The pedestrian crossing time serves as a constraint on the green time allocated to each phase of a cycle. Pedestrians can safely cross an intersection as long as there are not any conflicting movements occurring at the same time. (Permitted left and right turns are common exceptions to this rule.) This allows pedestrians to cross the intersection in both the green interval and the intergreen interval. Thus, the sum of the green interval and the intergreen interval lengths, for each phase, must be large enough to accommodate the pedestrian movements that occur during that phase.
At this point, two separate conditions arise. If you have an intersection in which the pedestrian movements are not assisted by a pedestrian signal, you need to make sure that the green interval that you provide for vehicles will service the pedestrians as well. In this case, the minimum green interval length is somewhere between 4 and 7 seconds. You already took care of the pedestrian crossing time considerations when you calculated the intergreen period length. (See the module on the intergreen period.)
If, on the other hand, you plan to provide a pedestrian signal, you need to calculate the pedestrian crossing time as described below. This will not only give you the information you need to program the pedestrian signal, but it will also allow you to find the minimum green interval for your vehicular movements as well.
We only need a few assumptions to calculate the pedestrian crossing time.
The total time required for the pedestrian movements (T) is the sum of the WALK allowance (Z) and the time required for a person to traverse the crosswalk (R).
R = (width of intersection, in feet)/(4 ft/sec)
T = Z + R
The pedestrian crossing time governs the minimum green time for the accompanying phase in the following way. If the time it takes the pedestrian to traverse the crosswalk (R) is greater than the intergreen time(I), the remainder of the time (Z+R-I) must be provided by the green interval. Therefore, the minimum green interval length (gmin) for each phase can be calculated using the equation below.
gmin = T - intergreen time(I) or gmin = Z + R I
If the above equation results in a minimum green interval that is less than the WALK time (Z), the minimum green interval length is equal to the WALK time (Z).
gmin = Z
You now have the minimum length of the green interval for the vehicular movements, as governed by the pedestrian movements. The WALK interval for the pedestrians is whatever you assumed, and the DON'T WALK flashes for the remainder of the green and intergreen intervals.
Many design manuals suggest that the distance the pedestrian is assumed to travel can be reduced to the distance between the curb and the center of the farthest lane. On another note, if the vehicular traffic requires an extended green period, feel free to let the pedestrains partake of the extra time as well.