Operations Management, 12e (Heizer/Render/Munson)
Module D Waiting-Line Models
Section 1 Queuing Theory
1) Waiting-line models are useful to operations in such diverse settings as service systems, maintenance
activities, and shop-floor control.
2) 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
3) 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
4) A waiting line or ________ is where items or people are in a line awaiting service; ________ is a body of
knowledge about waiting lines.
Section 2 Characteristics of a Waiting-Line System
1) 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.
2) A waiting-line system has three parts: the size of the arrival population, the behavior of arrivals, and
the statistical distribution of arrivals.
3) 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
4) In queuing problems, arrival rates are generally described by the normal probability distribution.
5) Balk and renege are elements of queue discipline.
6) A hospital emergency room always follows a FIFO queue discipline in the interest of fairness.
7) In queuing problems, the term “renege” refers to the fact that some customers leave the queue before
service is completed.
8) A waiting-line system with one waiting line and three sequential processing stages is a multiple-server,
single-phase system.
9) If the service time within a queuing system is constant, the service rate can be easily described by a
negative exponential distribution.
10) LIFS (last-in, first-served) is a common queue discipline, most often seen where people, not objects,
form the waiting line.
11) A bank office with five tellers, each with a separate line of customers, exhibits the characteristics of a
multiphase queuing system.
12) In the analysis of queuing models, the Poisson distribution often describes arrival rates, while service
times are often described by the negative exponential distribution.
13) 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
14) 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
15) The common measures of a queuing system‘s performance include:
A) probability that the service facility will be idle, average queue length, and 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, and
average time each customer spends in the queue.
C) average queue length, maximum time a customer may spend in the queue, and the utilization factor
for the system.
D) average time each customer spends in the system, maximum queue length, and probability of a
specific number of customers in the system.
E) maximum queue length, maximum time a customer may spend in the queue, and average queue
length.
16) 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) frustration
17) 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) arrivals or inputs, queue discipline or the waiting line itself, and the service facility.
E) sequencing policy, penalty for reneging, and expediting of arrivals.
18) 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
19) 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 arrival behavior?
A) first-in, first-out
B) balk
C) renege
D) random departure
E) frustration
20) 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
21) Which part of a waiting line has characteristics that involve a statistical distribution?
A) arrivals or inputs
B) the waiting line itself
C) the service facility
D) A and C
E) A, B, and C
22) 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
23) 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.
24) 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
25) 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.
26) 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 which of the following?
A) single-server, single-phase system
B) single-server, multiphase system
C) multiple-server, single-phase system
D) multiple-server, multiphase system
E) multiple-server, cross-phase system
27) An airline ticket counter, with several agents for one line of customers, is an example of which of the
following?
A) single-server, single-phase system
B) single-server, multiphase system
C) multiple-server, single-phase system
D) multiple-server, multiphase system
E) cross-server, single-phase system
28) A concert hall, employing both ticket takers and ushers to seat patrons, behaves typically as which of
the following?
A) multiple-server, single-phase system
B) multiple-server, multiphase system
C) single-server, single-phase system
D) single-server, multiphase system
E) multiple-server, cross-phase system
29) A McDonald’s single-lane drive-through that has one window for making the payment and a second
window for receiving the food behaves most like which of the following?
A) single-server, single-phase system
B) single-server, multiphase system
C) multiple-server, single-phase system
D) multiple-server, multiphase system
E) single-server, sequential-phase system
30) The sign at the bank that reads, “Wait here for the first available teller,” suggests the use of a ________
waiting line system.
A) dynamic-server, single-phase
B) random-server, single-phase
C) single-server, multiphase
D) multiple-server, single-phase
E) multiple-server, multiphase
31) 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 which of the following?
A) multiple-server, limited queue length
B) single-server, multiphase, limited queue length
C) multiple-server, unlimited queue length
D) multiple single-server systems, limited queue length
E) single-server, unlimited queue length
32) A system in which the customer receives service from only one station and then exits the system is
which of the following?
A) a single-phase system
B) a single-channel system
C) a multiple channel system
D) a multiphase system
E) a limited-access system
33) Which of the following is a measure of queue performance?
A) utilization factor for the system
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
34) 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) customers waiting to see a bank teller
35) Which of the following is NOT a measure of a queue’s performance?
A) average time spent in the queue
B) average queue length
C) probability that the service facility will be idle
D) utilization factor for the system
E) All of the above are performance measures.
36) A(n) ________ is a discrete probability distribution that often describes the arrival rate in queuing
theory.
37) 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 before being served.
38) A waiting line has a(n) ________ population if, as arrivals take place, the likelihood of additional
arrivals is decreased.
39) Of the three types of queue discipline, only ________ is assumed by the four primary waiting line
models.
40) A(n) ________ queuing system has one line and one server.
41) 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
42) A(n) ________ queuing system is one in which the customer receives service from only one station
and then exits the system.
43) The ________ probability distribution is a continuous probability distribution often used to describe
the service time in a queuing system.
44) Provide an example of a limited or finite population for a queue.
45) What does it mean to have a patient customer in a waiting line?
46) Describe the difference between FIFO and LIFO queue disciplines.
47) What are the components in a waiting-line system?
48) Identify the seven major measures of a queue system’s performance.
49) 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?
Section 3 Queuing Costs
1) The cost of waiting decreases as the service level increases.
2) The study of waiting lines calculates the cost of providing good service but does not value the cost of
customers’ waiting time.
3) Which of the following occurs as the level of service decreases?
A) Cost of waiting time decreases, and cost of providing service decreases.
B) Cost of waiting time decreases, and cost of providing service increases.
C) Cost of waiting time increases, and cost of providing service decreases.
D) Cost of waiting time increases, and cost of providing service increases.
E) Cost of waiting time first decreases, then increases; while cost of providing service decreases.
4) What costs are present in waiting line analysis? How do these costs vary with the level of service?
1) 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 Finite
population or D—all share three characteristics: Poisson arrivals, FIFO discipline, and exponential service
times.
2) 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.
3) The greater the margin by which the arrival rate exceeds the service rate, the better the performance of
the waiting line.
4) 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.
5) A finite population waiting line model is also called M/M/1 with finite source.
6) In the finite population waiting line model, the average length of the queue is calculated from the
probability the system is empty.
7) A waiting line meeting the assumptions of M/M/1 has an average time between arrivals of 20 minutes,
and it services items in an average of 10 minutes each. What is the utilization factor?
A) 0.25
B) 0.33
C) 0.50
D) 0.67
E) 3.00
8) 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. What is the utilization factor for the system?
A) 0.25
B) 0.33
C) 0.50
D) 0.67
E) 3.00
9) 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 servers
C) single number of phases
D) Poisson arrival rate pattern
E) finite population size
10) Which one of the following is NOT a characteristic of a Model B or M/M/S system?
A) unlimited population size
B) single server
C) exponential service time pattern
D) single phase
E) Poisson arrival rate pattern
11) Which one of the following is NOT a characteristic of a Model C or M/D/1 system?
A) single server
B) single phase
C) Poisson arrival rate pattern
D) exponential service time pattern
E) unlimited population size
12) In the basic queuing model (M/M/1), what probability distribution describes service times?
A) binomial
B) negative exponential
C) Poisson
D) normal
E) lognormal
13) In the basic queuing model (M/M/1), what probability distribution describes arrival rates?
A) continuous
B) normal
C) negative exponential
D) Poisson
E) lognormal
14) 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. What is the average
length of the queue Lq in units?
A) 0.4
B) 0.133
C) 4.167
D) 4.583
E) 6
15) 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 probability distribution.