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The resulting usable dataset for non-zero intervention cross- tion is critical to the implementation of the NCHRP Project
ing events is therefore very small. Recognizing that the event 3-78A analysis framework. Furthermore, it will be necessary
of an O&M intervention can be treated as a binary event to represent different populations of drivers (courteous or
(yes/no), it would be feasible to apply a logistic regression not) and pedestrians (blind and sighted) to adequately cap-
approach to these data. However, it is unclear how useful ture the crosswalk interaction as observed in this study.
such models would be to practitioners. Assuming that a particular model can adequately address
An alternative and potentially more promising approach these aspects and can be calibrated to represent specific behav-
for safety modeling is feasible with the introduction of new ioral and traffic conditions, a simulation analysis is ideally
dependent variables for pedestrian risk. Since the biggest lim- suited to extrapolate performance results to other geometry
itations of the O&M intervention measure are its binary and traffic patterns. The approach is also ideally suited for con-
nature and rare occurrence, a revised variable should be con- ducting sensitivity analyses of different parameters. In effect,
tinuous and frequently observable. a simulation-based analysis represents a second option for
In particular, the project team discussed the use of two vari- extending the field results from NCHRP Project 3-78A to other
ables that meet these criteria. The first is the theoretical time to conditions. The first extension is of course the use of the delay
collision of pedestrian and vehicle in seconds, which is calcu- models discussed in the previous section. Simulation has the
lated from the speed and position of the vehicle at the instant added benefit that it can evaluate unique traffic characteristics,
the pedestrian steps into the crosswalk. The second is the nec- the impacts of nearby intersections, or the use of pedestrian
essary deceleration rate in feet per second squared that is nec- signals (or PHBs) at the crosswalk in question. Finally, simu-
essary for the vehicle to come to a stop before the crosswalk. lation models are increasingly used to perform surrogate safety
This measure is also calculated from the speed and position analysis based on vehicle trajectories (FHWA 2008).
of the vehicle at the time the pedestrian steps into the cross- It is beyond the scope of this project to discuss in detail the
walk. This metric is further related to standard engineering sig- variety of simulation tools available and to what extent they
nal timing practice, where a similar deceleration rate is used to capture the interaction of pedestrians and vehicles at cross-
calculate the length of the yellow interval at signals (ITE 2009). walks. The focus of this section is to discuss the use of simu-
The development of these measures requires real-time field lation analysis in two principal ways:
measures of vehicle speed and position that were not avail-
able in this study. The feasibility of this approach has been 1. How to represent the analysis framework in simulation
demonstrated in other research (Schroeder 2008), where it and findings from a sensitivity analysis of different behav-
was used to develop predictive models for driver yielding ioral and traffic-related model parameters. The objective
and pedestrian gap acceptance at unsignalized crossings. The is to guide other efforts of those who wish to further extend
approach is being explored in ongoing research on the acces- results from this research in a simulation environment.
sibility of complex intersections to pedestrians who are blind This section is primarily based on the work published in
(NIH 2010). Schroeder and Rouphail (2007).
2. A detailed analysis of different signalization options at
single-lane and two-lane roundabouts, including a com-
Simulation Approach
parison of PHB and conventional signals, one-stage and
The NCHRP Project 3-78A analysis framework fits within two-stage crossings, and different crosswalk geometries.
the context of modern microsimulation tools. These software The analysis is performed using calibrated representative
tools work on the basis of algorithms that describe driver models of a single-lane and a two-lane roundabout and
behavioral rules for car following, lane changing, gap accept- explores operations for a range of vehicle and pedestrian
ance, and routing. Many of the commercially available prod- volumes. The emphasis is on pedestrian-induced vehicle
ucts further allow the user to code both motorized and non- delay and queuing impacts with the objective to provide
motorized transportation modes. The models differ in the decision support for agencies that are considering signal-
specifics of how the interaction between vehicles and pedes- ization as one of the treatments at roundabout pedestrian
trians is modeled and how much flexibility the user has in crossings. This section is primarily based on the work pub-
modifying and calibrating behavioral parameters. However, lished in Schroeder, Rouphail, and Hughes (2008).
