s T K L M N QIR S Example Multiple channel No of servers Parts clerk fills a request while the mechanic works Mechanics arrive at a rate of 40 per hour (Polsson) Clerks fill requests at the rate of 20 per hour Poisson distribution Rate of arrival 40 per hr A Service rate 20 perhe H cost of clerk $30 per hr cost of mechanic $60 per hr What is the optimum number of clerks to staff the counter? We need to reduce the cost of mechanics waiting! Determine that you need more than 2 Model: Assume 3 clerks first and work upwards Uses 3 (1 or 2 may not work)(because 1 clerk can do 20 and two can do 40 per hour but we have arrival rate at 40) Use Table Exhibit 7.12 average utilization of the customer p=N/ 2 La Expected no of mechanics waiting mechanic Cost of waiting (for s-3) add another clerk Use 5-4 Use Table Exhibit7.12 La Expected no of mechanics walting Cost of waiting for s-4) mechanic Time saved in dollars (Difference of cost of waiting) Cost of the additional clerk Cost reduction by adding the 4th clerk hence, 4 clerks