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The comparison does not mean that all twolane round Table 12. Pedestrian LOS stratification,
abouts will always produce higher delays than any singlelane adopted from the HCM (TRB 2000).
roundabout or CTL. It merely says that a pedestrian will expe
Delay Range (s/ped)
rience higher delay at a twolane roundabout than a singlelane Likelihood of
roundabout (or CTL) when encountering the exact same traf LOS Signalized Unsignalized Noncompliance
fic patterns and driver behavior and is furthermore capable of A <10 <5 Low
making the same judgments about gaps and yields. The actual B 1020 510
performance of a particular site and the relative difference to C >2030 >1020 Moderate
other sites depends on the underlying probabilities that make D >3040 >2030
up PCross and PDual_Cross. An approach for estimating these is dis E >4060 >3045 High
cussed in the next section. F >60 >45 Very high
Model Application
The mixedpriority pedestrian delay models presented in certainty that a crossing opportunity will eventually present
this section can theoretically be applied to other sites with dif itself. Consequently, pedestrians may be more willing to accept
ferent geometries, traffic volumes, and pedestrian behavior. greater delay at signals. However, the table recognizes quali
Clearly the application of any model beyond its realm of cal tatively that the likelihood of pedestrian risk taking (i.e., jay
ibration can be risky, and professional judgment should be walking against the signal or accepting short gaps in traffic)
applied. In general, these models are not intended to serve as increases with higher pedestrian delay. The HCM LOS strat
the sole determinant of pedestrian accessibility and should ification does not distinguish between onestage and two
not be used in isolation. As this report discusses, pedestrian stage crossings, so it is assumed here that the thresholds are
delay is only one aspect of accessibility, with pedestrian risk intended to be applied to the entire crossing, which in the case
being another that is equally if not more important. Clearly, of roundabouts represents the sum of delay experienced at
the risk to pedestrians or the fact that a crossing may be avoided the entry and exit leg. At channelized turn lanes, the total cross
entirely if the real or perceived risk is too high needs to be con ing delay accordingly includes the delay at the main inter
sidered first and foremost. Further, Chapter 2 of this report section and any additional CTLs that are in the path of the
discusses the other components of the crossing task, which pedestrian.
include locating the crosswalk, aligning to cross, deciding when It is important to emphasize here that (blind) pedestrian
to cross, and maintaining alignment after the crossing is ini delay can also be measured directly from field observations,
tiated. The delay models are focused on the third component which is usually the preferred approach. Any theoretical model
and therefore do not capture any additional delays that may is participant to variability and error, and direct field mea
occur when a pedestrian is challenged to locate the intended surements are likely to provide a more unbiased estimate of
crossing point. delay or any other parameter. In the absence of field data, the
remaining challenge in the application of the mixedpriority
delay models is to identify appropriate model inputs. This is
Selecting Delay Thresholds
the focus of the next sections.
The application of delay models is associated with the chal
lenge of defining thresholds for what is considered an accept
Estimating Probability Parameters
able wait time and whether these thresholds differ by facility
type. The Highway Capacity Manual (TRB 2000) uses delay The probability parameters that are used as the explana
to stratify LOS for (sighted) pedestrians and other modes at tory variables in the mixedpriority delay models can be esti
signalized and unsignalized starting points. Logically, the mated directly from field measurements or can be gleaned
HCM LOS tables could represent a starting point for the dis from the appropriate literature and traffic flow theory concepts.
cussion of acceptable delay thresholds. The HCM table for As with any model application, the use of fieldmeasured prob
signalized and unsignalized pedestrian crossings is presented abilities is preferable since these give the analyst the greatest
in Table 12. confidence. It is recognized that field measurements are often
The table shows a stratification of LOS from A (best) to F beyond the scope and budget of such analysis and are further
(worst) using ranges of average delay per pedestrian for the precluded for newly planned locations. Field studies are also
crossing. From the HCM exhibits it is evident that the pre not applicable for sensitivity analyses that explore the poten
sumed level of acceptable delay is greater at a signalized inter tial impact of implementing pedestrian treatments to improve
section because the presence of the signal is associated with a accessibility at a particular location.
