At a typical signalized intersection, the pedestrian phase consists of a walk interval and a change/clearance interval, during which pedestrians are given the right of way. The walk interval is intended to allow pedestrians to exit the curb ramp and enter the crosswalk. The clearance interval will enable them to cross entirely to the other side of the road. Unfortunately, the literature is quite vague on how long the walk interval should be and provides values ranging from 4 to 15 seconds based on qualitative pedestrian demand ranging from Negligible to High . To provide some quantitative guidance for walk interval selection, this paper reports on a study that collected 1,500 pedestrian movement data from 12 signalized intersections with varying pedestrian demand, pedestrian storage areas, and pedestrian push-button locations. The data was used to propose a quantitative model for designers to select the appropriate walk interval. Specifically, this paper seeks to add values to the Traffic Operations Handbook walk-interval guidelines as to how many pedestrians are considered “negligible volume” and can be accommodated by the 4 second minimum time, how many pedestrians are considered “typical volume” and require 7 to 10 seconds, and how many pedestrians are considered “high volume” and require 10 to 15 seconds, or perhaps longer. In addition to examining pedestrian demand, this paper looks at the impact of storage areas and pedestrian push-button location on pedestrian start-up time and, consequently, an appropriate walk interval.
At signalized intersections, the pedestrian phase, during which the right-of-way is given to pedestrians, consists of two intervals: 1) Walk interval typically begins with the adjacent vehicular through-movement green interval and is used to allow pedestrians to move from the curb into the crosswalk; 2) Pedestrian Clearance, also referred to as flashing don’t walk (FDW) or change interval: follows the walk interval and informs pedestrians should either complete their crossing if already in the intersection or refrain from entering the intersection until the next pedestrian walk interval is displayed. Finally, the pedestrian phase ends with the solid Don’t Cross
The duration of the pedestrian phase, seen in
G p = P . W . + P . C .
where;
Gp is the green interval duration needed for the pedestrian crossing time.
P.W. is the walk interval duration. The MUTCD indicates that the minimum walk duration should be at least 7 seconds but states that a duration as low as 4 seconds may be used if pedestrian volumes are low. The traffic signal operations handbook suggests using the walk values listed in
| Conditions | Walk Interval Duration (P.W.), s |
|---|---|
| High pedestrian volume areas | 15 |
| Typical pedestrian volume and longer cycle length | 10 |
| Typical pedestrian volume and shorter cycle length | 7 |
| Negligible pedestrian volume | 4 |
P.C. is the clearance/change interval duration. The duration of this interval is computed as the crossing distance divided by the walking speed. The MUTCD recommends a value of 4.0 feet per second (ft/s) walking speed. The Americans with Disabilities Act (ADA) Accessibility Guidelines for Buildings and Facilities recommended using 3.0 ft/s. Recent work completed by LaPlante and Kaeser has suggested a speed of 3.5 ft/s [
Pedestrian speeds and the clearance interval have been extensively studied in the literature and, consequently, well defined in designers’ guidebooks [
Studies investigating pedestrian dynamics (i.e., walking speed and start-up time) have considered factors such as pedestrians’ age and found that, on average, pedestrians above the age of 65 differ from those younger [
The walk interval (P.W.) should be designed to accommodate pedestrians’ perception-reaction delay and walking time to the crosswalk. Many factors can result in delaying a pedestrian in accomplishing this task. The social force model is widely used in defining the factors influencing pedestrian dynamics (i.e., avoiding obstacles and keeping a comfort zone away from other pedestrians). Such factors/forces make a pedestrian take some time to exit the curb onto the crosswalk once the walk interval is activated [
In terms of signal timing, the collective behavior of pedestrians matters and should be accounted for in timing the walk interval. Therefore, the walk interval should provide enough time to allow all waiting pedestrians to move onto the crosswalk from the onset of the walk signal illumination.
There is a gap in the literature regarding quantitative values for pedestrian demand that should be used to select pedestrian walk times. Similarly, the literature does not provide guidance on how other factors, such as pedestrian storage areas and distance to pedestrian push-buttons, influence the selection of walk times.
