In Example 6.18, suppose that the overall arrival rate is expected to increase to 160 per hour. If the service rates do not change, how many clerks will be needed at service centers 2 and 3, just to keep up with the customer load?

Example 6.18 Consider again the discount store described in Example 6.1 and shown in Figure 6.3. Suppose that customers arrive at the rate of 80 per hour and that, of those arrivals, 40% choose self-service; then, the arrival rate to service center 1 is a1 = (80)(0.40) = 32 per hour, and the arrival rate to service center 2 is 12 = (80)(0.6) = 48 per hour. Suppose that each of the c2 = 3 clerks at service center 2 works at the rate u2 = 20 customers per hour. Then the long-run utilization of the clerks is 48 P2 = = 0.8 (3)(20) All customers must see the cashier at service center 3. The overall arrival rate to service center 3 is a3 = a1 + a2 = 80 per hour, regardless of the service rate at service center 1, because, over the long run, the departure rate out of each service center must be equal to the arrival rate into it. If the cashier works at rate uz = 90 per hour, then the utilization of the cashier is 80 P3 = = 0.89 90