A bank needs to choose how many tellers to hire. Customers arrive to the bank as

Question

A bank needs to choose how many tellers to hire. Customers arrive to
the bank as a Poisson process with rate 60 per hour, and service times
are exponential with rate 10 per hour. Tellers are paid $20 per hour,
and it is determined that each minute a customer waits in the queue is
worth $10 in bad publicity. Assume the queue is M/M/N, where N is
the number of tellers.

(a) Find E(WN), the average waiting time (not including service time for N = 7, 8, 9, ... What happens if N 6?

(b) Formulate the optimization function, i.e., what is the bank's cost per hour when there are N tellers?

(c) Find N that minimizes the bank's average cost per hour.

Explanation / Answer

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