability of Drivers Yielding to Pedestrians (Percentage of Potential Yielders) Probability of Risky Pedestrian Crossing Behavior. Pedestrian will accept gaps of 3 seconds or more. Probability of Typical Pedestrian Crossing Behavior. Pedestrian will accept gaps of 6 seconds or more. n/a 50 'Sighted' Pedestrians per hour Pedestrians YS 10 20 Unassisted Crossing 20105 VD YSVD PI Run-Specific AttributesTreatment Functionality (assume 100% Yield Detection) NC UA n/a n/an/a It was assumed that the typical pedestrian has a critical lag of 6 seconds, which is considered safe compared to the actual crossing time of about 5 seconds at a walking speed of 4 ft/second. 144

Schroeder, Rouphail November 2006 Page 14 of 20 Accordingly, conservative pedestrians are assigned a longer critical lag value (12 seconds) and risky pedestrians have a short critical lag of only 3 seconds. Defining Conflicts Before analyzing the event data and extracting the frequency of pedestrian-vehicle conflicts, the cut-off values for critical leads and critical lags need to be defined. For this purpose, the team conducted 10 VISSIM runs of the No Control (NC), Unassisted (UA) and Perfect Information (PI) scenarios and extracted all lead and lag data. The team then gradually increased the critical values for leads and lags in 0.5 seconds increments and observed how the percentage of risky decisions was affected (Table 2). Table 2: Effect of Critical Lead/Lag Thresholds on % Risky Decisions % Risky Leads (as a Function of Different Critical Lead Times for 3 Scenarios) Critical Lag Time (sec.) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 No Control (NC) 16.7% 21.1% 22.9% 27.0% 30.1% 34.1% 36.4% 39.0% Unassisted Crossing (UA) 0.0% 0.0% 0.1% 2.1% 13.8% 26.6% 35.2% 37.4% Perfect Information (PI) 0.0% 0.0% 0.0% 0.0% 0.4% 0.7% 1.5% 2.6% % Risky Lags (as a Function of Different Critical Lag Times for 3 Scenarios) Critical Lag Time (sec.) 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 No Control (NC) 11.4% 15.4% 19.3% 23.7% 27.9% 31.1% 33.9% 36.8% Unassisted Crossing (UA) 0.5% 0.5% 0.5% 1.2% 11.2% 16.5% 22.0% 26.8% Perfect Information (PI) 0.0% 0.0% 0.0% 1.2% 36.6% 47.8% 52.0% 54.9% As expected, the percentage of risky decisions (leads and lags) steadily increases in the NC case as the cut-off values increase. As discussed earlier, these ‘conflicts’ in the NC case are merely a function of random pedestrian and vehicle arrival volume at the conflict point. By definition, there shouldn’t be any conflicts in the PI case, because all vehicles were specified to yield to pedestrians and no pedestrians were assigned ‘risky’ behavior. The critical values will therefore be defined as the largest value that does not result in any conflicts in the PI case. The resulting critical values for lead and lag are by definition 3.0 seconds and 2.5 seconds, respectively. Results The experimental set-up of the six treatment scenarios conceptually corresponds to a vertical line in Figure 2, implemented at a volume of 300 vehicles per hour. The resulting delay and risk measures of effectiveness from 10 simulation replications per scenario are shown in Table 3. 145

Schroeder, Rouphail November 2006 Page 15 of 20 Table 3: Measures of Effectiveness from VISSIM Averages Std. Dev. Average Std. Dev. Average Std. Dev. Average Std. Dev. 9.0% 1.33% 15.0% 2.00% Treatment Functionality (assume 100% Yield Detection) % Conflicts Pedestrian Delay (seconds) Vehicle Delay (seconds)Actual Driver Yield - % Yield Measures of Effectiveness (average of 10 VISSIM runs) 23.2% 2.60%NC No Control 0.0% 0.00% 0.0 0.00 2.4 - 3.1 0.321.3% 0.80% YS Yield Sign for Drivers 4.4 0.28UA Unassisted Crossing 3.8% 0.99% 9.3% 1.16% 0.20 4.2 0.290.6% 0.60% YSVD Yield Sign and Vehicle Detect 4.3 0.371.4% 0.80%VD Vehicle Detect for Pedestrians 3.7% 0.84% 3.9 0.27 4.2 0.310.6% 0.70% 3.1 0.27 4.1 0.0% 0.00%PI Perfect Information, Everybody Yields 3.5 0.30 5.4 0.41 The numbers suggest that an increased likelihood of drivers yielding (case YS) decreases the percentage of conflicts. Improving vehicle detection (VD) for pedestrians appears to slightly increase observed conflicts compared to the unassisted case. Looking at the large standard deviations of the risk estimates, it can not be stated if this is a real effect at the given sample size. This suggests the need for large sample sizes in the model trials to show significant effects when evaluating actual treatments. In comparison, the delay MOEs suggest that as drivers yield more, delay for pedestrians decreases while driver delay increases. The table also indicates that the percent of actual driver yields is considerably less than the specified percent theoretical yielders. This finding is expected at low pedestrian volumes, as the majority of drivers do not encounter a pedestrian waiting at the crosswalk. This observation suggests challenges to estimating the required model input of ‘potential yielders’ (P[Y]) from field observations of ‘actual yielders’. Volume Sensitivity In an attempt to replicate the effect of traffic volumes suggested in Figure 2, vehicle inputs were tested over a range from 100 to 900 vehicles per hour. Figure 3 shows the results for the three performance measures in the NC, UA, and PI cases. 146

