Test Bank | Module D Waiting-Line Models – 10e Global

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Operations Management, 10e, Global Edition (Heizer/Render)

Module D Waiting-Line Models

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

Diff: 1

Topic: Queuing theory

Objective: no LO

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.

Diff: 1

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

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

Diff: 1

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

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

Diff: 1

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

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

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

6) Balk and renege are elements of queue discipline.

Diff: 1

Topic: Characteristics of a waiting-line problem

Objective: LO-Module D-1

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

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

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

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

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

Diff: 1

Topic: Characteristics of a waiting-line problem

Objective: LO-Module D-1

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

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

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

Diff: 2

Topic: Queuing costs

Objective: no LO

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

Diff: 2

Topic: Characteristics of a waiting-line problem

Objective: LO-Module D-1

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

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

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.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

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

Diff: 2

Topic: Queuing costs

Objective: no LO

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.

Diff: 1

Topic: The variety of queuing models

Objective: LO-Module D-1

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.

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-5

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.

Diff: 1

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-1

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

Diff: 1

Topic: The variety of queuing models

Objective: LO-Module D-1

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.

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-5

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.

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

22) Study of waiting-line models helps operations managers better understand

A) service systems such as bank teller stations

B) maintenance activities that might repair broken machinery

C) shop-floor control activities

D) service systems such as amusement park rides

E) all of the above

Diff: 1

Topic: Queuing theory

Objective: no LO

23) Which of the following is not a common queuing situation?

A) grocery shoppers being served by checkout clerks

B) commuters slowing or stopping at toll plazas to pay highway tolls

C) machinery waiting to be repaired or maintained

D) parcel delivery truck following its computer-generated route

E) patients in a health clinic waiting to see one of several doctors

Diff: 1

Topic: Queuing theory

Objective: no LO

24) In queuing problems, which of the following probability distributions is typically used to describe the number of arrivals per unit of time?

A) binomial

B) normal

C) Poisson

D) exponential

E) lognormal

Diff: 1

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

25) In queuing problems, which of the following probability distributions is typically used to describe the time to perform the service?

A) binomial

B) normal

C) Poisson

D) negative exponential

E) lognormal

Diff: 1

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

26) The common measures of a queuing system's performance include

A) probability that the service facility will be idle, average queue length, probability that the waiting time will exceed a specified duration

B) average time each customer spends in the system, probability that the service system will be idle, average time each customer spends in the queue

C) average queue length, maximum time a customer may spend in the queue, the utilization factor for the system

D) average time each customer spends in the system, maximum queue length, probability of a specific number of customers in the system

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

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?

A) random arrival

B) renege

C) random departure

D) balk

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

28) A waiting line, or queuing, system has three parts, which are

A) distribution of arrival times, discipline while waiting, and distribution of service times

B) arrival rate, service rate, and utilization rate

C) arrival discipline, queue discipline, and service sequencing

D) arrival or inputs, queue discipline or the waiting line itself, and the service facility

E) sequencing policy, penalty for reneging, and expediting of arrivals

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

29) The source population is considered to be either __________ in its size.

A) finite or infinite

B) fixed or variable

C) known or unknown

D) random or scheduled

E) small or large

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

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?

A) first-in, first-out

B) balk

C) renege

D) random departure

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

31) Arrivals or inputs to a waiting-line system have characteristics that include

A) population size

B) population behavior

C) population's statistical distribution

D) A and C

E) A, B, and C

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

32) Which part of a waiting line has characteristics that involve statistical distribution?

A) arrivals or inputs

B) waiting line itself

C) service Facility

D) A and C

E) A, B, and C

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

33) Which of the following is an example of a finite arrival population?

A) copy machines in a copying shop that break down

B) students at a large university registering for classes

C) shoppers arriving at a supermarket

D) cars arriving at a suburban car wash

E) all of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

34) Which of the following represents a customer that reneged due to the waiting-line?

A) A husband and wife decide to eat out instead after seeing the movie ticket line.

B) A car drives past the first fast-food restaurant on Hamburger Row because the drive-through was full.

C) A Black Friday shopper skipped one store because the line went around the building.

D) A student ordered pizza online because the phone line was busy.