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The delay models for channelized turn lanes and single where
lane roundabouts are based on the variable PCross, which is a L = crosswalk length (ft),
function of the four probability terms P(Y_ENC), P(CG_ Sp = average pedestrian walking speed (ft/s), and
ENC), P(GOY), and P(GOCG). For twolane roundabouts, ts = pedestrian startup and clearance time (s).
the explanatory variable is PDual_Cross, which is a function of the
Using the above relationship, the probability of observing a
availability and utilization of crossing opportunities in both crossable gap in a stream of 400 vph at a 14ft lane at a round
lanes, PA_Dual and PU_Dual. An analyst can apply the delay about and a corresponding critical headway of tc = 14/3.5 +
models to new sites and conditions by estimating these param 2 = 6 s is:
eters from field measurements or literature sources.
For the field measurement of the explanatory variables, the  c
t 6
P (CG _ Enc ) = P ( headway 6s ) = e

rate of driver yielding and the availability of crossable gaps
t avg
=e 9 = 51.3%
can be measured using manual tally and stopwatch methods
described in the ITE Manual of Transportation Studies (1994) Yield Encounters. The probability of encountering a
or other sources. The estimation of yield and gap utilization yielding vehicle is a function of driver courtesy and is also
rates is more difficult for blind pedestrians since it requires dependent on the geometry of the site, particularly the result
controlled field experiments. In the absence of field data, the ing vehicle operating speeds. More yields are expected where
results from this research can be used in the interim, which is vehicle speeds are low and where drivers expect the presence
discussed in more detail below. For sighted pedestrians, uti of pedestrians, including university campuses and down
town areas. Most field studies estimate the probability of
lization rates of or near 1.0 can be assumed. For other special
yielding based on the number of vehicles that could have
pedestrian populations, including children and the elderly,
yielded, P(Yield). Note that this is different from the proba
analyst judgment will be required until further research char
bility P(Y_ENC) used in the delay model, which is calculated
acterizes their behavior. A basic sensitivity analysis can ensure
on the basis of all encountered vehicles and is a better rep
that a range of values are considered. In the absence of field
resentation of the flow rate that a pedestrian is likely to
data, probabilities can also be estimated from the literature,
experience. A reasonable approach for estimating P(Y_ENC)
which includes findings from this research and other field
from P(Yield) is to subtract the probability of crossable gaps
studies, as well as theoretical traffic flow relationships.
from the total number of vehicle events:
Crossable Gap Encounters. The availability of crossable Equation 6. Estimating yield encounters from yield
gaps can be estimated using trafficflow theory concepts probabilities.
based on traffic volume and an assumed headway distribu
PY _ ENC = PYield (100%  PCG _ ENC )
tion. Assuming random arrivals, one can use the negative
exponential distribution to estimate the probability of observ
This approach ensures that the sum of PY_ENC and PCG_ENC
ing a time headway greater than tc seconds, per Equation 4.
is less than or equal to 1.0, as is required by definition. The
This equation assumes random arrivals of vehicles. For non
reader is referred to Chapter 4 for more detail on these event
random arrivals, other distributions are available (May 1990). definitions.
Equation 4. Estimating P(CG_ENC) from traffic flow Probability estimates for the probability of yielding (PYield)
theory (May 1990). are available from research. A recent national survey on round
 c
t about operations (Rodegerdts et al. 2007) has estimated yield
P (CG _ ENC ) = P ( headway t c ) = e t avg
probabilities for many singlelane and twolane roundabouts.
Table 13 shows observed ranges for singlelane approaches
where from that research along with findings from this project.
tc = critical headway for crossable gap (s) The table shows significant variation across yielding rates
tavg = average headway, defined as tavg = (3,600 s/h)/(vph). for the studied sites. The averages and ranges from NCHRP
In the absence of pedestrian platoons, the critical gap for Report 572 represent five singlelane roundabouts. These were
pedestrians can be calculated by Equation 5 following the the only studied sites that featured notable pedestrian activity.
