Louisiana State University

ISDS 3115

Chapter7D

True/False

1)Waiting-line models are useful to operations in such diverse settings as service systems, maintenance activities, and shop-floor control.

2. The two characteristics of the waiting line itself are whether its length is limited or unlimited and the discipline of the people or items in it.

3. A waiting-line system has three parts: the size of the arrival population, the behavior of arrivals, and the statistical distribution of arrivals.

4. A copy center has five machines that serve many customers throughout the day; the waiting-line system for copy service has an infinite population while the waiting-line system for copier maintenance has a finite population

5. In queuing problems, arrival rates are generally described by the normal probability distribution.

6. Balk and renege are elements of queue discipline.

7. A hospital emergency room always follows a first-in, first-served queue discipline in the interest of fairness.

8. In queuing problems, the term “renege” refers to the fact that some customers leave the queue before service is completed.

9. A waiting-line system with one waiting line and three sequential processing stages is a multi- channel single-phase system.

10. If the service time within a queuing system is constant, the service rate can be easily described by a negative exponential distribution.

11. The cost of waiting decreases as the service level increases.

12. LIFS (last-in, first-served) is a common queue discipline, most often seen where people, not objects, form the waiting line.

13. A bank office with five tellers, each with a separate line of customers, exhibits the characteristics of a multi-phase queuing system.

14. In the analysis of queuing models, the Poisson distribution often describes arrival rates and service times are often described by the negative exponential distribution.

15. The study of waiting lines calculates the cost of providing good service but does not value the cost of customers' waiting time.

16. As the average service rate μ grows larger, the slope of the distribution of service time probabilities grows larger and larger, eventually becoming positive.

17. Four of the most widely used waiting line models—M/M/1 or A, M/M/S or B, M/D/1 or C, and Limited population or D—all share three characteristics: Poisson arrivals, FIFO discipline, and exponential service times.

18. In the M/M/1 waiting line model with an arrival rate of 2 per hour and a service rate of 6 per hour, the utilization factor for the system is approximately 0.333.

19. The greater the margin by which the arrival rate exceeds the service rate, the better the performance of the waiting line.

20. An M/M/1 model and an M/D/1 model each have an arrival rate of 1 per minute and a service rate of 3 per minute; the average queue length of the M/M/1 will be twice that of the M/D/1.

21. A finite population waiting line model has an average service time T of 100 minutes and an average time between service requirements U of 400 minutes; the service factor X is 0.25.

Multiple Choice

22. Study of waiting-line models helps operations managers better understand
    1. service systems such as bank teller stations
    2. maintenance activities that might repair broken machinery
    3. shop-floor control activities
    4. service systems such as amusement park rides
    5. all of the above

23. Which of the following is not a common queuing situation?
    1. grocery shoppers being served by checkout clerks
    2. commuters slowing or stopping at toll plazas to pay highway tolls
    3. machinery waiting to be repaired or maintained
    4. parcel delivery truck following its computer-generated route
    5. patients in a health clinic waiting to see one of several doctors

24. In queuing problems, which of the following probability distributions is typically used to describe the number of arrivals per unit of time?
    1. binomial
    2. normal

1. 3. Poisson
   4. exponential
   5. lognormal

25. In queuing problems, which of the following probability distributions is typically used to describe the time to perform the service?
    1. binomial
    2. normal
    3. Poisson
    4. negative exponential
    5. lognormal

26. The common measures of a queuing system's performance include
    1. probability that the service facility will be idle, average queue length, probability that the waiting time will exceed a specified duration
    2. average time each customer spends in the system, probability that the service system will be idle, average time each customer spends in the queue
    3. average queue length, maximum time a customer may spend in the queue, the utilization factor for the system
    4. average time each customer spends in the system, maximum queue length, probability of a specific number of customers in the system
    5. none of the above

27. The shopper who says to himself, “I’ve waited too long in this line. I don’t really need to buy this product today,” and leaves the store is an illustration of which element of arrival behavior?
    1. random arrival
    2. renege
    3. random departure
    4. balk
    5. none of the above

28. A waiting line, or queuing, system has three parts, which are
    1. distribution of arrival times, discipline while waiting, and distribution of service times
    2. arrival rate, service rate, and utilization rate
    3. arrival discipline, queue discipline, and service sequencing
    4. arrival or inputs, queue discipline or the waiting line itself, and the service facility
    5. sequencing policy, penalty for reneging, and expediting of arrivals

29. The source population is considered to be either                              in its size.
    1. finite or infinite
    2. fixed or variable
    3. known or unknown
    4. random or scheduled
    5. small or large