E) A customer at a gas station went inside to buy a soda, but after waiting in line for a minute left the soda behind and went outside empty-handed.

Diff: 1

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

35) Which of the following represents an unlimited queue?

A) drive-through lane at a fast-food restaurant

B) small barbershop with only 5 chairs for waiting customers

C) toll booth serving automobiles on an interstate

D) faculty office with limited seating during office hours

E) restaurant with no outside seating and limited capacity due to fire department restrictions

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

36) Which of the following is most likely to violate a FIFO queue?

A) supermarket with no express lanes

B) car repair garage

C) emergency room

D) fast-food restaurant

E) All of the above are equally likely to violate a FIFO queue.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

37) A college registrar's office requires you to first visit with one of three advisors and then with one of two financial professionals. This system is best described as

A) single channel, single phase system

B) single channel, multi-phase system

C) multi-channel, single phase system

D) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

38) An airline ticket counter, with several agents for one line of customers, is an example of a

A) single channel, single phase system

B) single channel, multi-phase system

C) multi-channel, single phase system

D) multi-channel, multi-phase system

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

39) A concert hall, employing both ticket takers and ushers to seat patrons, behaves typically as a

A) multi-channel, single phase system

B) multi-channel, multi-phase system

C) single channel, single phase system

D) single channel, multi-phase system

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

40) If the food service for the university operates a cafeteria with a single serving line, that system behaves most like a

A) single channel, single phase system

B) single channel, multi-phase system

C) multi-channel, single phase system

D) multi-channel, multi-phase system

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

41) The sign at the bank that reads "Wait here for the first available teller" suggests the use of a __________ waiting line system.

A) single phase

B) multi-phase

C) single channel

D) multi-channel

E) multiple line

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

42) 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

A) multiple-channel, multi-phase, limited queue length

B) single-channel, multi-phase, limited queue length

C) multi-channel, limited queue length

D) multiple single-channel systems, limited queue length

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

43) 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

A) multiple-channel, multi-phase, unlimited queue length

B) single-channel, multi-phase, limited queue length

C) multi-channel, unlimited queue length

D) multiple single-channel systems, limited queue length

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

44) A university has only one technician in the repair station to care for the computers in the student labs. This system is most likely

A) a single channel, limited queue system

B) a single channel, limited population system

C) a multi-channel, limited queue system

D) a multi-channel, limited population system

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

45) "Women and children first!" declares the captain of a sinking ship. His directive employs which of the following queue disciplines in disembarking passengers?

A) priority

B) random

C) FIFO or FIFS

D) LIFO or LIFS

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

46) A university has several technicians in the repair station to care for the computers in the student labs. This system is most likely

A) single channel, limited queue system

B) single channel, limited population system

C) multi-channel, limited queue system

D) multi-channel, limited population system

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

47) A system in which the customer receives service from only one station and then exits the system is

A) a single-phase system

B) a single channel system

C) a multiple-channel system

D) a multiple-phase system

E) none of the above

Diff: 1

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

48) In a repetitive focus factory, the number of phases found in the system might refer to

A) the number of successive operations that have to be performed on a part

B) the number of machines doing the same necessary operations

C) the number of parts waiting to be processed

D) all of the above depending on the layout

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

49) Which of the following is a measure of queue performance?

A) utilization factor

B) average queue length

C) probability of a specific number of customers in the system

D) average waiting time in the line

E) all of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

50) Which of the following is most likely to be served in a last-in, first-served (LIFS) queue discipline?

A) customers checking out at a grocery store

B) the in-basket on a manager's desk

C) patients entering a hospital emergency room

D) patrons waiting to be seated in a casual-dining restaurant

E) all of the above

Diff: 1

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

51) In a repetitive focus factory, the number of channels available for the processing of a certain part would likely refer to

A) the number of successive operations that have to be performed on that part

B) the number of machines doing the same necessary operations

C) the number of parts waiting to be processed

D) all of the above depending on the layout

E) none of the above

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

52) Which of the following is not a measure of a queue's performance?

