Question 1

Service time distribution can be either constant or random.

Accepted Answer

A) True 
 B)False  True

Question 2

Use this information to answer the following questions.
 $\begin{array}{l|c}
\text { Number of Servers } & 1.0 \
\text { Arrival Rate } & 7.00 \
\text { Service Rate } & 10.00 \
\mathrm{P}(0) \text {, probability that there are no customers in the system } & 30 \% \
\mathrm{Lq} \text {, average length of the queue } & 1.63 \
\mathrm{~W} \text {, average time in the system } & 0.33 \
\mathrm{~L} \text {, average number of customers in the system } & 2.33 \
\mathrm{Wq}, \text { average time in the queue } & 0.23 \
\text { Utilization factor of the system } & 70 \% \
\hline
\end{array}$

-Refer to the table.What is the probability that the service facility will be idle?

Accepted Answer

A) 0.23 
B) 0.70 
C) 0.33 
D) 0.30 
E) 0.233 
A) 0.23 
B) 0.70 
C) 0.33 
D) 0.30 
E) 0.233 D

Question 3

The service time pattern of a single lane automated car wash service would most likely be exponential.

Accepted Answer

A) True 
 B)False  False

Question 4

Use this information to answer the following questions.
A small suburban post office is frequented by customers at the rate of 15 per hour.The post office has a single employee who typically processes each customer's request at an average rate of 3 minutes per transaction.Assume that arrival rate follows a Poisson distribution and service time follows an exponential distribution.
-To determine the efficiency of operations,the postmaster 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 queue and being serviced?
e.What is the probability that the post office employee will be idle?

Accepted Answer

a.75%;b.2.

Question 5

A technician who works in a computer lab at a local college has the responsibility of maintaining 30 desktop computers.Past records indicate that each desktop needs repair after about 40 hours of use.Breakdowns have been found to be Poisson distributed.The one technician on duty can repair a desktop in an average of 1 hour,following an exponential distribution.
a.How many desktops are waiting for service (i.e. ,in the repair queue),on average?
b.What is the average waiting time in the queue?
c.What is the average wait in the system?
d.What is the probability that all desktops are in good working condition and not needing any repairs?

Accepted Answer

a.1.27;b.1.81 hours;

Question 6

The utilization factor (ρ)represents the proportion of time that the service facility is idle.

Accepted Answer

A) True 
 B)False

Question 7

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?

Accepted Answer

a.67%;b.1.33;c.0.67

Question 8

A professor is holding office hours for a class of 15 students.Each student arrives on average once per hour.The arrival process follows a Poisson distribution.The time the professor spends with each student follows an exponential distribution with an average of 5 minutes.(Assume that each student may seek help and may decide to make multiple trips to the professor's office. )Answer the questions below.
a.How many students are waiting to see the professor on average?
b.What is the average waiting time in the queue?
c.What is the average wait in the system?

Accepted Answer

a.3.11
b.0.28 hours

Question 9

Kendall's three-symbol notation is sometimes extended to include 5 symbols.

Accepted Answer

A) True 
 B)False

Question 10

The Poisson distribution is quite often used to represent arrival rates in queuing systems.

Accepted Answer

A) True 
 B)False

Question 11

This queuing system configuration is referred to as a:

Accepted Answer

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 
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

Question 12

A service system has a constant service time,Poisson arrival rates and 1 server.What is the Kendall notation for this system?

Accepted Answer

A) M/M/1 
B) M/D/1 
C) M/G/1 
D) D/M/1 
E) G/M/1 
A) M/M/1 
B) M/D/1 
C) M/G/1 
D) D/M/1 
E) G/M/1

Question 13

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?

Accepted Answer

A) 40 
B) 1.6 
C) 4 
D) 5 
E) 0.625 
A) 40 
B) 1.6 
C) 4 
D) 5 
E) 0.625

Question 14

Use this information to answer the following questions.
Cars arrive at Sparkling Clean automatic car wash at the rate of 15 per hour and follow the Poisson distribution.It takes exactly 3 minutes for each car to go through the automated process of wetting,soaping,scrubbing,and drying.
-Refer to the information above.
a.What is the average time that each car spends in the queue?
b.What is the average time that each car spends in the queue and gets washed?
c.What is the probability that the next car that arrives will not have to wait?

