ABC Bank faces a decision to hire two clerks or lease two automatic teller machines. Service rates of clerk 1 and clerk 2 are 41 customers per hour and 36 customers per hour respectively. Service rates of the machines are the same and equal to 35 customers per hour. The service distribution of the clerks is Poisson and the service distribution of the machines is constant. If the cost of a telling machine if 30% higher than the cost of the clerks, the manager of the bank wants to know which alternative will have a higher service level, that is, lower customer average waiting time, and which alternative will be most economical for the following cases:
(a) The customers arrive at the Bank Poisson distributed with a mean of 45 per hour. Dispatching is FIFO.
(b) The customers' average interarrival time is 1.33 min, normally distributed with standard deviation of 6 seconds.
(c) Using the appropriate queuing formula, analyse the problem for case (a). (Simulate up to 100 min. The queue length limit is 10).