A) average time spent in queue

B) average queue length

C) probability that service facility will be idle

D) utilization

E) All of the above are performance measures.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

53) 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

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

54) 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

Diff: 1

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

55) As the average service rate μ increases, the shape of the negative exponential distribution of service times

A) grows steadily steeper without limit

B) has an ever steeper slope that eventually turns positive

C) becomes less gently curved as it moves ever closer to the graph origin

D) takes on a more uniform slope over a wide range of service times

E) changes in appearance from convex to concave

Diff: 1

Topic: The variety of queuing models

Objective: LO-Module D-2

56) Which one of the following is not a characteristic of a Model A or M/M/1 system?

A) exponential service time pattern

B) single number of channels

C) single number of phases

D) Poisson arrival rate pattern

E) limited population size

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-2

57) Which one of the following is not a characteristic of a Model B or M/M/S system?

A) unlimited population size

B) single channel

C) single queue

D) single phase

E) Poisson arrival rate pattern

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-3

58) Which one of the following is not a characteristic of a Model C or M/D/1 system?

A) single channel

B) single phase

C) Poisson arrival rate pattern

D) exponential service time pattern

E) unlimited population size

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-4

59) In the basic queuing model (M/M/1), service times are described by

A) continuous probability distributions

B) negative exponential probability distributions

C) Poisson probability distributions

D) normal probability distributions

E) lognormal distributions

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-2

60) In the basic queuing model (M/M/1), arrival rates are distributed by

A) continuous probability distributions

B) normal probability distributions

C) negative exponential probability distributions

D) Poisson distributions

E) lognormal distributions

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-2

61) 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

Diff: 2

Topic: Characteristics of a waiting-line system

AACSB: Analytic Skills

Objective: LO-Module D-5

62) Which of the following is not an assumption of the M/M/1 model?

A) The first customers to arrive are the first customers served.

B) Each arrival comes independently of the arrival immediately before and after that arrival.

C) The population from which the arrivals come is very large or infinite in size.

D) Customers do not renege.

E) Service times occur according to a normal curve.

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-2

63) 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

Diff: 2

Topic: Characteristics of a waiting-line system

AACSB: Analytic Skills

Objective: LO-Module D-1

64) 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

Diff: 2

Topic: Characteristics of a waiting-line system

AACSB: Analytic Skills

Objective: LO-Module D-1

65) 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

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

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

A) -3

B) 3

C) 0.667

D) 150 percent

E) growing without limit, since λ is larger than μ.

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

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. What is the average service time for this problem?

A) 1 minute

B) 2 minutes

C) 3 minutes

D) 5 minutes

E) 20 minutes

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

68) 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

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

69) 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 __________.

A) 3; 100 percent

B) 0.33; 25 percent

C) 4; 33 percent

D) 6; 25 percent

E) 4; 25 percent

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

70) 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

A) normal arrivals, FIFO discipline, and normal service times

B) Poisson arrivals, FIFO discipline, and a single-service phase

C) Poisson arrivals, FIFO discipline, and exponential service times

D) Poisson arrivals, no queue discipline, and exponential service times

E) none of these

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-2, LO-Module D-3, LO-Module D-4, LO-Module D-5

71) 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

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

72) 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%

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

73) 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

C) 4

D) 5

E) 300 minutes

Diff: 1

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-6

74) 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

Diff: 1

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-6

75) 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?

A) 0.125 minute

B) 0.9 minute

C) 1.5 minutes

D) 7.5 minutes

E) 0.075 hour

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

76) 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?

A) 0.9 students

B) 1.5 students

C) 3 students

D) 4 students

E) 36 students

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

77) A waiting-line system that meets the assumptions of M/M/S has λ = 5, μ = 4, and M = 2. For these values, Po is approximately 0.23077 and Ls is approximately 2.05128. The average time a unit spends in this system

A) is approximately 0.1603

B) is approximately 0.2083

C) is approximately 0.4103

D) is approximately 0.8013

E) cannot be calculated because is larger than

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-4

78) A waiting-line system that meets the assumptions of M/M/1 has λ = 1, μ = 4. For this system, Po is __________ and utilization is __________.

