Refer to the supply room example in the chapter when no automation is used. Suppose that the service rate can be raised to 35 customers per hour by sending the clerk to special training. This results in a salary increase for the clerk, bringing the cost to $6 per hour. Suppose further that each unproductive employee now costs $8 per hour. Determine the average hourly queuing system cost.

A SUPPLY ROOM EXAMPLE Consider the queuing system involved in the operation of a central supply room for a large office. Employees pick up needed supplies there, just like cus- tomers who make purchases at a stationery store. An average of 25 employee customers withdraw supplies during each hdur of normal operation. A full-time clerk is required to check persons out of central supply, primarily to assure proper accounting control of requisitioned items. Each requisition takes an av- erage of 2 minutes, so the clerk may check out 30 customers per hour. We will assume that the pattern of arrivals at the checkout counter is a close approxima- tion to a Poisson process and that the checkout times are exponentially distrib- uted. Thus, = 25 customers per hour = 30 customers per hour The mean number of customers either waiting in line or being checked out is L= 25 = 5 customers 30-25 H-2 and the mean time spent by customers in the system is 1 1 W= 1 30 - 25 hour 5 u- or 12 minutes, which could also have been calculated W = L/X = 5/25 = 1/5. The mean qumber of customers in the waiting line (or its length) is = 22 (-) 25 = 45 customers 4 (25) 30(30 -25) and the mean customer waiting time is 25 1 wa hour ucu-1) 30(30 25) or 10 minutes, which could also have been calculated W, = L /1 = (25/6) 25 = 1/6. The server utilization factor is 5 a = = 25 30 .so that the supply room clerk is busy five-sixths of the time