For the multiteller bank model of Sec. 2.6, suppose that we want to know the maximum number of customers who are ever waiting in the queues. Do the following parts in order, i.e., with each part building on the previous ones.
(a) Explain why this cannot be obtained by adding up the maxima of the individual queues.
(b) Modify the program to collect this statistic, and write it out. Run for each of the cases of n = 4, 5, 6, and 7 tellers.
(c) Add to this an additional output measure, being the utilization of the servers. Since there are multiple servers, the utilization is defined here as the time-average number of servers busy, divided by the number of servers. Note that this will be a number between 0 and 1.
(d) Now suppose that the bank’s lobby is large enough to hold only 25 customers in the queues (total). If a customer arrives to find that there are already a total of 25 customers in the queues, he or she just goes away and the business is lost; this is called balking and is clearly unfortunate. Change the program to reflect balking, where the capacity of 25 should be read in as an input parameter. In addition to all the other output measures, observe the number of customers who balk during the course of the simulation.
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