A) 0.75; 0.25

B) 0.80; .20

C) -3; -4

D) 3; 4

E) none of these

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

79) A waiting-line system that meets the assumptions of M/M/S has λ = 5, μ = 4, and M = 2. For these values, Po is approximately 0.23077 and Ls is approximately 2.05128. The average number of units waiting in the queue

A) is approximately 0.1603

B) is approximately 0.4103

C) is approximately 0.8013

D) is approximately 1.0417

E) cannot be calculated because is larger than

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-4

80) A waiting-line system that meets the assumptions of M/M/1 has λ = 1, μ = 4. For this system, the probability of more than two units in the system is approximately

A) zero

B) 0.015625

C) 0.0625

D) 0.25

E) 0.9375

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

81) A waiting-line system that meets the assumptions of M/M/1 has λ = 1, μ = 4. For this system, the probability of fewer than two units in the system is approximately

A) 0.0625

B) 0.25

C) 0.75

D) 0.9375

E) certain

Diff: 3

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

82) Little's Law is not applicable in which of the following situations?

A) the opening of a toy store on Black Friday morning

B) a 24-hour supermarket

C) a gas station with 24-hour self-service pumps

D) B and C

E) It is applicable to A, B, and C.

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-4

83) Which of the following is a requirement for application of Little's Law to be valid?

A) unlimited queue

B) limited queue

C) steady state conditions

D) single channel

E) multiple phase

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-4

84) A waiting line or __________ is where items or people are in a line awaiting service; __________ is a body of knowledge about waiting lines.

Diff: 1

Topic: Queuing theory

Objective: no LO

85) A(n) __________ is a discrete probability distribution that often describes the arrival rate in queuing theory.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

86) The __________ of a waiting line and the probability that the queue is empty add to one.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

87) A(n) __________ occurs when an arrival refuses to enter a waiting line; a(n) __________ occurs when an arrival joins a waiting line, then leaves it.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

88) A waiting line has a(n) __________ population if, as arrivals take place, the likelihood of additional arrivals is decreased.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

89) Of the three types of queue discipline, only __________ is assumed by the four primary waiting line models.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

90) A(n) __________ queuing system has one line and one server.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

91) A(n) __________ queuing system has one waiting line, but several servers; a(n) __________ queuing system is one in which the customer receives services from several stations before exiting the system

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

92) A(n) __________ queuing system is one in which the customer receives service from only one station and then exits the system.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

93) The __________ probability distribution is a continuous probability distribution often used to describe the service time in a queuing system.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

94) In a finite or limited population waiting line, the __________ is calculated from the average service time and average time between service requirements before the problem can be completed.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

95) Provide an example of a limited or finite population for a queue.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

96) What does it mean to have a patient customer in a waiting line?

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

97) What is queue discipline? State three rules for queue discipline. Which of these rules appears most frequently in the four main models?

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

98) Describe the difference between FIFO and LIFO queue disciplines.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

99) Customers take a number as they join the waiting line of the customer service counter at a discount store. There are two customer service agents. Provide the most likely characteristics of this system.

a. name of model

b. number of channels

c. number of phases

d. arrival rate distribution

e. service time distribution

f. population size

g. queue discipline

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-4

100) Students arrive randomly at the help desk of a computer lab. There is only one service agent, and the service time varies from one student to the other. Provide the most likely characteristics for this system.

a. name of model

b. number of channels

c. number of phases

d. arrival rate distribution

e. service time distribution

f. population size

g. queue discipline

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-2

101) Why does it matter whether a population of arrivals is limited or unlimited? Compose your answer in a well-organized, convincing paragraph.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

102) What are Ls and Lq, as used in waiting line terminology? Which is larger, Ls or Lq? Explain.

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

103) There is only one bay and one type of service at an automatic car wash. Provide the most likely characteristics of this system.

a. name of model

b. number of channels

c. number of phases

d. arrival rate distribution

e. service time distribution

f. population size

g. queue discipline

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-5

104) What is the waiting-line problem? Why is it important to operations?

Diff: 1

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

105) What are the components in a waiting-line system?

Diff: 1

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

106) Describe the important operating characteristics of a queuing system.

