Managerial Decision Modeling w/ Spreadsheets, 3e (Balakrishnan/Render/Stair)
Chapter 9 Queuing Models
9.1 Chapter Questions
1) Reneging refers to customers who:
A) do not join a queue
B) switch queues
C) join a queue but abandon their shopping carts before checking out
D) join a queue but are dissatisfied
E) join a queue and complain because of long lines
2) This queuing system configuration is referred to as a:
A) single-server, multiphase system
B) multiple-server, multiphase system
C) multiple-server, single-phase system
D) single-server, single-phase system
E) single-server, parallel phase system
3) This queuing system configuration is referred to as a:
A) single-server, multiphase system
B) multiple-server, multiphase system
C) multiple-server, single-phase system
D) single-server, single-phase system
E) single-server, parallel phase system
4) The average time each customer spends in the queue is referred to as:
A) W
B) Wq
C) L
D) Lq
E) ρ
5) In a drive-in fast food restaurant, customers form a single lane, place their order and pay their bill at
one window, and then pick up their food at a second window. This queuing configuration is referred to
as:
A) single-server, multiphase system
B) multiple-server, multiphase system
C) multiple-server, single-phase system
D) single-server, single-phase system
E) single-server, parallel phase system
6) A beauty salon employs three hairdressers. All customers get their hair washed in one area of the
salon before being taken to another area to get their hair cut. Customer arrival rate and service time
follows the Poisson and exponential distributions, respectively. What is the Kendall notation for this
system?
A) M/M/1
B) D/M/3
C) M/D/3
D) M/G/3
E) M/M/3
7) A service system has a constant service time, Poisson arrival rates and 1 server. What is the Kendall
notation for this system?
A) M/M/1
B) M/D/1
C) M/G/1
D) D/M/1
E) G/M/1
8) A queuing system has an arrival rate of 5 customers per hour and a service rate of 8 customers per
hour. What is the utilization factor (ρ) of the system?
A) 40
B) 1.6
C) 4
D) 5
E) 0.625
9) Customers arrive at a grocery store following a Poisson distribution at an average rate of 70 per hour.
On average, how many customers arrive per minute?
A) 1.2 customers per minute
B) 7 customers per minute
C) 0.86 customers per minute
D) 0.02 customers per minute
E) 0.7 customers per minute
Use this information to answer the following questions.
Number of Servers
1.0
Arrival Rate
7.00
Service Rate
10.00
P(0), probability that there are no customers in the system
30%
Lq, average length of the queue
1.63
W, average time in the system
0.33
L, average number of customers in the system
2.33
Wq, average time in the queue
0.23
Utilization factor of the system
70%
10) Refer to the table. Assuming a Poisson distribution arrival rate and an exponential distribution
service rate, what is the Kendall notation of this system?
A) M/M/1
B) M/D/1
C) M/G/1
D) D/M/1
E) G/M/1
11) Refer to the table. What is the probability that the service facility will be idle?
A) 0.23
B) 0.70
C) 0.33
D) 0.30
E) 0.233
12) Refer to the table. What percent of the time is the server busy?
A) 10%
B) 33%
C) 23%
D) 70%
E) 30%
13) Refer to the table. What is the average number of customers in the queue plus the number being
served?
A) 0.70
B) 2.33
C) 1.63
D) 0.23
E) 0.33
14) Refer to the table. What is the average time a customer spends waiting in line and being served?
A) 0.23
B) 2.33
C) 0.33
D) 1.63
E) 0.70
15) Refer to the table. What is the average number of customers waiting to be served?
A) 0.23
B) 2.33
C) 0.33
D) 1.63
E) 0.70
16) Refer to the table. If a second server was added with the same service rate, what would be the
revised utilization factor of the system?
A) 70%
B) 50%
C) 49%
D) 35%
E) 25%
Use this information to answer the following questions.
Number of Servers
1.0
Arrival Rate
8.00
Service Rate
10.00
Standard deviation of service time
0.09
17) Refer to the table. What is the average server utilization?
A) 125%
B) 100%
C) 80%
D) 10%
E) 9%
18) Refer to the table. What is the average number of customers in the queue plus the number being
served?
A) 0.12
B) 1.76
C) 2.12
D) 2.90
E) 3.30
19) What is the Kendall notation for the queuing system that develops when students from a single class
wait to see a professor for office hours, assuming Poisson arrivals and exponential service time?
A) M/M/1/∞/N
B) M/M/1
C) M/G/1
D) M/D/1
E) G/M/1
20) Service time in queuing systems often follows the Poisson distribution.
21) The Exponential distribution is used in many queuing models to represent service time patterns.
22) An M/M/1 system denotes a single server queuing system with exponential arrival and Poisson
service time distributions.
23) An M/M/s system implies there is a single number of servers.
24) The utilization factor (ρ) represents the proportion of time that the service facility is idle.
25) A multiphase queuing system is one in which service is received from more than one station, one
after the other.
26) If the average arrival rate (λ) is greater than the average service rate (µ), the queue length will grow
indefinitely.
27) The Poisson distribution is quite often used to represent arrival rates in queuing systems.
28) Cars arriving at a highway tollbooth would be an example of a limited (finite) population.
29) As service levels increase, the cost of providing service also increases, but the cost of customer
dissatisfaction decreases.
30) One of the M/M/1 queuing model assumptions is that the average number of arrivals (the arrival
rate) does not change over time.
31) The two primary components of queuing system costs are the cost of providing service and the cost
of wages.
32) Service time distribution can be either constant or random.
33) The cost of providing service is generally easier to quantify than the cost of waiting time.
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34) The service time pattern of a single lane automated car wash service would most likely be
exponential.
35) Kendall’s three-symbol notation is sometimes extended to include 5 symbols.
9.2 Excel Problems
1) A local bank has a single drive-in teller window. Customers arrive at the drive-in window following
a Poisson distribution at an average rate of 20 per hour. Assume that service is provided at the drive-in
window at a rate of 30 customers per hour and that service time follows an exponential distribution.
Moreover, assume that the population size is infinite and the queue length is unrestricted. To determine
the efficiency of operations, the bank wishes to examine several queue operating characteristics.
a. What is the utilization rate of this service system?
b. What is the average number of customers in line?
c. What is the average time that each customer spends in the queue?
d. What is the average time that each customer spends in the system?
e. What is the probability that the drive-in window will be idle?
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2) A college cafeteria has a single checkout lane manned by a single cashier. Students arrive at the cash
register at the rate of 2 per minute during peak lunch hour. It takes about 20 seconds to check out each
student’s tray. Assume that arrival rate follows a Poisson distribution and service time follows an
exponential distribution. To determine the efficiency of operations, the cafeteria manager wishes to
examine several queue operating characteristics.
a. What is the utilization rate of this service system?
b. What is the average number of students in line?
c. What is the average time that each student spends in the queue?
d. What is the average time that each student spends in the queue and being checked out?
e. What is the probability that the cashier will be idle?
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