G H A E Example 7-1 Single-channel - 2 Drive through window in a bank 3 + Model: 5 Rate of arrival 15 per hr a line: 6 Service rate 20 per hr system: 7 8 average utilization of the teller 9 + 10 Lq=1/H(-) avarage no in waiting line in line includes serving time 11 12 Ls=N/(-A) average no in the system 13 14 15 16 Wq=19/1 average waiting time in line WsLSA average waiting time in system 17 18 Example Multiple channel No of servers Parts clerk fills a request while the mechanic works Mechanics arrive at a rate of 40 per hour (Poisson) Clerks Bill requests at the rate of 20 per hour Poisson distribution Rate of arrival 40 per hr X Service rate 20 per hr 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 i 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 mechanic add another clerk La Expected no of mechanics waiting Cost of waiting for s-3) Use S 4 Use Table Exhibit 7.12 LG Expected no of mechanics waiting Cost of waiting for s-4) Time saved in dollars (Difference of cost of walting) Cost of the additional clerk Cost reduction by adding the 4th clerk mechanic hence, 4 clerks Z AA AB AC AD Problem 3: AE AF AG To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on average, 10 persons per hour request a test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of five minutes each. Assume the queue length can be infinite with FCFS discipline. Model: Rate of arrival Service rate 10 per hr 12 per hr CONSTANT Lq=X/24(1 avarage no in waiting line customers Ls+La+Ni average no in the system customers Wq 19/1 average walting time in line hour 0 minutes Ws=Ls/ average waiting time in system hour 18 minutes