Question 1

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 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

Accepted Answer

The average number of customers in the queue plus the number being served is equal to the average number of customers in the system, which is given as 2.33.

There is no specific question provided for the second part, so we cannot determine the best choice.

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.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

Accepted Answer

The Kendall notation of the system is M/M/1, where M stands for exponential distribution for arrival and service times, and 1 represents a single server. This is because the arrival rate is given to follow a Poisson distribution and the service rate is exponential, which are both memoryless processes.

Question 3

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

Accepted Answer

Reneging refers specifically to customers who join a queue but abandon their shopping carts before checking out. The other options are not examples of reneging.

Question 4

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 average number of customers waiting to be served?
A)0.23
B)2.33
C)0.33
D)1.63
E)0.70

Accepted Answer

The average number of customers waiting to be served is equal to the average length of the queue, which is given as 1.63.

Question 5

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

Accepted Answer

The correct Kendall notation for a service system with Poisson arrival rates, constant service time, and 1 server is M/D/1. "M" stands for memoryless or exponential inter-arrival times (Poisson arrivals), "D" stands for deterministic or constant service times, and "1" indicates a single server.

Question 6

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

Accepted Answer

Utilization factor (ρ) = arrival rate/service rate
ρ = 5/8 = 0.625

Question 7

Use this information to answer the following questions.
 $$\begin{array} { l | c } 
\hline \text { Number of Servers } & 1.0 \
\text { Arrival Rate } & 8.00 \
\text { Service Rate } & 10.00 \
\text { Standard deviation of servicetime } & 0.09 \
\hline
\end{array}$$
-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

Accepted Answer

The answer of Use this information to answer the following...

Question 8

Service time in queuing systems often follows the Poisson distribution.

Accepted Answer

Service times in queuing systems are more commonly modeled using the exponential distribution, while the Poisson distribution is typically used to model the arrival of customers into the system.

Question 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

Accepted Answer

To find the average number of customers arriving per minute, divide the hourly rate by 60 (since there are 60 minutes in an hour). Thus, $70 \div 60 = 1.166$, which rounds to approximately 1.2 customers per minute.

Question 10

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

Accepted Answer

From the given information, we know that the probability of there being no customers in the system is 0.3 or 30%. This means that there is a 30% probability of the service facility being idle. Therefore, the answer is D) 0.30.

As for the second question, it is not clear what is being asked. Please provide more information for an accurate answer.

Question 11

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

Accepted Answer

The answer of This queuing system configuration is referred to...

Question 12

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

Accepted Answer

The system has multiple servers (the three hairdressers), so the first letter is M for Markovian or Memoryless. 
The second letter is M because customer interarrival time follows the Poisson distribution. 
The third letter is 3 because there are three servers (hairdressers).
The service time follows the exponential distribution, which is considered Markovian or Memoryless, so the last letter is also M. Therefore, the Kendall notation for this system is M/M/3.

Question 13

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

Accepted Answer

The answer of This queuing system configuration is referred to...

Question 14

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.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%

Accepted Answer

The current utilization factor of the system is 70%. 
If a second server is added, the service rate doubles to 20.00 while the arrival rate remains the same at 7.00. 
The new utilization factor can be calculated as: 
Utilization factor = Arrival rate/ (number of servers * service rate) 
Utilization factor = 7.00 / (2 * 20.00) 
Utilization factor = 0.175 or 17.5% 
Therefore, the revised utilization factor after adding a second server is 35%, which is option D.

Question 15

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 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

Accepted Answer

The average time a customer spends waiting in line and being served is given by $\mathrm{W}= \mathrm{Wq}+\dfrac{1}{\mu},$ where $\mu$ is the service rate. From the table, $\mathrm{Wq}=0.23$ and $\dfrac{1}{\mu}=\dfrac{1}{10}=0.10$. Therefore, $\mathrm{W}=0.23+0.10=0.33$.

Answer: None
 The information provided in the table is not sufficient to determine the best choice(s).

Question 16

The average time each customer spends in the queue is referred to as:
A)W
B)Wq
C)L
D)Lq
E)ρ

Accepted Answer

The average time each customer spends in the queue is represented by the symbol Wq.

Question 17

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

Accepted Answer

The answer of What is the Kendall notation for the...

Question 18

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

Accepted Answer

This is a single-server, multiphase system because there is one line (or server) that customers go through, but there are multiple steps (phases) in the process: ordering and paying at one window, and then picking up food at another.

Question 19

Use this information to answer the following questions.
 $$\begin{array} { l | c } 
\hline \text { Number of Servers } & 1.0 \
\text { Arrival Rate } & 8.00 \
\text { Service Rate } & 10.00 \
\text { Standard deviation of servicetime } & 0.09 \
\hline
\end{array}$$
-Refer to the table.What is the average server utilization?
A)125%
B)100%
C)80%
D)10%
E)9%

Accepted Answer

The average server utilization can be calculated using the formula- Utilization = Arrival Rate * Service Time. Here, service time can be calculated using the reciprocal of the service rate, i.e., Service Time = 1/Service Rate = 1/10 = 0.1. Thus, Utilization = Arrival Rate * Service Time = 8 * 0.1 = 0.8 or 80%. 
As for the best choice(s), it is not clear what the question is asking for. More context is needed to provide an answer.

Question 20

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 percent of the time is the server busy?
A)10%
B)33%
C)23%
D)70%
E)30%

Accepted Answer

The utilization factor of the system, which is 70%, directly indicates the percentage of time the server is busy.

Quiz 9: Queuing Models

Reneging refers to customers who:

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?

Service time in queuing systems often follows the Poisson distribution.

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?

This queuing system configuration is referred to as a:

This queuing system configuration is referred to as a:

The average time each customer spends in the queue is referred to as:

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?

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: