Suppose that pedestrians individually (i. e., no groups) arrive to a group of doors according to a deterministic rate of 40 people per minute for the first two minutes; a deterministic rate of 60 people per minute for the next six minutes; and a deterministic rate of 20 people per minute for the following five minutes. After that, there are no arrivals. You may treat this as a D/D/1 queuing system, no matter how many doors are open. a. If only one door is open, what is the queue clearance time?
b. If only one door is open, what is the average delay?
c. What is the minimum number of doors that should be open so that there is no queue at 15 minutes?