most models apply some sort of a gap acceptance algorithm
to model pedestrians selecting gaps in traffic or to model driv-
Applying the Framework to Simulation
ers yielding to pedestrians. Depending on the model, the user
also may have the ability to model mixed-priority situations The NCHRP Project 3-78A analysis framework uses the
where some drivers yield and some pedestrians cross in large principles of gap and yield availability as well as the rate of uti-
gaps, as was discussed in the previous section. This distinc- lization of both types of crossing opportunities. The availabil-
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ity parameters represent characteristics of the traffic stream and better gap judgment so as to decrease the frequency of
are a function of traffic volumes, speed, and driver behavior. risky or overly conservative decisions. Examples include
The utilization parameters are pedestrian behavior attrib- improved lighting conditions and automated gap detec-
utes that describe a pedestrian's ability and willingness to cross tion technology.
in a yield or gap situation. The analysis framework further uses
the performance measure of delay and risk to quantify the The functional effect of a treatment installation is repre-
pedestrian's ability to cross at a particular location. sented in simulation through a net increase (or decrease) in
The four availability and utilization probability parameters one or more of the probability terms. The proposed approach
serve as inputs when the analyst sets up the simulation model. for modeling treatments is therefore implicit, through changed
The analyst codes these after defining model geometry, traf- behavioral parameters, rather than explicit, through a build-
fic control strategies (signals), volumes, and other inputs. The ing block included in the simulation tool. The one exception
remaining delay and risk performance measures are model to this approach is when a treatment involves the use of sig-
outputs that are calculated from the simulation. It is beyond the nalized traffic control. This aspect is discussed toward the end
scope of this report to describe the details of simulation mod- of this chapter.
eling and the wide variety of modeling and calibration param-
eters that are available to the analyst. The FHWA has extensive
Setting up Behavioral Parameters
resources available through the "Traffic Analysis Toolbox"
(2010) that the analyst can use for further information on sim- This section discusses how the four probability parameters
ulation modeling, calibration, and validation. The remainder could be implemented in a simulation. Differences among
of this section focuses on the proposed approach for modeling drivers and pedestrians are best represented through the use
the interaction between pedestrians and vehicles. of multiple vehicle and pedestrian classes. For example, two
driver classes may be modeled: those with and those without
the propensity to yield. Similarly, two or more pedestrian
Modeling Treatments
classes may be modeled with different gap acceptance thresh-
Based on the framework described above, the purpose of a olds. In particular, the four probability parameters would be
treatment is to enhance or minimize delay and risk for pedes- modeled as follows:
trians without negatively affecting traffic flow. It was hypothe-
sized and demonstrated that the functional effect of a treatment · The availability of yielding should be modeled through the
can be described through a combination of the four underlying use of multiple vehicle classes. The gap acceptance algo-
probability parameters. This can be done in one of four ways: rithm at the crosswalk that effectively tells drivers to look
for gaps in the pedestrian traffic will lead a potential yielder
1. Increasing the occurrence of driver yielding: Previous to slow in the presence of a pedestrian. The vehicle classifi-
research implies that slower speeds, increased driver aware- cation of whether or not a driver is a potential yielder is sto-
ness, and education/enforcement may be able to achieve chastically assigned to each vehicle as it enters the simulated
this. Some natural speed reduction also occurs at high flows. system. Note that these are actually "potential yielders"
Treatments addressing yielding could include warning signs, since some vehicles tagged as yielders may not encounter a
flashing lights, or raised crosswalks. pedestrian at the crosswalk or may be too close to the cross-
2. Increasing the occurrence of crossable gaps: It is unclear ing to be able to yield when the pedestrian shows up. This
if there are treatments whose sole purpose is an increase in probability will vary for the entry and exit legs of a round-
the availability of crossable gaps, but a number of situa- about and for different sites. Simulation models vary in
tions will have an impact, including upstream signals or their ability to apply customized gap acceptance algorithms
more conservative driver behavior. Ultimately, the biggest for different simulated crossings.
factor affecting this parameter is the amount of conflict- · The availability of a crossable gap is determined from the
ing traffic. headway distribution of traffic upon entering the system.
3. Increasing the probability of yield utilization: Treat- This probability is implicit in the individual vehicle gener-
ments may help blind pedestrians and others to more reli- ation, and the gap sizes can be tracked by the model at any
ably detect the presence of yielding vehicles or increase point in the simulated system. Some tools may have the
their level of confidence in accepting yields. The list of flexibility of coding a custom headway distribution. Fur-
potential treatments includes pavement sound strips, sur- ther, the headway arrivals at a crosswalk will be affected
face treatments, and automated yield detection technology. by upstream signals. If significant vehicle platooning is
4. Increasing the probability of gap utilization: There observed at a crosswalk, this effect should be accounted for
may be treatments that enable pedestrians to perform in the simulation.