Schroeder, Rouphail November 2006 Page 16 of 20 Figure 3: VISSIM Volume Sensitivity for Conflicts and Delay Performance Measures VISSIM Volume Sensitivity - Pedestrian Delay 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 0 200 400 600 800 1000 Conflicting Vehicle Volume (vph) Pe de st ria n D el ay (s ec ) . No Control, NC Unassisted, UA Perfect Information, PI VISSIM Volume Sensitivity - Vehicle Delay 0.00 2.00 4.00 6.00 8.00 10.00 12.00 14.00 0 100 200 300 400 500 600 700 800 900 1000 Conflicting Vehicle Volume (vph) Ve hi cl e D el ay (s ec ) . No Control, NC Unassisted, UA Perfect Information, PI VISSIM Volume Sensitivity - % Ped/Veh. Conflicts 0.00% 10.00% 20.00% 30.00% 40.00% 50.00% 60.00% 70.00% 80.00% 90.00% 100.00% 0 200 400 600 800 1000 Conflicting Vehicle Volume (vph) % C on fli ct s . No Control, NC Unassisted, UA Perfect Information, PI The graphs in Figure 3 show the anticipated and previously hypothesized effects. As vehicle volumes increase, pedestrian delay stays at zero in the NO CONTROL case, while the percentage of conflicts increases. Vehicle delay also increases, not because of the interaction with pedestrians, but as a function of increasing congestion (car-following algorithm). The percentage of conflicts increases drastically as volumes increase, because pedestrians become more likely to encounter a vehicle in the crosswalk. Interestingly, there appears to be a maximum limit for conflicts in this case, presumably as a function of dropping vehicle speeds with congestion. 147

Schroeder, Rouphail November 2006 Page 17 of 20 In the unassisted case, pedestrian delay increases with increasing traffic in the turn lane. The percentage of conflicts also increases, but at a much slower rate than the pedestrian delay. The curve for vehicle delay also increases and is slightly higher than in the NO CONTROL case. This difference can be interpreted as the added vehicle delay due to interaction with pedestrians (pedestrian-induced vehicle delay). In the perfect information case, conflict stays zero throughout the range of volumes as a result of the safe pedestrian and vehicle parameters. Vehicle delay is highest in this case, because all drivers are coded to yield to pedestrians. Interestingly, pedestrian delay peaks at around 300-400 conflicting vehicles per hour and then decreases as vehicle flows increase further. This can be explained, because at slower congested travel speeds, vehicles are more likely to exhibit yielding behavior, which in turn creates more crossing opportunities for pedestrians. CONCLUSION The analysis presented in this document showed that it is possible to use microsimulation models to extract conflict and delay data for pedestrian-vehicle interaction as a function of run-specific attributes of the two groups. The approach describes the interaction of the two modes in terms of four probability parameters; the likelihood of crossable gap occurrence P[G], the likelihood of gap detection P[GD], the likelihood of driver yielding, P[Y] and the likelihood of yield detection, P[YD]. From a preliminary analysis, it appears that the delay and conflicts estimates produced by the model in fact follow expectations. There is some concern that the results presented here are a function of the built-in algorithms in the selected simulation program. Additional research, model calibration, and expansion to other simulation models are needed to strengthen the framework proposed in this paper. The advantage of the proposed framework is that the measures of effectiveness used to define performance and access at pedestrian crossing facilities can be readily measured in the field, or predicted for future designs using simulation models. As long as treatment effects can be defined in terms of improved driver yielding, and improved pedestrian yield detection or gap detection, the procedure should be able to predict their effect on traffic performance for all users. For future analysis, the run-specific attributes of pedestrians and vehicles need to be calibrated from field data. To predict the impact of pedestrian crossing treatments on the four parameters, early engineering assumptions will eventually have to be confirmed through field observations and can be adjusted as necessary during model calibration. Early trial runs have shown large sample variances, so that it is expected that the modeling of future treatments will require a large number of simulation runs, depending on the effect-size of interest. Future research may also include a more detailed assessment of a decay function for critical gap times as a function of waiting time or the number of rejected gaps. Finally, a long-term goal of continued data collection and model calibration may be the development of deterministic equations and attribute tables that can be used independent of simulation models. 148

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