• The average time each customer or object spends in the queue

• The average length of the queue

• The average time each customer spends in the system (waiting time plus service time)

• The average number of customers in the system

• The probability that the service facility will be idle

• The utilization factor

• The probability of a specific number of customers in the system

Diff: 2

Topic: Characteristics of a waiting-line system

Objective: LO-Module D-1

107) In an earlier chapter, you were introduced to a "traditional" view of costs and a "full cost" view of costs, with respect to a certain type of analysis. How might that lesson apply here? In particular, might operations managers pay more attention to some kinds of costs than others?

Diff: 1

Topic: Queuing costs

AACSB: Reflective Thinking

Objective: no LO

108) What costs are present in waiting line analysis? How do these costs vary with the level of service?

Diff: 1

Topic: Queuing costs

Objective: no LO

109) What are the assumptions underlying the M/M/1 waiting line model? Which of these also hold for the M/D/1 model?

1. Arrivals are served on a "first come, first served" (FCFS, or FIFO) basis; and every arrival waits to be served regardless of the length of the line or queue.

2. All arrivals are independent of preceding arrivals, and the average number of arrivals per unit time (arrival rate) does not change over time.

3. Arrival rates are described by a Poisson probability distribution, and arrivals come from an infinite or very large source.

4. Service times vary from one customer to another and are independent of one another, but their average rate is known.

5. Service times are described by a negative exponential probability distribution.

6. The effective service rate is faster than the arrival rate.

Assumptions 4 and 5 do not apply to M/D/1.

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-5

110) You have seen that, in an M/D/1 problem, the average queue length is exactly one-half the average queue length of an otherwise identical M/M/1 problem. Are all other performance statistics one-half as large also? Explain.

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-2, LO-Module D-5

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

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-2

112) Most banks have changed from having a line in front of each teller to a system where one line feeds all tellers. Which system is better? Why?

Diff: 2

Topic: The variety of queuing models

Objective: LO-Module D-4

113) A waiting line meeting the M/M/1 assumptions has an arrival rate of 4 per hour and a service rate of 12 per hour. What is the probability that the waiting line is empty?

Diff: 1

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

114) A waiting line meeting the M/M/1 assumptions has an arrival rate of 4 per hour and a service rate of 12 per hour. What is the average time a unit spends in the system and the average time a unit spends waiting?

Diff: 1

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

115) A waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour. What is the average time a unit spends in the system and the average time a unit spends waiting?

Diff: 1

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

116) A waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour. What is the probability that the waiting line is empty?

Diff: 1

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

117) A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 7.5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution.

a. What is the utilization rate for this service system?

b. What is the average time before the facility can return a breakdown to service?

c. How much of that time is spent waiting for service?

d. How many vehicles are likely to be in the system at any one time?

Diff: 1

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

118) A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 7 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ= 11 vehicles per day with a repair time distribution that approximates an exponential distribution.

a. What is the utilization rate for this service system?

b. What is the average time before the facility can return a breakdown to service?

c. How much of that time is spent waiting for service?

d. How many vehicles are likely to be waiting for service at any one time?

Diff: 1

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

119) A crew of mechanics at the Highway Department garage repair vehicles which break down at an average of λ = 5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ= 10 vehicles per day with a repair time distribution that approximates an exponential distribution.

a. What is the probability that the system is empty?

b. What is the probability that there is precisely one vehicle in the system?

c. What is the probability that there is more than one vehicle in the system?

d. What is the probability of 5 or more vehicles in the system?

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

120) A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ= 11 vehicles per day with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $300 per day. The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof). What is the expected cost of this system?

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

121) A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ= 10 vehicles per day with a repair time distribution that approximates an exponential distribution.

a. What is the probability that the system is empty?

b. What is the probability that there is precisely one vehicle in the system?

c. What is the probability that there is more than one vehicle in the system?

d. What is the probability of 5 or more vehicles in the system?

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

122) A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ= 11 vehicles per day with a repair time distribution that approximates an exponential distribution. The crew cost is approximately $300 per day. The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof). Which is cheaper, the existing system with one service crew, or a revised system with two service crews?