This paper reports on the observation of pedestrian start-up time and propose a quantitative model for designers to select the appropriate walk interval. Specifically, this paper seeks to add values to
As a result of having a proper understanding of pedestrian demand and geometrics influencing start-up time and, consequently, the selected walk interval, designers will be able to provide satisfactory service that minimizes delay for pedestrians and motorists.
Using video footage from 12 signalized intersection cameras collected between late 2021 and early 2022 in the City of West Lafayette, Indiana, 1500 observations of pedestrian start-up time are examined.
Data were extracted from videos recorded using 12 cameras mounted on the traffic light mast arms. Installed cameras recorded continuously since the day of installation. Video imagery provides a 360 view of all intersection approaches and curb ramps, as seen in
During each cycle, videos were analyzed in terms of start-up time. Start-up time is the duration needed for a waiting pedestrian, or a group of pedestrians, to clear the curb into the crosswalk once the Walk Interval is activated.
In addition, each intersection observation was analyzed in terms of the total number of pedestrians waiting per quadrant, the available storage area for pedestrians per quadrant (curb ramp area), and the distance from the pedestrian push-button to the crosswalk.
After that, a set of statistical regression models was built to explain the variability in pedestrian start-up time (y) given pedestrian demand in terms of the number of pedestrians per cycle per quadrant (X1), available storage area (X2), and distance from the pedestrian push-button to the crosswalk (X3).
| Intersection | Location | ||
|---|---|---|---|
| Long | Lat | ||
| 1 | Roebuck Drive and State Street | 40.4212 | −86.9019 |
| 2 | State Street and South River Road | 40.4218 | −86.9042 |
| 3 | State Street and Chauncey Avenue | 40.4233 | −86.9069 |
| 4 | Northwestern Avenue and State Street | 40.4240 | −86.9082 |
| 5 | State Street and Andrew Place | 40.4240 | −86.9092 |
| 6 | South Grant Street and State Street | 40.4239 | −86.9103 |
| 7 | State Street and University Street | 40.4242 | −86.9168 |
| 8 | State Street and S. Martin Jischke Drive | 40.4242 | −86.9217 |
| 9 | State Street and Airport Road | 40.4241 | −86.9302 |
| 10 | South Chauncey Avenue and West Wood Street | 40.4219 | −86.9076 |
| 11 | University Street and 3rd Street | 40.4272, | −86.9166 |
| 12 | West Stadium Avenue and University Street | 40.4313 | −86.9168 |
Intersections with heavy pedestrian traffic constitute the majority of the 1500 observations.
The guidelines in place for determining the duration of the pedestrian walk interval, presented in
The relation between pedestrian start-up time and the explanatory variables was near linear, so linear regression was used to explain the variability in the response variable y: start-up time. Three models were built, and a report of the findings is listed in
Since this data was collected on and near a college campus, the authors propose using the 50th percentile values in the pedestrian volume categories listed in
| Start-up Time | Pedestrian Volume | ||||||||
|---|---|---|---|---|---|---|---|---|---|
| Obs. | Avg | Min | Max | Std. | Percentile | ||||
| 25th | 50th | 75th | 90th | ||||||
| 1 - 4 s | 1107 | 2.75 | 1 | 12 | 1.88 | 1 | 2 | 4 | 5 |
| 4 - 7 s | 313 | 6.41 | 1 | 20 | 2.87 | 4 | 6 | 8 | 10 |
| 7 - 10 s | 67 | 11.99 | 3 | 33 | 5.91 | 8 | 11 | 15 | 19.2 |
| 10 - 15 s | 13 | 15.92 | 10 | 40 | 8.45 | 11 | 14 | 15 | 24.4 |
| Model 1: Startup Time = β1 (Ped Volume) | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|
| Explanatory Variable Coefficient | Explanatory Variable Significance | Goodness-of-Fit | |||||||||
| Coefficient | t-stat | p-value | Adj. R2 | 0.817 | |||||||
| β1 | 0.7709 | X1 (peds) | 82.12 | 0.0000 | Std. Err. | 1.962 | |||||
| Obs. | 1500 | ||||||||||
