Introduction to Operations and Supply Chain Management, 4e (Bozarth/Handfield)
Chapter 6S Advanced Waiting Line Theory and Simulation Modeling
Learning Objective 6S-1
1) In waiting line theory, the number of channels refers to the number of customer waiting lines
in the system.
2) In most waiting line models, customers are assumed to arrive at random intervals, based on a
normal distribution.
3) The Greek letter lambda (λ) is used to represent the service rate of a waiting line system.
4) A waiting line cannot be both multiple-channel and multiple-phase.
5) All waiting line formulas assume that customers are served on a first-come first-served
(FCFS) basis.
6) With only a half hour for lunch I screamed into the parking lot of the nearest Golden Arches
Supper Club at 40 miles an hour. When I saw the drive-through line was 15 cars deep, I didn’t
bother getting in line; I was off to visit the Colonel. This behavior might be described as balking.
7) There is but one difference between a waiting line system with a constant service time and one
with a Poisson distributed service time. Customers using the system with the constant service
time will have half the waiting time of the customers using the system with Poisson distributed
service times.
8) A customer enters a business and has the opportunity to select any one of three lines to receive
service. The service is performed by one customer service representative after which the
customer leaves the establishment. Which description of this waiting line system is appropriate?
A) single channel, single phase
B) single channel, multiple phase
C) multiple channel, single phase
D) multiple channel, multiple phase
9) A customer enters a business and joins the one line that snakes back and forth through the
lobby in order to receive service. The initial part of the service is performed by one customer
service representative, after which the customer enters a second, shorter line to complete the
service before leaving the establishment. Which description of this waiting line system is
appropriate?
A) single channel, single phase
B) single channel, multiple phase
C) multiple channel, single phase
D) multiple channel, multiple phase
10) Customer arrivals at a dry cleaning service occur randomly throughout the day. The
distribution that is usually used to model the interval between arrivals is the:
A) Poisson distribution.
B) uniform distribution.
C) random distribution.
D) normal distribution.
11) The department chair is out of town at a conference and you, as the assistant department
chair, find yourself besieged by dozens of students needing permission to get into a very popular
(but closed) class. Student arrivals are governed by the Poisson distribution with a mean of 10
minutes. Telling the students that they can’t get into the closed class takes about 3 minutes, and
this average is exponentially distributed. About how many students are waiting outside your
office door?
A) 0.13 students
B) 0.43 students
C) 1.25 students
D) 2.25 students
12) The department chair is out of town at a conference and you, as the assistant department
chair, find yourself besieged by dozens of students needing permission to get into a very popular
(but closed) class. Student arrivals are governed by the Poisson distribution with a mean of 10
minutes. Telling the students that they can’t get into the closed class takes about 5 minutes, and
this average is exponentially distributed. About how long do students wait outside your office
door?
A) 0.083 minutes
B) 0.083 hours
C) 0.50 minutes
D) 0.50 hours
13) The department chair is out of town at a conference and you, as the assistant department
chair, find yourself besieged by dozens of students needing permission to get into a very popular
(but closed) class. Student arrivals are governed by the Poisson distribution with a mean of 5
minutes. Telling the students that they can’t get into the closed class takes about 3 minutes, and
this average is exponentially distributed. About how many students are waiting outside your
office door and in your office?
A) 0.5
B) 1.0
C) 1.5
D) 2.0
14) The department chair is out of town at a conference and you, as the assistant department
chair, find yourself besieged by dozens of students needing permission to get into a very popular
(but closed) class. Student arrivals are governed by the Poisson distribution with a mean of 5
minutes. Telling the students that they can’t get into the closed class takes about 3 minutes, and
this average is exponentially distributed. About how long does it take a student to wait in line
and receive your valuable service?
A) 0.125 minutes
B) 0.075 hours
C) 4.5 minutes
D) 7.5 minutes
15) Anxious cruise vacationers besiege Tatiana, their excursion coordinator, at the Port of
Cozumel when they realize that all water excursions have been cancelled for no reason in
particular. It takes her 2.5 minutes to find the customers an alternative excursion activity and
customers cluster around her at the rate of 20 per hour. About how long does a customer wait in
line to receive her valuable service if the service times are exponentially distributed and the
arrivals follow a Poisson distribution?