Diff: 3

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

123) A dental clinic at which only one dentist works is open only two days a week. During those two days, the traffic is uniformly busy with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes.

a. What is the probability that the clinic is empty (except for the dentist)?

b. What percentage of the time is the dentist busy?

c. What is the average number of patients in the waiting room?

d. What is the average time a patient spends in the office (wait plus service)?

e. What is the average time a patient waits for service?

(e) Wq = 3 / 4*(4-3) = 0.75 hours.

Diff: 1

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

124) A dental clinic at which only one dentist works is open only two days a week. During those two days, the traffic arrivals follow a Poisson distribution with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes.

a. What is the probability that the clinic is empty (except for the dentist)?

b. What is the probability that there are one or more patients in the system?

c. What is the probability that there are four patients in the system?

d. What is the probability that there are four or more patients in the system?

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

125) At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machine is at the rate of 100 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour.

a. What is the utilization rate of the system?

b. What is the average number of packages waiting to be sorted?

c. What is the average number of packages in the sorting system?

d. How long must the average package wait until it gets sorted?

e. What would Lq and Wq be if the service rate were exponential, not constant?

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

126) At the order fulfillment center of a major mail-order firm, customer orders, already packaged for shipment, arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel's address. The arrival rate at the sorting machine is at the rate of 140 per hour following a Poisson distribution. The machine sorts at the constant rate of 150 per hour.

a. What is the utilization rate of the system?

b. What is the average number of packages waiting to be sorted?

c. What is the average number of packages in the sorting system?

d. How long must the average package wait until it gets sorted?

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

127) A waiting-line system that meets the assumptions of M/M/1 has = 1, = 4. Calculate Po. Build a table showing the probability of more than 0, 1, 2, 3, 4, 5, 6,and 7 units in the system. Round to six decimal places in your work

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

128) Genco, Inc., a small manufacturer of diesel-generator sets has four shearing machines. Because of the age of these machines, they need minor repairs after 30 hours of use. Analysis of previous breakdowns indicates that breakdowns follow a Poisson distribution. The facility employs one repairman specifically to repair these machines. Average repair time is two hours following an exponential distribution.

a. What is the service factor for this system?

b. What is the average number of these machines in service?

c. What is the impact of adding a second repairman?

Diff: 3

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-4

129) A finite population waiting line model with a single server has an average service time T of 200 minutes and an average time between service requirements U of 300 minutes. Calculate the service factor X. If the population consists of 5 elements, what are the average number waiting, the average number being serviced, and the average number running? Refer to Table D.8.

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-6

130) A finite population waiting line model with a single server has an average service time T of 50 minutes and an average time between service requirements U of 350 minutes. Calculate the service factor X. If the population consists of 5 elements, what are the average number waiting, the average number being serviced, and the average number running? Refer to Table D.8.

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-6

131) Suppose that a service facility has an average line of 2 customers that must wait, on average, 5 minutes for service. How many customers are arriving per hour?

X=.4 customers/minute = 24 customers arrive each hour

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

132) Suppose that a fast food restaurant wants the average line to be 4 customers and that 80 customers arrive each hours. How many minutes will the average customer be forced to wait in line?

X=.05 hours = 3 minute average wait

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

133) A manufacturing plant is trying to determine how long the average line for a repair process will be. If 10 machines arrive each hour and must wait 6 minutes in the line, how long will the line be, on average?

X=1 machine long line, on average

Diff: 2

Topic: The variety of queuing models

AACSB: Analytic Skills

Objective: LO-Module D-2

134) Suppose that customer arrivals are governed by a Poisson distribution. If the average arrival rate is 60 customers each hour, how many times will 60 customers arrive during a one hour period for each time that only 40 customers arrive.

P(40)= e^-40 * 60^40/ 40! = .001435

P(60)/P(40) = 35.85 = 36 times

Diff: 2

Topic: Characteristics of a waiting-line system

AACSB: Analytic Skills

Objective: LO-Module D-1

135) Suppose that 1 customer arrives each minute in a Poisson distribution. Is it more likely that 2 customers or 0 customers will arrive each minute?

P(2)=e^-1*1^2/2! = .184

Thus it is more likely that 0 customers will arrive each minute.

Diff: 2

Topic: Characteristics of a waiting-line system

AACSB: Analytic Skills

Objective: LO-Module D-1