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Equation 7. Estimating yield encounters from yield Among the most common treatments are those intended
probabilities. to increase the probability of drivers to yield to pedestrians,
which was one of the key focus areas of NCHRP Report 562
PA _ Dual = PY _ ENC 1 PY _ ENC 2 + PY _ ENC 1 PCG 2 (Fitzpatrick et al. 2006). While data collection in that research
+ PCG1 PY _ ENC 2 + PCG1 PCG 2 was focused on midblock crossings, the results provide an
overview of the average and range of yielding rates observed
where for different treatments across the country. The reader is
PA_Dual = probability of encountering crossing opportunity encouraged to consult that and similar research for further
in both lanes, information.
PY_ENC1 = probability of encountering a yield in lane 1,
PY_ENC2 = probability of encountering a yield in lane 2, Delay Model Discussion
PCG1 = probability of encountering a crossable gap in
lane 1, and The previous section demonstrated the application of a
PCG2 = probability of encountering a crossable gap in framework based on pedestrian and driver behavioral param-
lane 2. eters for estimating pedestrian delay at single- and two-lane
roundabouts as well as at channelized turn lanes. The under-
The results from this research can again be used as guid- lying dataset was obtained from controlled experiments using
ance for the estimation of the probability of utilizing a dual more than 100 blind participants at seven different sites. The
crossing opportunity. Table 16 summarizes field-observed focus on blind pedestrians provided a framework that distin-
probabilities of encountering and utilizing dual crossing oppor- guished between available crossing opportunities and the
tunities for the studied two-lane roundabout in the pretest actual utilization of these opportunities. A dataset containing
condition. only sighted pedestrians would not be expected to capture the
The analyst can follow the procedure above to estimate the utilization effect.
PA_Dual and PU_Dual probabilities for a two-lane round- The resulting delay models are statistically significant
about and calculate the predicted average pedestrian delay and produce good estimates of pedestrian delay that match
using Equation 3 for two-lane approaches. A numerical exam- observed field data. The underlying probability terms can
ple is not provided but is consistent with the example presented be estimated from field observations for other sites or can be
for single-lane roundabouts. estimated from literature or traffic flow theory concepts. The
resulting models allow the analyst to distinguish delay encoun-
Impacts of Pedestrian Crossing Treatments tered at CTLs, single-lane roundabouts, and two-lane round-
abouts. It further allows the analyst to represent the impact of
The underlying hypothesis of the NCHRP Project 3-78A pedestrian crossing treatments on delay.
analysis framework and these delay models is that there exists
the ability to represent the impact of pedestrian crossing treat-
ments through changes in the probability terms. This allows Extension to Safety Modeling
the analyst to quantify the impact of any treatment on pedes- As discussed earlier in this chapter and emphasized through-
trian delay. Chapter 5 presented a detailed discussion of the out this report, delay is only one factor when evaluating the
measured impacts for the pedestrian treatments studied in accessibility and usability of a crosswalk. Another, potentially
this research. Consistent with the discussion in Chapter 2, more critical aspect is the safety or risk associated with cross-
various pedestrian treatments not tested in this research have ing at a particular location. This report uses the measure of
a similar ability to reduce pedestrian delay. O&M interventions to quantify the risk involved in crossing
decisions by blind study participants. Clearly, it would be
desirable to develop study extension tools for the assessment
Table 16. Field-observed performance at of pedestrian safety, similar to the delay models described
two-lane roundabout.
above.
The development of predictive models for pedestrian risk
Average Range
or safety is constrained by a limitation of the risk perfor-
PA_Dual PRE 55.8% 15%93%
mance measure of O&M interventions. Since interventions are
POST-RCW 76.9% 57%100%
very rare events, it is difficult to apply the regression-based
POST-PHB 89.3% 72%100%
modeling approach to this measure. The reason is that most
PU_Dual PRE 90.0% 44%100%
of the observations result in a dependent variable value of
POST-RCW 98.1% 94%100% zero (no interventions) while being associated with a range
POST-PHB 98.3% 83%100% of underlying yield, gap, and utilization probability terms.
