A bank wishes to decide how many staff to schedule during its lunch period. During this period customers arrive at a rate of 6 per hour and the enquiries that customers have (such as opening new accounts, arranging loans, etc.) take on average 20 minutes to deal with. The bank manager feels that 3 staff should be on duty during this period but wants to make sure that the customers do not wait more than 3 minutes on average before they are served.
The manager has been told by his small daughter that the distributions that describe both arrival and processing times are likely to be exponential. Therefore:
5.1
Calculate the utilization of the system where u = ra/ (re x m).
(6)
5.2
Using the formula for waiting time for an M/M/ m system, calculate the average waiting time.
(14)
