1. A local radio call-in show has about 15 calls arrive each hour, and the radio host spends about 3 minutes per caller, exponentially distributed. Assume no commercials and callers are immediately taken on the air if there is one waiting; all other appropriate assumptions also hold. Also assume that there is an infinite line possible, that is, callers will not get a busy signal but will always be put into a line to go on the air.
a. What is the average number of callers waiting to go on the air?
b. What is the average time to wait before going on the air?
c. What is the utilization?
2. An airline ticket counter has one line feeding into 2 ticket agents. The airline is considering adding a third agent. Arrivals are spaced at an average of 4 minutes, Poisson distribution. An agent spends about 5 minutes per customer, exponentially distributed. All other appropriate assumptions hold.
a. What is the average number in line waiting for service?
b. What is the average wait time in line waiting for service?
c. If a third agent is added, what is the average number in line waiting for service?
d. If a third agent is added, what is the average wait time in line waiting for service?