A call center has 24 phone lines and 3 customer service representatives.
Suppose that calls arrive to the center according to a Poisson process with rate ? = 15 per hour. The time to process each call is exponential with a mean of 10 minutes. If all of the service representatives are busy, an arriving customer is placed on hold, but ties up on the phone lines. If all of the phone lines are tied up, the customer receives a busy signal and the call is lost.
(a) What is the average time that a customer spends on hold?
(b) What is the average number of lines busy at one time?
(c) Suppose that you pay $0.03 per minute for each call to your center (including the time on hold). Also, the cost for each lost call is estimated at $20. Fixing the number of service representatives, what is the optimal number of phone lines you should have?