National Bank is considering opening a teller window for customer service. Management estimates that customers will arrive for service at the rate of 15 per hour. The teller whom it is considering to staff the window can service customers at the rate of one every three minutes. Because of limited space availability and a desire to provide an acceptable level of service, the bank manager would like to assure, with 95 per cent confidence, that not more than three customers will be in the system at any one time. Assume Poisson arrivals and exponential service, compute (i) utilization of the teller, (ii) average number in the waiting line, (iii) average number in the system, (iv) average waiting time in line, (v) average waiting time in the system.
What is the present level of service for the three person limit? What level of utilization of the teller must be attained and what must be the service rate of the teller to assure the 95 per cent level of service?