Reference no: EM132813510

When customers of the Trojan Bank believe a mistake has been made on their account statements, their claims are forwarded to the bank's research department, whose trained clerks carefully research and document the transactions in question. Upon completing her investigation, a clerk phones the customer with her findings. The research department has three clerks. Each handles claims from a separate geographic district and never works on claims from outside her own district. The average number of complaints arising from each district is the same, 3.5 per week. The clerks are equally experienced and completely process the average claim in 1.2 days. The inter-arrival times from each district are exponentially distributed, and the processing time for any clerk is exponentially distributed. Assume a five- day week.

(a) What is the utilization of each bank clerk? (Show your work.)

(b) In a week, how many days is a clerk idle? (Show your work.)

(c) How long (in days) does a customer have to wait on average to hear back from the bank? (Show your work.)

(d) How many customers are waiting to hear back from the bank on average in each district? How many customers are waiting to hear back from the bank in all three districts? (Show your work.)

Suppose Trojan Bank decides to "pool" servers. Now, claims arrive at the bank at the rate of 3.5*3=10.5 claims per week, and are processed by a "pool" of 3 servers; a server process a claim from any district. As mentioned earlier, the clerks are equally experienced and completely process the average claim in 1.2 days; the inter-arrival times of claims are exponentially distributed, and that processing time for any clerk is exponentially distributed.

(e) What is the utilization of the bank clerks? (Show your work.)