The issue of waiting time has been a persistent concern at ServiceOntario. Edward, the chair of the investigation, wants to reconfigure the clerks at the Yonge St. branch such that the wait time is shortened for the hour 12-1pm. He has managed to collect data on services times and customer arrival patterns to explore the following options:

Plan A: Prepare for one waiting line area, keep 5 clerks at work and the first visitor in line goes to the next available clerk.

Plan B: Prepare for two waiting line areas where 1 clerk and one line are devoted to easy visitors who can be served at a faster pace and the other 4 clerks are assigned to handle difficulty visitors in the other line.

According to the records, 80 visitors on average arrive during the hour. 60% of arriving visitors are in the difficult group while the other 40% belongs to the easy group. The average service time for easy visitors is 90 seconds, while each of the difficult visitors requires 4 minutes to serve. Assume the arrival rate of visitors follows a Poisson distribution, and the processing time is exponentially distributed.

Part a) What is the average queue length and waiting time for plan A? On average, how many people are in the bank branch during peak hour service?

Part b) What are the average queue length and wait times for each of the lines in plan B? Using plan B, on average, how many people are in the branch during the hour?

Part c) When Edward sends head office the monthly TPS (Testing Procedure Specification) report, what should he put as the average wait time for a customer when using option B? Which option (A or B) should Edward promote and why?

Part d) Edward is not convinced of the results of the analysis and decides to do a one-year trial. For the first half of the year, he will implement option A and examine the results. For the second half of the year, he will implement option B and examine the results.

What wait time should Edward expect for the Yonge St. Branch over the entire one year?

For the trial period, how many people are in the branch during the service hour 12-1pm on average?