A conventional tollbooth is setup on an expressway. When vehicles pass the tollbooth, all of them need to stop and pay the toll cost. On average, each vehicle needs 30 seconds to stop, make payment and depart from the tollbooth. The AM peak hour starts from 7:00 AM and ends at 8:00 AM. During the peak hour, the arrival rate is 2.5 veh/min. After that, the arrival rate is 1.5 veh/min. Solve the following problem using D/D/1 queuing model.

a. At which time-of-day the queue will be dissipated?
b. At which time-of-day is the queue the longest?
c. How many vehicles are there in the queue when the queue is the longest?
d. What is the longest waiting time? 1pt 5) What is the total waiting time?
e. What is the average waiting time of vehicles in the queue?