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69 The comparison does not mean that all two-lane round- Table 12. Pedestrian LOS stratification, abouts will always produce higher delays than any single-lane 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 two-lane roundabout than a single-lane 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 mixed-priority 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 one-stage 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 mixed-priority 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 mixed-priority 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 field-measured 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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70 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(GO|Y), and P(GO|CG). For two-lane roundabouts, ts = pedestrian start-up 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 14-ft 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 traffic-flow 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 single-lane and two-lane roundabouts. Table 13 shows observed ranges for single-lane 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 single-lane 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 single-lane roundabout yielding rates Equation 5. Pedestrian critical gap after HCM Equa- observed during this project are much lower than the ones tion 18-17 (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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71 Table 13. Yield probabilities (PYield), for single-lane approaches. Single-Lane Roundabouts CTL NCHRP Report 572 NCHRP Project 3-78A Averages NCHRP Project 3- Average Range DAV-CLT PS-RAL GOL-PRE 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 3-78A 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 (SS-ONLY) 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 Single-Lane Roundabout. of utilization for those events would therefore be assumed This section presents an example calculation for a single-lane 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 single-lane 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 single-lane roundabout and CTL crossings in = -0.78 - 14.99 LN ( PY _ ENC PGO Yield + PCG _ ENC PGO CG ) this research, respectively. Two-lane 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. GOL-PRE single-lane 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 single-lane roundabouts. Single-Lane Roundabout DAV-CLT PS-RAL GOL-PRE Avg. Range Avg. Range Avg. Range P(GO|Y) 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(GO|CG) 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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72 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(GO|Y) PRE 51.9% 0%100% 75% = 55.2% and would improve the delay for the blind POST-SS-ONLY 40.5% 10%75% pedestrian to: POST-SS+FB 64.6% 20%100% P(GO|CG) PRE 61.8% 4%100% d p = -0.78 - 14.99 LN ( 0.552 0.4 + 0.264 0.3) = 17.3 s POST-SS-ONLY 68.2% 6%100% POST-SS+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 Two-Lane Approaches. crossable gap greater than 6 s in this traffic stream is given by: Since the probability terms for two-lane roundabouts are - tc 6 different than for single-lane approaches, their estimation P (CG _ ENC ) = P ( headway 6s ) = e - t avg . =e 4.5 = 26.4% is discussed separately. The two-lane 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 mixed-priority 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 per-lane 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: