Waiting at a stop sign: Consider a side road connecting to a major highway at a stop sign. According to a study by D. R. Drew,44 the average delay D, in seconds, for a car waiting at the stop sign...

Waiting at a stop sign: Consider a side road connecting to a major highway at a stop sign. According to a study by D. R. Drew,44 the average delay D, in seconds, for a car waiting at the stop sign toenter the highway is given by

where q is the flow rate, or the number of cars per second passing the stop sign on the highway, and T is the critical headway, or the minimum length of time in seconds between cars on the highway that will allow for safe entry. We assume that the critical headway is T = 5 seconds.

a. What is the average delay time if the flow rate is 500 cars per hour (0.14 car per second)?

b. The service rate s for a stop sign is the number of cars per second that can leave the stop sign.

It is related to the delay by

Use function composition to represent the service rate as a function of flow rate. Reminder: (a/b)−1 = b/a.

c. What flow rate will permit a stop sign service rate of 5 cars per minute (0.083 car per second)?