A) 12.5 minutes
B) 5 minutes
C) 21 minutes
D) 15 minutes
16) Nervous cruise vacationers besiege Tatiana, their excursion coordinator, at the Port of
Cozumel when they realize that all water excursions have been cancelled for no reason in
particular. It takes her 2.5 minutes to find the customers an alternative excursion activity and
customers cluster around her at the rate of 20 per hour. About how many customers are waiting
in line to receive her valuable service if the service times are exponentially distributed and the
arrivals follow a Poisson distribution?
A) 2.78
B) 4.17
C) 3.25
D) 5.00
17) Nervous cruise vacationers besiege Tatiana, their excursion coordinator, at the Port of
Cozumel when they realize that all water excursions have been cancelled for no reason in
particular. It takes her 2.5 minutes to find the customers an alternative excursion activity and
customers cluster around her at the rate of 20 per hour. About how long does a customer spend
waiting in line and receiving her valuable service if the service times are exponentially
distributed and the arrivals follow a Poisson distribution?
A) 12.5 minutes
B) 4.17 minutes
C) 5 minutes
D) 15 minutes
18) Anxious cruise vacationers besiege Tatiana, their excursion coordinator, at the Port of
Cozumel when they realize that all water excursions have been cancelled for no reason in
particular. It takes her 2.5 minutes to find the customers an alternative excursion activity and
customers cluster around her at the rate of 20 per hour. About how many customers are clustered
around her, either receiving service or waiting in line to receive her valuable service if the
service times are exponentially distributed and the arrivals follow a Poisson distribution?
A) 2.78
B) 4.17
C) 3.25
D) 5.00
19) Anxious cruise vacationers besiege Tatiana, their excursion coordinator, and her fourteen
assistants at the Port of Cozumel when they realize that all water excursions have been cancelled
for no reason in particular. It takes them 4 minutes to find the customers an alternative excursion
activity and customers cluster around them at the rate of 200 per hour. About how long does a
customer wait in line to receive their valuable service if the service times are exponentially
distributed and the arrivals follow a Poisson distribution?
A) 6.50 minutes
B) 5.00 minutes
C) 2.13 minutes
D) 1.36 minutes
20) Hysterical cruise vacationers besiege Tatiana, their excursion coordinator, and her fourteen
assistants at the Port of Cozumel when they realize that all water excursions have been cancelled
for no reason in particular. It takes them 4 minutes to find the customers an alternative excursion
activity and customers cluster around them at the rate of 200 per hour. About how many
customers are waiting in line to receive their valuable service if the service times are
exponentially distributed and the arrivals follow a Poisson distribution?
A) 2.78
B) 3.17
C) 4.52
D) 5.00
21) Hysterical cruise vacationers besiege Tatiana, their excursion coordinator, and her fourteen
assistants at the Port of Cozumel when they realize that all water excursions have been cancelled
for no reason in particular. It takes them 4 minutes to find the customers an alternative excursion
activity and customers cluster around them at the rate of 200 per hour. About how long does a
customer spend waiting in line and receiving their valuable service if the service times are
exponentially distributed and the arrivals follow a Poisson distribution?
A) 7.50 minutes
B) 5.36 minutes
C) 4.17 minutes
D) 3.67 minutes
22) Frenzied cruise vacationers besiege Tatiana, their excursion coordinator, and her fourteen
assistants at the Port of Cozumel when they realize that all water excursions have been cancelled
for no reason in particular. It takes them 4 minutes to find the customers an alternative excursion
activity and customers cluster around them at the rate of 200 per hour. About how many
customers are clustered around them, either receiving service or waiting in line to receive their
valuable service if the service times are exponentially distributed and the arrivals follow a
Poisson distribution?
A) 17.86
B) 14.17
C) 13.25
D) 19.66
23) Frenzied cruise vacationers besiege Tatiana, their excursion coordinator, and her fourteen
assistants at the Port of Cozumel when they realize that all water excursions have been cancelled
for no reason in particular. It takes them 4 minutes to find the customers an alternative excursion
activity and customers cluster around them at the rate of 200 per hour. What is the probability
that there are no customers awaiting service or being served if the service times are exponentially
distributed and the arrivals follow a Poisson distribution?