30. The potential restaurant customer who says to her husband, “The line looks too long; let's eat somewhere else,” is an illustration of which element of queue discipline?
    1. first-in, first-out
    2. balk
    3. renege
    4. random departure
    5. none of the above

31. An airline ticket counter, with several agents for one line of customers, is an example of a
    1. single channel, single phase system
    2. single channel, multi-phase system
    3. multi-channel, single phase system
    4. multi-channel, multi-phase system
    5. none of the above

32. A concert hall, employing both ticket takers and ushers to seat patrons, behaves typically as a
    1. multi-channel, single phase system
    2. multi-channel, multi-phase system
    3. single channel, single phase system
    4. single channel, multi-phase system
    5. none of the above

33. If the food service for the university operates a cafeteria with a single serving line, that system behaves most like a
    1. single channel, single phase system
    2. single channel, multi-phase system
    3. multi-channel, single phase system
    4. multi-channel, multi-phase system
    5. none of the above

34. The sign at the bank that reads “Wait here for the first available teller” suggests the use of a                                   

waiting line system.

1. 1. single phase
   2. multi-phase
   3. single channel
   4. multi-channel
   5. multiple line

35. A small hair styling salon has several operators. While customers do not have appointments, each is waiting to be served by a specific operator. This scenario provides an example of a
    1. multiple-channel, multi-phase, limited queue length
    2. single-channel, multi-phase, limited queue length
    3. multi-channel, limited queue length
    4. multiple single-channel systems, limited queue length
    5. none of the above

36. A large discount store and supermarket has a hair styling salon on its premises. The salon has several operators. Salon customers can shop in other parts of the store until their name is called for salon service, at which time the customer will be served by the next available stylist. This scenario provides an example of a
    1. multiple-channel, multi-phase, unlimited queue length
    2. single-channel, multi-phase, limited queue length
    3. multi-channel, unlimited queue length
    4. multiple single-channel systems, limited queue length
    5. none of the above

37. A university has only one technician in the repair station to care for the computers in the student

labs. This system is most likely

1. 1. a single channel, limited queue system
   2. a single channel, limited population system
   3. a multi-channel, limited queue system
   4. a multi-channel, limited population system
   5. none of the above

38. “Women and children first!” declares the captain of a sinking ship. His directive employs which of the following queue disciplines in disembarking passengers?
    1. priority
    2. random
    3. FIFO or FIFS
    4. LIFO or LIFS
    5. none of the above

39. A university has several technicians in the repair station to care for the computers in the student labs. This system is most likely
    1. single channel, limited queue system
    2. single channel, limited population system
    3. multi-channel, limited queue system
    4. multi-channel, limited population system
    5. none of the above

40. A system in which the customer receives service from only one station and then exits the system is
    1. a single-phase system
    2. a single channel system
    3. a multiple-channel system
    4. a multiple-phase system
    5. none of the above

41. In a repetitive focus factory, the number of phases found in the system might refer to
    1. the number of successive operations that have to be performed on a part
    2. the number of machines doing the same necessary operations
    3. the number of parts waiting to be processed
    4. all of the above depending on the layout
    5. none of the above

42. Which of the following is a measure of queue performance?
    1. utilization factor
    2. average queue length
    3. probability of a specific number of customers in the system
    4. average waiting time in the line
    5. all of the above

43. Which of the following is most likely to be served in a last-in, first-served (LIFS) queue discipline?
    1. customers checking out at a grocery store
    2. the in-basket on a manager's desk
    3. patients entering a hospital emergency room
    4. patrons waiting to be seated in a casual-dining restaurant
    5. all of the above

44. In a repetitive focus factory, the number of channels available for the processing of a certain part would likely refer to
    1. the number of successive operations that have to be performed on that part
    2. the number of machines doing the same necessary operations
    3. the number of parts waiting to be processed
    4. all of the above depending on the layout
    5. none of the above

45. A waiting line meeting the assumptions of M/M/1 has average time between arrivals of 20 minutes and services items in an average of 10 minutes each; the utilization factor is approximately

a. 0.25

b. 0.33

c. 0.50

d. 0.67

e. 3.00

46. A waiting line model meeting the assumptions of M/M/1 has an arrival rate of 2 per hour and a service rate of 6 per hour; the utilization factor for the system is approximately

a. 0.25

b. 0.33

c. 0.50

d. 0.67

e. 3.00

47. As the average service rate μ increases, the shape of the negative exponential distribution of service times
    1. grows steadily steeper without limit
    2. has an ever steeper slope that eventually turns positive
    3. becomes less gently curved as it moves ever closer to the graph origin
    4. takes on a more uniform slope over a wide range of service times
    5. changes in appearance from convex to concave

