Queuing Theory:

Exercise 11.6.3 A bank manager observes that when all three of his tellers are busy and the line of customers waiting to reach a teller reaches six, further arriving customers give this line one glance and promptly leave, thinking of coming back some other time or even changing banks in frustration. Assuming that the arrival process of bank customers is such that a potential customer enters the bank every 90 seconds and the time to serve a customer averages five minutes, is the bank manager better off by hiring another teller, or by means of incentives, persuading his three tellers to work about 20% faster so that the time to serve each customer is reduced to four minutes? You may assume that the arrival process of customers is Poisson, that the service time distribution is exponential, and that only one of the two options is available to the manager. The main criterion for choosing one option over the other should be to minimize the probability of customers leaving because the line is too long. You should also consider waiting time as a secondary criterion. Exercise 11.6.3 A bank manager observes that when all three of his tellers are busy and the line of customers waiting to reach a teller reaches six, further arriving customers give this line one glance and promptly leave, thinking of coming back some other time or even changing banks in frustration. Assuming that the arrival process of bank customers is such that a potential customer enters the bank every 90 seconds and the time to serve a customer averages five minutes, is the bank manager better off by hiring another teller, or by means of incentives, persuading his three tellers to work about 20% faster so that the time to serve each customer is reduced to four minutes? You may assume that the arrival process of customers is Poisson, that the service time distribution is exponential, and that only one of the two options is available to the manager. The main criterion for choosing one option over the other should be to minimize the probability of customers leaving because the line is too long. You should also consider waiting time as a secondary criterion