Question

A small store has a single phone line. Calls to the store are well modeled by an M / M /1 retrial queue with arrival rate ʎ = 10 per hour, service rate µ = 15 per hour, and retrial rate   β= 6 per hour.

(a) What is the average length of time for a customer to reach a clerk at the store?

(b) What is the average rate that call attempts are made to the store?

(Call attempts include calls that are answered and calls that receive a busy signal.) (c) What is the fraction of call attempts that receive a busy signal? (d) Suppose that you are measuring call attempts to the store and you are not aware that some customers are making redial attempts. That is, you assume each call attempt is from a distinct customer. You decide to model the system as an M/M/l/l queue, where the arrival rate is the rate of call attempts found in (b). Based on these assumptions, what is the fraction of calls that receive a busy signal? Compare this to the actual result found in (c).

Answer 1