chapter 12

14. When managers find standard queuing formulas inadequate or the mathematics unsolvable, they often resort to ____________ to obtain their solutions

simulation

Briefly describe three situations in which the FIFO discipline rule is not applicable in queuing analysis

First-in, first-out (FIFO) is often not applicable. Some examples 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

Why must the service rate be greater than the arrival rate in a single-channel queuing system?

If the service rate is not greater than the arrival rate, an infinite queue will eventually build up.

In a multichannel, single-phase queuing system, the arrival will pass through at least two different service facility a-true b false

false

3. The service time in the queuing model is M/M/1 assumed to be ____________.

negative exponential distributed

Provide examples of four situations in which there is a limited, or finite, population.

. 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, and (5) a hospital ward with only 20 patients who need care.

(d) small grocery store

. Small grocery store: usually a single-channel, single-server system. Arrivals = customers buying food items Waiting line = customers with carts or baskets of groceries who arrive first at the cash register; sometimes not FIFO; grocer may care for regular customers first or give priority to person making a small, quick, purchase Service = ringing up sale on cash register, collecting money, and bagging groceries

Give an example of a situation in which the waiting time cost would be based on waiting time in the queue. Give an example of a situation in which the waiting time cost would be based on waiting time in the system.

. The waiting time cost should be based on time in the queue in situations where the customer does not mind how long it takes to complete service once the service starts. The classic example of this is waiting in line for an amusement park ride. Waiting time cost should be based on the time in the system when the entire time is important to the customer. When a computer or an automobile is taken into the shop to be repaired, the customer is without use of the item until the service is finished. In such a situation, the time in the system is the relevant time

. Describe the important operating characteristics of a queuing system.

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 (p) 6. Percent idle time (Po) 7. Probability there are more than k customers in the system

What are the assumptions underlying common queuing models?

The seven 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. Service times are negative exponential. 7. Average service rate exceeds average arrival rate

Do you think the Poisson distribution, which assumes independent arrivals, is a good estimation of arrival rates in the following queuing systems? Defend your position in each case. (a) cafeteria in your school (b) barbershop (c) hardware store (d) dentist's office (e) college class (f) movie theater

The use of Poisson to describe arrivals: a. Cafeteria: probably not. Most people arrive in groups and eat at the same time. b. Barbershop: probably acceptable, especially on a weekend, in which case people arrive at the same rate all day long. c. Hardware store: okay. d. Dentist's office: usually not. Patients are most likely scheduled at 15- to 30-minute intervals and do not arrive randomly. e. College class: probably not. Number of students come in groups at the beginning of class period; very few arrive during the class or very early before class. f. Movie theater: probably not if only one movie is shown (if there are four or more auditoriums each playing a different movie simultaneously, it may be okay). Patrons all tend to arrive in batches 5 to 20 minutes before a show

What is the waiting line problem? What are the components in a waiting line system?

The waiting line 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

1. Most systems use the queue discipline known as the FIFO rule. a. True b. False

True

A company has one computer technician who is responsible for repairs on the company's 20 computers. As a computer breaks, the technician is called to make the repair. If the repairperson is busy, the machine must wait to be repaired. This is an example of a. a multichannel system. b. a finite population system. c. a constant service rate system. d. a multiphase system

a finite population system.

Cars enter the drive-through of a fast-food restaurant to place an order, and then they proceed to pay for the food and pick up the order. This is an example of a. a multichannel system. b. a multiphase system. c. a multiqueue system. d. none of the above

a multiphase system

What are the components of the following systems? Draw and explain the configuration of each. (a) barbershop

a. Barbershop: usually a single-channel, multiple-service 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 = haircut, style, shampoo, and so forth; if service involves barber, then shampooist, then manicurist, it becomes a multiphase system

2. Before using exponential distributions to build queuing models, the quantitative analyst should determine if the service time data fit the distribution. a. True b. False

a. True

(b) car wash

b. Car wash: usually either a single-channel, 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

c. Laundromat: basically a single-channel, multiserver, two-phase system. Arrivals = customers with dirty clothes Waiting line = usually first-come, first-served in terms of selecting an available machine Service = first phase consists of washing clothes in washing machines; second-phase is again queuing for the first available drying machine

5. A queuing system described as M/D/2 would have a. exponential service times. b. two queues. c. constant service times. d. constant arrival rates

c. constant service times.

Customers enter the waiting line at a cafeteria on a first come, first-served basis. The arrival rate follows a Poisson distribution, and service times follow an exponential distribution. If the average number of arrivals is 6 per minute and the average service rate of a single server is10 per minute, what is the average number of customers in the system? a.0.6 b.0.9 c.1.5 d.0.25

c.1.5

In performing a cost analysis of a queuing system, the waiting time cost (Cw)is sometimes based on the time in the queue and sometimes based on the time in the system. The waiting cost should be based on time in the system for which of the following situations? a. waiting in line to ride an amusement park ride b. waiting to discuss a medical problem with a doctor c. waiting for a picture and an autograph from a rock star d. waiting for a computer to be fixed so it can be placed back in service

d. waiting for a computer to be fixed so it can be placed back in service

Which of the following is not an assumption in M/M/I models? a. arrivals come from an infinite or very large population b. arrivals are Poisson distributed c. arrivals are treated on a FIFO basis and do not balk or renege d. service times follow the exponential distribution e.renege d. service times follow the exponential distribution e. the average arrival rate is faster than the average service

e. the average arrival rate is faster than the average service

Which of the following would not have a FIFO queue discipline? a. fast-food restaurant b. post office c. checkout line at grocery store d. emergency room at a hospital

emergency room at a hospital

12. In the standard queuing model, we assume that the queue discipline is ____________

first come, first serves

The utilization factor for a system is defined as a. mean number of people served divided by the mean number of arrivals per time period. b. the average time a customer spends waiting in a queue. c. proportion of the time the service facilities are in use. d. the percentage of idle time. e. none of the above

proportion of the time the service facilities are in use