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Unformatted text preview: CHAPTER 9 QUEUEING MODELS SOLUTIONS TO DISCUSSION QUESTIONS 9-1. The queuing problem concerns the question of finding the ideal level of service that an organization should provide. The three components of a queuing system are arrivals, waiting line, and service facility. 9-2. The underlying assumptions are: 1. Arrivals are FIFO. 2. There is no balking or reneging. 3. Arrivals are independent. 4. Arrivals are Poisson. 5. Service times are independent. 6. Average service rate exceeds average arrival rate. 9-3. The seven operating characteristics are: 1. Average number of customers in the system ( L ) 2. Average time spent in the system ( W ) 3. Average number in the queue ( Lq ) 4. Average time in the queue ( Wq ) 5. Utilization factor (ρ) 6. Percent idle time ( P o) 7. Probability there are exactly n customers in the system ( Pn ) 9-4. If the service rate is not greater than the arrival rate (that is, μ < λ), an infinite queue will eventually build up. 9-5. First-in, first-out (FIFO) is often not applicable. Some example are (1) hospital emergency rooms, (2) an elevator, (3) an airplane trip, (4) a small store where the shopkeeper serves whoever can get his or her attention first, (5) a computer system set to accept priority runs, (6) a college registration system that allows juniors and seniors to register ahead of freshmen and sophomores, (7) a restaurant that may seat a party of 2 before a party of 4 even though the latter group arrived earlier, (8) a garage that repairs cars with minor problems before it works on major overhauls. 9-6. Examples of finite queuing situations include (1) a firm that has only 3 or 4 machines that need servicing, (2) a small airport at which only 10 or 15 flights land each day, (3) a classroom that seats only 30 students for class, (4) a physician who has a limited number of patients, (5) a hospital ward with only 20 patients who need care, and (6) a restaurant that can serve only 15 tables per seating and takes no more reservations beyond that number. 9-7. (a) Barbershop: usually a multiple-server system (if there is more than one barber). Arrivals Customers wanting haircuts Waiting line Seated customers who informally recognize who arrived first among them Service Shampoo, haircut, style, and so forth; if service involves shampooist, then barber, then manicurist, it becomes a multiphase system (b) Car wash: usually either a single-server system, or else a system with each service bay having its own queue. Arrivals Dirty cars or trucks Waiting time Cars in one line (or more lines if there are service parallel wash systems); always FIFO Service Either multiphase (if car first vacuumed, then soaped, then sent through automatic cleaner, then dried by hand) or single-phase if all automatic or performed by one person (c) Laundromat: basically a multi-server, two-phase system....
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- Spring '10