| Regression Statistics | |||||||||||
| df | SS | MS | F | ||||||||
| Regression | 1 | 25979.6336 | 25979.6336 | 6744.0812 | |||||||
| Residual | 1499 | 5774.4664 | 3.8522 | ||||||||
| Total | 1500 | 31754.1 | |||||||||
| Model 2: Startup Time = β1 (Ped Volume) + β2 (Storage Area) + β3 (Push Button Offset) | |||||||||||
| Explanatory Variable Coefficient | Explanatory Variable Significance | Goodness-of-Fit | |||||||||
| Coefficient | t-stat | p-value | Adj. R2 | 0.896 | |||||||
| β1 | 0.5460 | X1 (peds) | 55.82 | 0.0000 | Std. Err. | 1.477 | |||||
| β2 | 0.1933 | X2 (ft2) | 24.95 | 3.4E−115 | Obs. | 1500 | |||||
| β3 | −3.4E−06 | X3 (ft) | −0.03 | 0.9739 | |||||||
| Regression Statistics | |||||||||||
| df | SS | MS | F | ||||||||
| Regression | 3 | 28488.2356 | 9496.0785 | 4352.7923 | |||||||
| Residual | 1497 | 3265.8643 | 2.1816 | ||||||||
| Total | 1500 | 31754.1 | |||||||||
| Model 3: Startup Time = β1 (Ped Volume) + β2 (Push Button Offset) | |||||||||||
| Explanatory Variable Coefficient | Explanatory Variable Significance | Goodness-of-Fit | |||||||||
| Coefficient | t-stat | p-value | Adj. R2 | 0.8964 | |||||||
| β1 | 0.5460 | X1 (peds) | 56.37 | 0.0000 | Std. Err. | 1.4765 | |||||
| β2 | 0.1931 | X2 (ft) | 33.92 | 1.2E−187 | Obs. | 1500 | |||||
| Regression Statistics | |||||||||||
| df | SS | MS | F | ||||||||
| Regression | 2 | 28488.2332 | 14244.1166 | 6533.5448 | |||||||
| Residual | 1498 | 3265.8667 | 2.1801 | ||||||||
| Total | 1500 | 31754.1 | |||||||||
| Start-up Time | Pedestrian Volume (peds/quad/cycle) | |||
|---|---|---|---|---|
| Percentile | ||||
| 25th | 50th | 75th | 90th | |
| 1 - 4 s | 1 | 2 | 4 | 5 |
| 4 - 7 s | 4 | 6 | 8 | 10 |
| 7 - 10 s | 8 | 11 | 15 | 19.2 |
| 10 - 15 s | 11 | 14 | 15 | 24.4 |
The relationship between start-up time and the collected explanatory variables was near-linear, so linear regression models were used to predict start-up time. The statistical models built indicate the significant influence of the variables: 1) pedestrian volume and 2) offset from the push-button to the crosswalk on the pedestrian start-up time. The built model explains start-up time with a relatively high accuracy of 0.8964 R2.
This paper presented a quantitative analysis of the pedestrian walk interval duration given pedestrian volume conducted on 12 signalized intersections across the City of West Lafayette, Indiana, for ten months. In addition, data on the storage area and offset from the pedestrian push button to the crosswalk was used to explain the variability in pedestrian start-up time. The built statistical model can aid designers in identifying proper walk interval timing on an intersection-by-intersection basis. In addition, designers now have quantitative data for new construction to support prioritizing close-to-crosswalk push-button locations to help minimize pedestrian start-up time.
Future research should consider examining the impact of different types of pedestrian phasing (i.e., exclusive service and standard concurrent service) on pedestrian start-up time. In addition, seasonality can be included in the analysis (i.e., summer, fall, winter, and spring) as pedestrian behavior can be expected to change with inclement weather.
The authors acknowledge the assistance of Ben Anderson and Justin Hitchcock of the City of West Lafayette for their general assistance in data collection. The contents of this paper reflect the views of the authors, who are responsible for the facts and the accuracy of the data presented herein, and do not necessarily reflect the official views or policies of the City of West Lafayette, nor do the contents constitute a standard, specification, or regulation.
The authors declare no conflicts of interest regarding the publication of this paper.
Nafakh, A.J., Bullock, D.M. and Fricker, J.D. (2022) A Quantitative Approach for Timing the Pedestrian Walk Interval. Journal of Transportation Technologies, 12, 732-743. https://doi.org/10.4236/jtts.2022.124042