HCM methodology. It appears that the singlelane roundabout yielding rates
Equation 5. Pedestrian critical gap after HCM Equa observed during this project are much lower than the ones
tion 1817 (TRB 2000). observed in that project. A potential explanation for this is the
different levels of pedestrian use and associated driver courtesy.
L The statistics do, however, point to the general trend that yield
tc = + ts
Sp ing rates at the exit lane are often lower than at the entry lane.
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Table 13. Yield probabilities (PYield), for singlelane approaches.
SingleLane Roundabouts CTL
NCHRP Report 572 NCHRP Project 378A Averages NCHRP
Project 3
Average Range DAVCLT PSRAL GOLPRE 78A Sites
Entry Lane
Curbisland 85% 65%100%
10.8% 41.5% 65.6%
Islandcurb 90% 50%100%
Exit Lane 26.1%
Curbisland 71% 17%100%
11.8% 32.8% 36.1%
Islandcurb 85% 33%100%
A comparison between roundabouts and the CTL studies it difficult to generalize for the entire population of blind pedes
under NCHRP Project 378A further points to low CTL yield trians. If a user chooses to apply the average utilization rate,
ing behavior at the tested sites. It is expected that a wider range higher delays (due to lower utilization rates) can be expected for
of rates would be observed with a greater sample of CTL sites half of the population of blind travelers. As discussed in Chap
with varying geometry. ter 5, the installation of crossing treatments at the CTL had
some impact on the utilization statistics. The installation of
Gap and Yield Utilization. The remaining explanatory sound strips only (SSONLY) resulted in a slight decrease of
probability variables are the rates of utilization for yield and yield utilization. The added use of a flashing beacon (SS+FB)
crossable gap opportunities. It was hypothesized above that increased both yield and crossable gap utilization.
most sighted pedestrians would be assumed to accept most
or all first yield and crossable gap opportunities. Their rates Numerical Illustration for SingleLane Roundabout.
of utilization for those events would therefore be assumed This section presents an example calculation for a singlelane
to equal 1.0. For blind pedestrians, utilization rates much roundabout that will be used by a population of blind pedes
lower than 100% have been observed in this research as well trians. The delay equation for a singlelane roundabout was
as in prior studies. Individual differences and unique audi given previously by Equation 2, which expands to:
tory characteristics of different sites are expected to affect
these rates. Tables 14 and 15 summarize the utilization rates d p = 0.78  14.99 LN ( PCROSS )
observed at singlelane roundabout and CTL crossings in = 0.78  14.99 LN ( PY _ ENC PGO Yield + PCG _ ENC PGO CG )
this research, respectively. Twolane roundabouts are dis
cussed separately. where all terms are as defined previously.
The tables show average utilization rates for all sites in the To estimate the delay at a site, the analyst would first esti
range of 50% to 80%. The utilization rates are highest at the mate the availability of yield and crossable gap opportunities.
GOLPRE singlelane roundabout. The statistics further show In this context, it is critical that these two probabilities use the
a large range of these values across study participants, making same common denominator in the total number of vehicle
Table 14. Yield and crossable gap utilization rates at studied
singlelane roundabouts.
SingleLane Roundabout
DAVCLT PSRAL GOLPRE
Avg. Range Avg. Range Avg. Range
P(GOY)
Entry lane 64.1% 0%100% 83.0% 50%100% 82.8% 36%100%
Exit lane 70.4% 0%100% 87.8% 60%100% 76.0% 25%100%
P(GOCG)
Entry lane 66.3% 25%100% 52.0% 0%100% 83.2% 33%100%
Exit lane 60.3% 33%100% 63.6% 19%100% 86.8% 40%100%
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Table 15. Yield and crossable gap utilization for a sighted pedestrian facing the same traffic conditions and
rates at studied channelized turn lanes. driver behavior.