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· The propensity to utilize yields is also stochastically assigned · Geometry: The general geometry of the particular round-
to each pedestrian as he or she arrives at the crossing loca- about or CTL is often available in the form of a design draw-
tion. This value will depend on whether the simulated ing or a scaled aerial photograph. Geometric data of the site
pedestrian is blind or sighted (also assigned stochastically include correct lane widths and crosswalk locations.
based on their respective volumes) and whether natural or · Origin/destination (O/D) volumes by lane: The typical
augmented yield detection systems are in place. This aspect simulation analysis uses traffic and pedestrian volumes for
of the interaction is likely to be the most challenging to rep- a duration of one hour. The flows in the model should rep-
resent in simulation. resent actual turning percentages by approach (and by lane
· The utilization of crossable gaps is handled through a gap in the case of a two-lane roundabout).
acceptance algorithm, and different gap thresholds will be · Traffic composition: The traffic composition at each site
assigned to different populations of pedestrians. The chal- includes the percentage of heavy vehicles and the presence
lenge here lies with the fact that most simulation gap accept- of special driver and/or pedestrian classes (yield/no yield or
ance algorithms are based on minimum gaps, to the effect safe/risky).
that a pedestrian will always utilize any gap greater than the · Signal timings: Where applicable, signal timings in the
minimum. To represent a utilization rate of less than 100%, model are based on the actual signal timing plan for the
additional customization may be necessary, which depends intersection or, if necessary, on field measurements of
on the particular model used. average green times. In some cases, as in the evaluation of
proposed treatments, signal timing reflects the proposed
operation of the signal.
Model Calibration and Validation
The following parameters are used for calibration to match
The quality of the simulation analysis results relies on cor-
the operations in the model to field conditions.
rect modeling inputs and adequate calibration and validation
of model outputs. Model inputs are defined as those param-
· Speeds: The modeler can input field-collected data on aver-
eters that always need to be collected in order to develop a
age vehicle speeds on the approaches upstream of the cross-
simulation model. These parameters include detailed site
walk, the entry to the roundabout, in the circulating lane
geometry, origindestination traffic and pedestrian volumes,
of the roundabout, and in the turn lane. If actual speed data
traffic composition, and signal timing. In addition, calibration
cannot be obtained, the posted speed limit can be used to
parameters are available that have default settings included in
infer a speed distribution on the approaches, and the liter-
the model but that can and should be customized by the user.
ature (FHWA 2000, AASHTO 2004) can be used to approx-
These include speed distribution, gap acceptance behavior,
imate speeds in the roundabout or turn lane.
gap distribution, yielding behavior, and yield utilization. In · Gap acceptance: Gap acceptance parameters for pedestrian
most cases, these parameters are adjusted (i.e., calibrated) to crossings and for vehicle merges (into the roundabout or
ensure that the model accurately represents field conditions. downstream traffic at a CTL) can be obtained either from
Finally, validation parameters are model outputs that allow the field data or from sources in the literature. The model can
modeler to compare the model to field conditions or other include distributions of gap acceptance times by coding
models. Validation parameters include travel time, delay, multiple vehicle and/or pedestrian classes. In this fashion
queuing, and risk. In other words, model validation is achieved it is possible to model pedestrians who make risky decisions,
by altering calibration parameters and comparing the valida- pedestrians with average behavior, and pedestrians with poor
tion parameters to field conditions; input parameters stay gap detection (who need very long gaps to cross).
constant throughout the calibration/validation process. · Driver yielding (potential): Different classes of drivers will
For model validation, simulation outputs are either com- be coded to achieve a certain percentage of potential yield-
pared to field-collected data or to outputs from other software ers. Driver behavior will be based on observations at the
packages for roundabouts and signalized intersections. These site with help from sources in the literature.
traffic analysis models are mostly designed for the analysis of · Yield detection: As discussed previously, some blind pedes-
vehicle traffic and are limited in their ability to model mixed- trians may not be able to accurately detect drivers yielding
priority pedestrianvehicle interaction. Consequently, the use for them at the crosswalk. The proportion of this group of
of these traffic analysis tools is primarily to ensure that the pedestrians is a calibration parameter.
vehicle operations in the simulation are modeled correctly. · Headway distribution: Modeling a user-defined headway
The analyst will have to rely on field observations or expert distribution may be necessary in some occasions, for exam-
judgment to validate pedestrian results. ple if an upstream signal causes platoon arrivals of vehicles
The following list of model input parameters needs to be or if class changes on campus cause pedestrians to arrive in
collected to set up the initial simulation model: groups.
