Deck 24: Waiting-Line Models

Question 1

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

Answer 1

False

Question 2

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

Answer 2

False

Question 3

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.

Answer 3

True

Question 4

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

Question 5

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

Question 6

The cost of waiting decreases as the service level increases.

Question 7

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

Question 8

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

Question 9

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

Question 10

Balk and renege are elements of queue discipline.

Question 11

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.

Question 12

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

Question 13

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

Question 14

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.

Question 15

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

Question 16

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

Question 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.

Question 18

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

Question 19

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

Question 20

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

Question 21

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

Question 22

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

Question 23

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

Question 24

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

Question 25

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

Question 26

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

Question 27

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

Question 28

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

Question 29

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

Question 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

Question 31

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.

Question 32

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

Question 33

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

Question 34

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

Question 35

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.

Question 36

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

Question 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) multi-channel, multi-phase system
E) multi-channel, cross-phase system

Question 38

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

Question 39

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

Question 40

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.

Question 41

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

Question 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

Question 43

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

Question 44

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

Question 45

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

Question 46

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

Question 47

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.

Question 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

Question 49

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

Question 50

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

Question 51

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

Question 52

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

Question 53

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

A) dynamic-channel
B) random-channel
C) single channel
D) multi-channel
E) multiple line

Question 54

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) multi-channel, limited 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) single-channel, unlimited queue length

Question 55

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

Question 56

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

A) binomial probability distributions
B) negative exponential probability distributions
C) Poisson probability distributions
D) normal probability distributions
E) lognormal distributions

Question 57

"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) SPT

Question 58

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

Question 59

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

Question 60

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

Question 61

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

Question 62

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

Question 63

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

Question 64

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 λ is larger than μ

Question 65

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 λ is larger than μ

Question 66

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

Question 67

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

Question 68

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.

Question 69

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

Question 70

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.

Question 71

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

Question 72

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

Question 73

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

Question 74

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

Question 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. 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

Question 76

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

Question 77

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%

Question 78

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

Question 79

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

Question 80

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