Problem description The problem at hand relates to a waiting time management of queues in a typical bank. In a bid to improve the level of service at the tellers, a bank manager seeks to find strategies to employ for better service offering that will improve customer satisfaction. The manager is prepared to employ up to 5 cashiers, but not less than 1. The main management objectives are (i) To have a average customer to wait less than 2 minutes for service, and (ii) the average length of the queue (waiting line) to be 2 persons or fewer. The manager tests several models to help in the decision process. Model 1 Suppose the manager makes the following assumptions: The distribution of the length of time it takes the cashiers to carry out a service is exponential, with mean 2 minutes and standard deviation of 1.25 minutes; There is no limit to the queue length during business hours as the bank has a large floor area; Customers arrive is a Poisson distribution, with mean of 25 per hour Service is done on a first come first serve basis. Model 2 Suppose the manager uses empirical data collected from past observations, from which it is esti- mated that the bank serves 150 customers per day, and existing arrival and service times are as given in the tables below: Interarrival time (minutes) Probability 0 1 2 3 4 5 Table 1: Interarrival times 0.10 0.15 0.10 0.35 0.25 0.05 Service Time Probability 1 0.25 2 0.20 3 0.40 4 0.15 Table 2: Service times Model 3 Suppose management needs to adjust the service strategies in order to comply to the Covid 19. restrictions imposed for the use of public space. A typical requirement that banks needed to imple- ment was to have a limited number of customers within the service area and provide limited sitting outside the service area. Question 1 Describe the problem using the terminology of continuous time stochastic processes used in the study of this module, stating the processes and their distributions underlying the modelling. Your Assignment As a consultant you want to model the different scenarios so that you can make recommenda- tions to management, stating the criteria used and findings for your recommendations. To meet management expectation, you decide to base your decision analysis one the questions below. Question 2 How many tellers should be employed to meet the management objectives, based on the arrival and service patterns assumed in Model 1? Question 3 Is the customer service level in Model 2 satisfactory according to the manager guidelines/objectives? If not, determine (through modelling), the minimal changes for tellers required to accomplish the manager's goal. Question 4 In Model 3, do the Covid 19 restrictions require change in any of the assumptions made in Model: 1? With justification, you want to analyse the new scenario of Model 3 and determine how manage- ment should adjust their service level strategy to comply with the restrictions while meeting their objectives.