A pedestrian treatment that improves driver yielding from
Average Range 30% to say 75% would increase PY_ENC to (100% 26.4%)
P(GOY) PRE 51.9% 0%100% 75% = 55.2% and would improve the delay for the blind
POSTSSONLY 40.5% 10%75% pedestrian to:
POSTSS+FB 64.6% 20%100%
P(GOCG) PRE 61.8% 4%100% d p = 0.78  14.99 LN ( 0.552 0.4 + 0.264 0.3) = 17.3 s
POSTSSONLY 68.2% 6%100%
POSTSS+FB 89.3% 58%100% Compared to the baseline delay of 26.0 s, this pedestrian
treatment resulted in a 33.6% reduction in delay to the
blind travelers. The total delay for both legs is reduced to
events. By definition, the sum of PY_ENC and PCG_ENC can there 34.6 s. The treatments also helped sighted pedestrians and
fore never exceed 1.0, which would correspond to every vehi reduced their delay from 10.1 s to only 2.6 s on average:
cle event constituting a crossing opportunity. Since the two
probabilities are related, it is expected that an increase in d p = 0.78  14.99 LN ( 0.552 1.0 + 0.264 1.0 ) = 2.3 s
yielding will correspond to a lower fraction of encountered
events being crossable gaps. The analyst can easily perform additional sensitivity analy
For the example, assume peak hour conflicting traffic flow ses to test the hypothesized effects of other treatments or
at the site is 800 vph and the pedestrian critical gap is esti changes in the conflicting traffic volumes.
mated at 6 s. At 800 vph, the average headway between vehi
cles is 3600/800, or 4.5 s. The probability of encountering a Estimating Probabilities for TwoLane Approaches.
crossable gap greater than 6 s in this traffic stream is given by: Since the probability terms for twolane roundabouts are

tc 6 different than for singlelane approaches, their estimation
P (CG _ ENC ) = P ( headway 6s ) = e

t avg .
=e 4.5 = 26.4% is discussed separately. The twolane roundabout crossing
process is characterized by the availability and utilization
It is further assumed that the analyst knows from field of dual crossing opportunities, which can be in the form of
studies that 30% of the remaining traffic is expected to yield. either a yield or a crossable gap in both conflicting lanes at the
The probability of encountering a yield is therefore given by same time. The mixedpriority delay equation given above
(100% 26.4%) 30% = 22.1% of vehicle encounters. expands to:
Referring to Table 15, the analyst estimates that the utiliza
tion rates for yields and crossable gaps are 40% and 30%, d p = 1.9  21.0 LN ( PDualCROSS )
respectively. This is about half of the average rates found in
= 1.9  21.0 LN ( PA _ Dual PU _ Dual )
this research, and was selected to represent a more conserva
tive and less skilled blind traveler:
where all terms are as defined previously.
d p = 0.78  14.99 LN ( 0.221 0.4 + 0.264 0.3) = 26.0 s The probability of encountering either a crossable gap or a
yield in both lanes, PA_Dual, is calculated as follows.
Since this delay estimate is per crossing leg, the total
approach delay is estimated at 52.0 s on average, which falls 1. The analyst calculates the likelihood of encountering a
within HCM LOS = F for unsignalized crossings. This assumes crossable gap in each lane, based on the estimated perlane
that the behavioral parameters at the entry and exit legs are traffic volumes using Equation 4. The resulting probabil
exactly the same. This simplifying assumption was only done ities are PCG1 and PCG2, for lanes 1 and 2, respectively. Lane 1
for this example. In reality, the analyst should carefully con is defined to be the one closest to the pedestrian.
sider the differences between entry and exit legs, including 2. The analyst estimates the probability of yielding in each
traffic volumes, vehicle speeds, and yielding behavior. As a lane, PYield_Lane1 and PYield_Lane2, from field observations or
comparison, a sighted pedestrian would have experienced a literature.
delay of: 3. The analyst calculates the probabilities of encountering a
yield event in each lane PY_ENC1 and PY_ENC2 using Equation
d p = 0.78  14.99 LN ( 0.221 1.0 + 0.264 1.0 ) = 10.1 s 6 and the results of steps 1 and 2.
4. The analyst estimates the probability of encountering a
Consequently, the delay for a blind pedestrian with the dual crossing opportunity in both lanes by the following
assumed lower utilization rates would be 2.6 times higher than equation: