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37
3. Forced yield (FY): Pedestrians initiates crossing before the gap is defined as the time needed to cross the width of the
vehicle initiated the yield, forcing the driver to slow down crosswalk at a walking speed of 3.5 ft/s while allowing for a 2-s
by entering the crosswalk. safety buffer. This 2-s buffer allows for some pedestrian reaction
4. Crossable gap (CG): Pedestrian encounters a gap large time before initiating the crossing as well as the safety buffer
enough to safely cross the street without the need for a between a completed crossing and the next vehicle arrival.
driver yield. A crossable gap is defined as the time needed Similar to the yield statistics, three gap-related parameters
to cross at an assumed walking speed plus a safety buffer. are defined, but only the last two are used in the analysis:
5. Non-crossable gap (non-CG): Pedestrian encounters a gap
between vehicles shorter than the crossable gap threshold. · P(CG): The probability of a gap being crossable, defined as
the number of crossable gaps divided by the number of
For event categories 13, the event is associated with the crossable and non-crossable gaps encountered.
vehicle (driver) executing the yielding maneuver. For event · P(CG_ENC): The probability of encountering a CG event,
categories 4 and 5, the event is associated with the second of the defined as the number of crossable gaps divided by the
two vehicles that define the gap (the vehicle that "closes" total of all pedestrianvehicle events encountered by the
the gap). Conceptually, event type 5 also represents a vehi- pedestrian.
cle that did not yield to the pedestrian. The sum of event · P(GO|CG): The probability of crossable gap utilization,
types 1 through 5 corresponds to the total number of vehicles defined as the number of crossings in a CG divided by the
encountered by the pedestrian. The five event categories are total number of CGs encountered by the pedestrian. The
used to define the operational variables below. gap utilization concept is related to other traffic engineer-
ing studies that evaluate the numbers of accepted and
rejected gaps.
Performance Measures
Using the five event outcomes defined above, the NCHRP A walking speed of 3.5 ft/s in the determination of the cross-
Project 3-78A analysis framework defines performance mea- able gap threshold is based on the proposed walking speed in
sures to describe the four accessibility criteria: crossing oppor- the latest release of the MUTCD (FHWA 2009). This estimate
tunity, opportunity utilization, delay, and safety. represents the 15th percentile walking speed of the general
The first analysis component describes the availability pedestrian population, which is a conservative estimate. As a
and utilization of yields. Initially, all three yield types (rolling, result, the crossable gap threshold used in this project is also
stopped, and forced) are combined, but they can also be broken conservative. It is expected that most sighted pedestrians
out for a more detailed assessment. Three performance mea- would likely accept gaps that are shorter than this calculated
sures related to yielding are defined, although only the latter threshold, and this may also be observed for some of the blind
two are used in the analysis: study participants. The calculated crossable gap threshold may
therefore introduce a potential analysis bias: The probability
· P(Yield): The probability of a driver yielding, defined as the of encountering a crossable gap, P(CG_ENC), may be lower
number of yields divided by the total number of drivers that than what would be perceived by a pedestrian who readily
could have yielded. walks at a faster speed and therefore utilizes shorter gaps. Sim-
· P(Y_ENC): The probability of encountering a yield event, ilarly, the probability of utilizing a crossable gap is expected to
defined as the number of yields divided by the total of all be high, given that the threshold for what is considered cross-
pedestrianvehicle events encountered by the pedestrian able is high for 85% of the general pedestrian population.
until he/she completes the crossing. Nonetheless, the chosen walking speed is considered a reason-
· P(GO|Y): The probability of yield utilization, defined as the able assumption in light of national policy documents like the
number of crossings in a yield divided by the total number MUTCD, and in light of the fact that the threshold is consis-
of yields encountered by the pedestrian. tently applied to all sites to allow for a relative comparison.
The same crossable gap definition is also proposed in Chap-
The P(Y_ENC) performance measure is different from the ter 6, which talks about extension of the research results.
traditionally used probability of yielding, P(Yield), since it is The combined effect of gap and yield availability and uti-
calculated on the basis of all pedestrianvehicle events and lization is reflected in the delay experienced by pedestrians.
not just potential yielders. Figure 14 and the associated dis- Three delay performance measures are defined in the analysis:
cussion provide an example that illustrates the distinction
between the two measures. · Observed Delay per Leg (s): The pedestrian delay in sec-
The analysis next considers the availability and utilization onds, defined as the time difference between when the trial
of crossable gaps. For the purpose of this analysis, a crossable started and when the pedestrian initiated the crossing.

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Start of Trial MEASURES
Veh. # 1 2 2 3 4 4 5 6 7 7 8 8 9 10 # of Events
Cross Yield Cross Cross Yield Cross Cross Cross Yield Cross Yield Cross Cross Cross = 10 Vehicles
Vehicle Events
(n=10)
GO # of Crossings
Pedestrian =1 Crossing
Events (n=1)
NY Y NY Y NY NY Y Y NY P(Yield)
Yield Events = 4/(4+5) = 4/9
(n=9) = 44.4%
non-CG CG non-CG CG non-CG CG P(CG)
Gap Events = 3/(3+3) = 3/6
(n=6) = 50.0%
YY Y Y P(Y_ENC)
Yield Encounters = 4/10
(n=10) = 40.0%
CG CG CG P(CG_ENC)
CG Encounters = 3/10
(n=10) = 30.0%
Rej. Y Rej. Y Rej. Y Rej. Y P(GO|Yield)
Yield Utilization = 0/4
(n=4) = 0.0%
Rej. CG Rej. CG Utlz. CG P(GO|CG)
CG Utilization = 1/3
(n=4) = 33.3%
Delay (sec.)
= t(crossing) - t(start
Delay trial)
First Opportunity Delay>Min (sec.)
= t(crossing) - t(first
Delay>Min. opportunity)
P(Crossing Opportunity) P(Crossing)
= P(Y_ENC) + P(CG_ENC) = P(Y_ENC)*P(GO|Yield) + P(CG_ENC)*P(GO|CG)
= 4/10 + 3/10 = 7/10 = (4/10)*0% + (3/10)*33.3%
= 70% = 10%
This figure shows an illustrative example of how pedestrianvehicle 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).