An average of 50 customers per hour arrive at a small post office. Interarrival times are exponentially distributed. Each employee can serve a customer in 2.4 minutes on the average. Service times are exponentially distributed.
a. Assume that there are 3 employees with a single line in front of them. How long a customer waits in the queue and in the system? What is the number of customers in the queue? What is the utilization in the system? (Use $P(L \ge 3) = 0.45$, 4 performance measures are asked)
b. Assume that it costs $25 per hour for each employee, and the post office values the time a customer spends waiting in line (not in the system) at $15 per customer-hour. What is the cost of the system per hour?
c. Now assume that the service time is a general distribution with standard deviation of service time=1.5 minute. (Same average service time as the one above). Find the same performance measures you found in a, approximately.
d. What is the minimum number of servers for this system to be stable in the long-run?