Question 4 When customers of the Trojan Bank believe a mistake has been made on their account statements, their claims are forwarded to the banks 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? 0.84 (b) In a week, how many days is a clerk idle? 0.8 day (c) How long (in days) does a customer have to wait on average to hear back from the bank? 7.5 days (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? 5.25 customers in each district are waiting to hear back. 15.75 customers are waiting to hear back 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 the processing time for any clerk is exponentially distributed. (e) What is the utilization of the bank clerks?