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Finally, the following simulation outputs are proposed for drivers at unsignalized crosswalks in simulation. To illustrate
model validation: the use of multiple vehicle and pedestrian classes, the two
populations are divided into several groups. Vehicles are cat-
· Travel times: Simulation tools can estimate travel times egorized as either yielding or non-yielding drivers, P(Y). Pedes-
on user-specified segments that can be used to compare trians are categorized into blind and sighted groups and within
actual travel times obtained in the field and so validate those groups in categories with different gap acceptance
uncongested operations at the sites. Travel time data can parameters--risky, typical, and conservative--where critical
be obtained as an average over the analysis period, sepa- gap times are increasing in that order.
rated by pedestrian/vehicle class or as raw data for each It will generally be assumed that most sighted pedestri-
individual pedestrian/vehicle. ans will make typical decisions, while blind pedestrians will be
· Delay times: Vehicle and pedestrian delays in the defined more strongly represented at either extreme. As crossing treat-
travel time segments are estimated by subtracting the theo- ments are implemented at a facility, more pedestrians will shift
retical (undelayed) travel time from the actual travel time away from risky and conservative decisions, thereby reducing
through a given segment. These data can be obtained as an conflicts and delay, respectively. In the following, we will assess
average over the analysis period separated by pedestrian/ the operational impacts of six treatment functionalities:
vehicle class or as raw data for each individual pedestrian/
vehicle and can be used to validate congested operations. · No control (NC): This configuration represents the default
It is also possible to validate using stopped delay. interaction in a simulation model without any interaction
· Queue lengths: The simulation tools generally provide between modes. Delay is a function of car-following param-
estimates of average vehicle queues at a specified location eters only, and risk is the result of random arrivals at the
that can be compared with field measurements. This mea- conflict point.
sure may be most helpful in validating approach queuing at · Unassisted crossing (UA): Pedestrians and drivers are
roundabouts. assigned priority rules that govern the interaction. Pedes-
· Driver yielding (actual): It is hypothesized that the num- trians have different gap acceptance parameters, and some
ber of actual yielders is significantly lower than the num- drivers will yield if encountering a pedestrian. No further
ber of potential yielders entered in the model. In order for treatments are implemented.
a yield to occur, the event of an approaching potential · Yield sign for drivers (YS): The likelihood of drivers yield-
yielder needs to coincide with the presence of a pedestrian ing is increased through treatments such as a raised cross-
at the crosswalk and with sufficient time for the driver to walk, warning signs, pedestrian flashers, enforcement, or
decelerate at a comfortable rate. By comparing the fraction education measures. It is assumed that the treatment has
of actual yield events, the analyst can validate the assump- no effect on pedestrian behavior.
tions used to derive the relationship between actual and · Vehicle detection (VD): Some treatments will help blind
potential yielders. pedestrians to more effectively detect the arrival of a vehicle.
The assumption is that this will enable them to make bet-
ter (safer and more efficient) crossing decisions. Examples
Measures of Risk from Simulation
include a gap-detection system and noise-generating rum-
It is further possible to use a simulation-based analysis ble strips. It is assumed that driver behavior is not affected.
approach to obtain an estimate of pedestrian risk by extracting · Yield sign and vehicle detect (YSVD): This treatment cat-
the occurrence of pedestrianvehicle conflicts. The FHWA egory combines YS and VD treatments to increase driver
surrogate safety assessment methodology (SSAM) is a post- yielding and improve the vehicle detection capabilities of
processing tool that can interpret outputs from simulation tools blind pedestrians. Examples include a combination of auto-
and quantify the number of conflicts observed in the simulation mated vehicle detection with a pedestrian flasher or rumble
(FHWA 2008). A conflict in this case is defined by one of sev- strips in the approach of a raised crosswalk.
eral performance measures, including the time to collision. A · Perfect information (PI): This configuration represents per-
methodology for estimating pedestrianvehicle conflicts from fect unsignalized crossing conditions from a pedestrian per-
simulation independent of SSAM is discussed in Schroeder and spective. Pedestrian delay and risk are minimized because
Rouphail (2006), which is also included in Appendix I. 100% of vehicles yield to pedestrians. This form of driver
behavior may represent a strictly enforced right-of-way law.
Illustrative Example
The six treatment scenarios are implemented in the simu-
This section is intended to demonstrate the proposed lation at a CTL location for a one-way, one-lane pedestrian
approach for modeling the interaction of pedestrians and crossing, using assumed run-specific pedestrian and driver