A) 0.000
B) 0.043
C) 0.025
D) 0.066
24) The bank manager of a busy downtown location found herself unable to find good teller help
so she invested in an ATM to handle the routine withdrawals that tended to occupy an inordinate
amount the teller’s time. Before she installed the ATM she found that customers were arriving on
average every 2 minutes (Poisson distributed) and it took a teller 30 seconds (exponentially
distributed) to process their request. The ATM is able to maintain a constant 30 second service
time. What is the impact on system utilization?
A) There is no change.
B) Utilization has dropped by 15%.
C) Utilization has dropped by 30%.
D) Utilization has dropped by 45%.
25) The bank manager of a busy downtown location found herself unable to find good teller help
so she invested in an ATM to handle the routine withdrawals that tended to occupy an inordinate
amount the teller’s time. Before she installed the ATM she found that customers were arriving on
average every 2 minutes (Poisson distributed) and it took a teller 30 seconds (exponentially
distributed) to process their request. The ATM is able to maintain a constant 30 second service
time. What is the impact on the number of customers waiting in line?
A) There is no change.
B) The ATM line is half as long as the teller line.
C) The ATM line is twice as long as the teller line.
D) The ATM line is 25% shorter than the teller line.
26) The bank manager of a busy downtown location found herself unable to find good teller help
so she invested in an ATM to handle the routine withdrawals that tended to occupy an inordinate
amount the teller’s time. Before she installed the ATM she found that customers were arriving on
average every 60 seconds (Poisson distributed) and it took a teller 20 seconds (exponentially
distributed) to process their request. The ATM is able to maintain a constant 30 second service
time. What is the impact on the waiting time for the customers?
A) There is no change.
B) The wait in the ATM line is 50% shorter than the wait in the teller line.
C) The wait in the ATM line is 50% higher than the wait in the teller line.
D) The wait in the ATM line is 25% shorter than the teller line.
27) Patrons line up to spin the giant slot machine at the entrance to Ace Rothstein’s Tangiers
casino. They pour in the door at the rate of 300 per hour and it takes exactly ten seconds every
time for the wheels to spin and inform the unlucky patron that they have lost a dollar rather than
win a new Corvette. How many customers are in line on average?
A) 2.08 customers
B) 1.93 customers
C) 1.67 customers
D) 1.50 customers
28) Regulars line up to spin the giant slot machine at the entrance to Ace Rothstein’s Tangiers
casino. They pour in the door at the rate of 300 per hour and it takes exactly ten seconds every
time for the wheels to spin and inform the unlucky patron that they have lost a dollar rather than
win a new Corvette. How long do customers wait in line on average?
A) 10 seconds
B) 15 seconds
C) 20 seconds
D) 25 seconds
29) Hopeful patrons line up to spin the giant slot machine at the entrance to Ace Rothstein’s
Tangiers casino. They pour in the door at the rate of 300 per hour and it takes exactly ten seconds
every time for the wheels to spin and inform the unlucky patron that they have lost a dollar rather
than win a new Corvette. How long do customers spend waiting in line and finding out the
unhappy news on average?
A) 35 seconds
B) 30 seconds
C) 25 seconds
D) 20 seconds
30) Barber College is the best deal in town! For only $5, you can get a shampoo and cut by any
one of four untrained stylists completed in 7.5 minutes on average. Perhaps this is why
customers show up on average two minutes apart (both arrival times and service times are
exponentially distributed).
What percentage of the time are the four stylists working with customers?
A) 94%
B) 90%
C) 84%
D) 80%
31) Barber College is the best deal in town! For only $5, you can get a shampoo and cut by any
one of four untrained stylists completed in 7.5 minutes on average. Perhaps this is why
customers show up on average two minutes apart (both arrival times and service times are
exponentially distributed).
On average, how many customers are waiting in line?
A) 9
B) 11
C) 13
D) 15
32) Barber College is the best deal in town! For only $5, you can get a shampoo and cut by any
one of four untrained stylists completed in 7.5 minutes on average. Perhaps this is why
customers show up on average two minutes apart (both arrival times and service times are
exponentially distributed).
How long does a customer spend waiting for a haircut?
A) 17 minutes
B) 20 minutes
C) 23 minutes
D) 26 minutes