48. Which one of the following is not a characteristic of a Model A or M/M/1 system?
    1. exponential service time pattern
    2. single number of channels
    3. single number of phases
    4. Poisson arrival rate pattern
    5. limited population size

49. Which one of the following is not  a characteristic of a Model B or M/M/S system?
    1. unlimited population size
    2. single channel
    3. single queue
    4. single phase
    5. Poisson arrival rate pattern

50. Which one of the following is not a characteristic of a Model C or M/D/1 system?
    1. single channel
    2. single phase

1. 3. Poisson arrival rate pattern
   4. exponential service time pattern
   5. unlimited population size

51. In the basic queuing model (M/M/1), service times are described by
    1. continuous probability distributions
    2. negative exponential probability distributions
    3. Poisson probability distributions
    4. normal probability distributions
    5. lognormal distributions

52. In the basic queuing model (M/M/1), arrival rates are distributed by
    1. continuous probability distributions
    2. normal probability distributions
    3. negative exponential probability distributions
    4. Poisson distributions
    5. lognormal distributions

53. A single-phase waiting-line system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 10 minutes on average. Service takes a constant 4 minutes. The average length of the queue Lq is

a. 0.4

b. 0.133

c. 4.167

d. 4.583

e. 6

54. Which of the following is not an assumption of the M/M/1 model?
    1. The first customers to arrive are the first customers served.
    2. Each arrival comes independently of the arrival immediately before and after that arrival.
    3. The population from which the arrivals come is very large or infinite in size.
    4. Customers do not renege.
    5. Service times occur according to a normal curve.

55. A single-phase waiting-line system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 12 minutes on average. Service takes a constant 8 minutes. The average length of the queue Lq is approximately

a. 0.67

b. 2.5

c. 4.5

d. 5.0

e. 7.5

56. A single-phase waiting-line system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 12 minutes on average. Service takes a constant 8 minutes. The average number in the system Ls is approximately

a. 2.25

b. 2.5

c. 3.0

d. 1.33

e. 5.0

57. A queuing model which follows the M/M/1 assumptions has λ = 2 and μ = 3. The average number in the system is

a. 2/3

b. 1

c. 1.5

d. 2

e. 6

58. A queuing model which follows the M/M/1 assumptions has λ = 3 and μ = 2. The average number in the system is
    1. -3
    2. 3

c. 0.667

d. 150 percent

e. growing without limit, since λ is larger than μ.

59. Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow

the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the average service time for this problem?

1. 1. 1 minute
   2. 2 minutes
   3. 3 minutes
   4. 5 minutes
   5. 20 minutes

60. A queuing model which follows the M/M/1 assumptions has λ = 10 and μ = 12. The average number in the system is

a. 0.83

b. 2

c. 2.5

d. 5

e. 6

61. A queuing model which follows the M/M/1 assumptions has λ = 2 and μ = 8. The average number in the system Ls is                      and the utilization of the system is                         .
    1. 3; 100 percent
    2. 0.33; 25 percent
    3. 4; 33 percent
    4. 6; 25 percent
    5. 4; 25 percent

62. Four of the most widely used waiting line models—M/M/1 or A, M/M/S or B, M/D/1 or C, and Limited population or D—all share three characteristics, which are
    1. normal arrivals, FIFO discipline, and normal service times
    2. Poisson arrivals, FIFO discipline, and a single-service phase
    3. Poisson arrivals, FIFO discipline, and exponential service times
    4. Poisson arrivals, no queue discipline, and exponential service times
    5. none of these

63. A queuing model which follows the M/M/1 assumptions has λ = 2 and μ = 3. The average waiting time in the system is

a. 2/3

b. 1

c. 1.5

d. 2

e. 6

64. Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow

the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the utilization factor?

a. 20%

b. 30%

c. 40%

d. 50%

e. 60%

65. A finite population waiting line model has an average service time T of 100 minutes and an average time between service requirements U of 400 minutes; the service factor X is

a. 0.20

b. 0.25

3. 4
4. 5
5. 300 minutes

66. A finite population waiting line model has an average service time T of 200 minutes and an average time between service requirements U of 300 minutes; the service factor X is

a. 0.20

b. 0.40

c. 0.60

d. 0.67

e. 2.5

67. Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow

the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. A student has just entered the system. How long is she expected to stay in the system?

1. 1. 0.125 minute
   2. 0.9 minute
   3. 1.5 minutes
   4. 7.5 minutes
   5. 0.075 hour

68. Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow

the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. How many students, on the average, will be waiting in line at any one time?