A senior citizen using a crosswalk at a local intersection was struck by a vehicle. Following the incident, a number of other citizens complained that the allocated pedestrian crossing time was insufficient at the intersection. You have been asked to evaluate the situation.
You estimate the width of the intersection as 60 ft and the average pedestrians pace as 4 ft/sec. You also record the WALK time (10 sec), concurrent green interval length (14 sec), and the intergreen time (6 sec). Can you prove that the green interval given to the concurrent vehicular movement was insufficient based on the pedestrian crossing time? If this pedestrian movement has an extremely low flow rate, which is why this incident didn't happened before, how would you correct the safety problem without increasing the delay observed by the vehicular movements?[Solution Shown Below]
The first step in this solution is to calculate the time required for a person to cross the intersection. This time can be calculated from the equation below.
R = (width of intersection)/(walking speed of person)
Substituting the given information into this equation, we get a crossing time (R) of 15 seconds. Next, the total time that should be devoted to pedestrians is calculated by adding the WALK time (Z) to the crossing time (R). This gives us a required pedestrian total time of 25 seconds. Adding the vehicular green interval length (14 sec) and intergreen times (6 sec) that were provided gives us a value of 20 seconds. Since the pedestrian phase requires 25 seconds and is currently only given a total time of 20 seconds, conflicting traffic will begin moving a full 5 seconds before the last pedestrian has made it to safety. No wonder this incident occurred. This problem could be remedied by increasing the length of the vehicular movement's green interval by 5 seconds. You might want to prove this using the equation g = Z + R - I.
One way to alleviate the problem without increasing the cycle length is to reduce the WALK time that is given to the pedestrians by 5 seconds. This would bring the required pedestrian total time to the 20 seconds that is currently provided. This option is only available because the pedestrian flow rate is very low for this intersection.