Accepted Answer

a.4.5 minu

Question 15

Use this information to answer the following questions.
A small suburban post office is frequented by customers at the rate of 15 per hour.The post office has a single employee who typically processes each customer's request at an average rate of 3 minutes per transaction.Assume that arrival rate follows a Poisson distribution and service time follows an exponential distribution.
-Refer to the information above.The postmaster has been receiving complaints from customers about long waiting times.The postmaster is considering hiring an additional employee who will also be able to process each customer's request at the same rate of 3 minutes per transaction.Assume that the post office pays its employees $12 per hour and that the cost of customer waiting time,in terms of customer dissatisfaction and goodwill,is $10 per hour.Assume that arrival rate follows a Poisson distribution and service time follows an exponential distribution.Should the postmaster hire an additional employee? Compare the total costs of this two-employee system with the old single-server queuing system.

Accepted Answer

Total cost with 1 employee = (

Question 16

This queuing system configuration is referred to as a:

Accepted Answer

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 
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

Question 17

Reneging refers to customers who:

Accepted Answer

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 
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

Question 18

An M/M/s system implies there is a single number of servers.

Accepted Answer

A) True 
 B)False

Question 19

Use this information to answer the following questions.
A fast food restaurant currently has 2 cashiers.Upon arrival,customers form a single line and place their food order at the next available register.Assume that customers arrive at the rate of 35 per hour.It takes an average of 3 minutes to place and process each customer's order.Assume that arrival rate follows a Poisson distribution and service time follows an exponential distribution.
-Refer to the information above.To determine the efficiency of operations,the cafeteria manager wishes to examine several queue operating characteristics.Based upon the analysis,the manager believes that if the average waiting time per customer in the system is greater than 5 minutes,then a request for an additional employee should be made.Should the manager make a request to hire an additional employee?

Accepted Answer

Yes,current waiting

Question 20

As service levels increase,the cost of providing service also increases,but the cost of customer dissatisfaction decreases.

Accepted Answer

A) True 
 B)False

Service time distribution can be either constant or random.

The service time pattern of a single lane automated car wash service would most likely be exponential.

The utilization factor (ρ)represents the proportion of time that the service facility is idle.

Kendall's three-symbol notation is sometimes extended to include 5 symbols.

The Poisson distribution is quite often used to represent arrival rates in queuing systems.

This queuing system configuration is referred to as a:

A service system has a constant service time,Poisson arrival rates and 1 server.What is the Kendall notation for this system?

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?

This queuing system configuration is referred to as a:

Reneging refers to customers who:

An M/M/s system implies there is a single number of servers.

As service levels increase,the cost of providing service also increases,but the cost of customer dissatisfaction decreases.

Introduction to Managerial Decision Making

Linear Programming Models: Graphical and Computer Methods

Linear Programming Modeling Applications with Computer Analyses in Excel

Linear Programming Sensitivity Analysis

Transportation, Assignment, and Network Models

Integer, Goal, and Nonlinear Programming Models

Project Management

Decision Analysis

Simulation Modeling

Forecasting Models

Inventory Control Models

Filters

Exam 9: Queuing Models

Service time distribution can be either constant or random.

The service time pattern of a single lane automated car wash service would most likely be exponential.

The utilization factor (ρ)represents the proportion of time that the service facility is idle.

Kendall's three-symbol notation is sometimes extended to include 5 symbols.

The Poisson distribution is quite often used to represent arrival rates in queuing systems.

This queuing system configuration is referred to as a:

A service system has a constant service time,Poisson arrival rates and 1 server.What is the Kendall notation for this system?

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?

This queuing system configuration is referred to as a:

Reneging refers to customers who:

An M/M/s system implies there is a single number of servers.

As service levels increase,the cost of providing service also increases,but the cost of customer dissatisfaction decreases.

Introduction to Managerial Decision Making

Linear Programming Models: Graphical and Computer Methods

Linear Programming Modeling Applications with Computer Analyses in Excel

Linear Programming Sensitivity Analysis

Transportation, Assignment, and Network Models

Integer, Goal, and Nonlinear Programming Models

Project Management

Decision Analysis

Simulation Modeling

Forecasting Models

Inventory Control Models

Filters