Deck 13: Queuing Theory

Question 1

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
The objective in queuing problems is to find the service level that achieves an acceptable balance between the cost of providing service and customer satisfaction.

Answer 1

True

Question 2

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
A situation where cars arrive at an intersection can be modeled as an M/D/s queue with finite capacity.

Answer 2

False

Question 3

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
The amount of time a customer spends with the server is referred to as

A) system time.
B) queue time.
C) service time.
D) served time.

Answer 3

service time.

Question 4

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
One way to improve performance of a queuing system from the customer perspective is to reduce the number of servers.

Question 5

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
What is the service policy in the queuing systems presented in this chapter that is considered "fair" by the customers?

A) FIFO
B) LIFO
C) FILO
D) Priority

Question 6

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.

-If the number of arrivals in a given period of time follows a Poisson distribution with mean , the interarrival times follow an exponential probability distribution with mean 1/λ

Question 7

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
Which of the following best describes queuing theory?

A) The study of arrival rates.
B) The study of service times.
C) The study of waiting lines.
D) The evaluation of service time costs.

Question 8

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
If the arrival process is modeled as a Poisson random variable with arrival rate λ, then the average time between arrivals is

A) 1/μ
B) 1/λ
C) 1/λ²
D) σ

Question 9

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
The term queuing theory refers to the body of knowledge dealing with waiting lines.

Question 10

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
The M in M/G/1 stands for

A) Markovian inter-arrival times.
B) Mendelian inter-arrival times.
C) Mean inter-arrival times.
D) Mathematical inter-arrival times.

Question 11

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
In a queuing problem, Wq > W.

Question 12

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
If the service rate decreases as the arrival rate remains constant, then, in general

A) customer waiting time increases.
B) customer waiting time decreases.
C) service costs increase.
D) customer dissatisfaction decreases.

Question 13

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
Joe's Copy Center has 10 copiers. They break down and require service quite often. Time between breakdowns follows an exponential distribution for each copier. The repair person services machines as quickly as possible, but the service time follows an exponential distribution. What type of system is it?

A) M/M/1 with Finite Population
B) M/M/1 with Finite Queue
C) M/M/1
D) M/M/10

Question 14

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
What is the formula for P(t ≤ T) under the exponential distribution with rate μ?

A) 1 − eμ^T
B) eμ^T
C) 1 − e−μ^T
D) 1 − e^T

Question 15

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
An arrival process is memoryless if the time until the next arrival occurs is inversely proportional to the time elapsed since the last arrival.

Question 16

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
The number of arrivals that occurs in a given time period represents a random variable in a queuing system.

Question 17

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
A barber shop has one barber, a Poisson arrival rate and exponentially distributed service times. What is the Kendall notation for this system?

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

Question 18

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
The memoryless property is also referred to as the ____ property.

A) Markov
B) Erlang
C) Poisson
D) Normal

Question 19

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
A balk refers to

A) a customer who refuses to join the queue.
B) a customer who refuses service by a specific server.
C) a customer who joins the queue but leaves before service is complete.
D) a customer who requires extra service time.

Question 20

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
In the Kendall notation M/D/4, D stands for

A) memoryless arrival distribution
B) deterministic departure distribution
C) memoryless arrival and departure distributions
D) none of the above

Question 21

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
In the Kendall notation M/G/4, G stands for

A) memoryless arrival distribution
B) general departure distribution
C) memoryless arrival and departure distributions
D) none of the above

Question 22

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
In the Kendall notation M/G/4, the number 4 indicates

A) the number of servers
B) deterministic departure distribution
C) memoryless arrival and departure distributions
D) queue capacity

Question 23

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
The Kendall notation for a queuing system with Poisson arrivals, exponential service and 3 service providers is

A) M/M/3
B) M/G/1
C) G/G/3
D) G/G/1

Question 24

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
What is the mean arrival rate based on the following 8 arrival rate observations? ​
Number of arrivals per hour: 6, 5, 3, 4, 7, 6, 4, 5
​

A) 3
B) 4
C) 5
D) 6

Question 25

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
A Poisson distribution shape can be described as

A) slightly skewed to the left.
B) symmetric around the parameter λ.
C) skewed to the right.
D) discrete so it lacks any definable shape.

Question 26

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
If a company adds an additional identical server to its M/M/1 system, making an M/M/2 system, what happens to a customer's average service time?

A) increases
B) decreases
C) it is unchanged
D) depends on the arrival rate

Question 27

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
An arrival process is memoryless if

A) the time until the next arrival depends on the time elapsed since the last arrival.
B) the time until the next arrival is based on the time elapsed since the last arrival.
C) the time until the next arrival does not depend on the time elapsed since the last arrival.
D) the time until the next arrival is based on the arrival rate.

Question 28

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
The standardized queuing system notation such as M/M/1 or M/G/2 is referred to as

A) Kendall notation.
B) Erlang notation.
C) Poisson notation.
D) Queuing notation.

Question 29

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
The service times for a grocery store with one checkout line have a mean of 3 minutes and a standard deviation of 20 seconds. Customer arrivals at the checkout stand follow a Poisson distribution. What type of system is it?

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

Question 30

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
For a Poisson random variable, λ represents the ____ number of arrivals per time period

A) maximum
B) minimum
C) average
D) standard deviation of

Question 31

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
If cell B2 contains the value for μ and cell A5 contains the value for T, what formula should go in cell B5 to compute the P(Service time) ≤ T for this exponential distribution?

A) =1-EXP($B$2*A5)
B) =EXP(-$B$2*A5)
C) =1-EXP(-$B$2)
D) =1-EXP(-$B$2*A5)

Question 32

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
A store is considering adding a second clerk. The customer arrival rate at this new server will be

A) twice the old rate.
B) half the old rate.
C) the same as the old rate.
D) unpredictable.

Question 33

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
One reason to use queuing models in business is

A) to trade-off the cost of providing service and the cost of customer dissatisfaction
B) to maximize the number of service providers
C) to minimize the cost of providing service
D) all of the above

Question 34

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
Refer to Exhibit 13.1. What is the probability that a customer must wait in queue before being served?

A) 0.00
B) 0.25
C) 0.75
D) 1.00

Question 35

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
What is the formula for the probability of x arrivals, p(x), under a Poisson distribution with arrival rate λ?

A)
B)
C)
D)

Question 36

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
Which of the following is a reason to employ queuing theory?

A) To reduce customer wait time in line.
B) To reduce service times.
C) To generate more arrivals to the system.
D) To reduce worker idle time in line.

Question 37

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
Which type of queuing system are you likely to encounter at a Wendy's restaurant?

A) Single waiting line, single service station.
B) Multiple waiting lines, single service station.
C) Single waiting line, multiple service stations.
D) Multiple waiting lines, multiple service stations.

Question 38

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
Which type of queuing system are you likely to encounter at an ATM?

A) Single waiting line, single service station.
B) Multiple waiting lines, single service station.
C) Single waiting line, multiple service stations.
D) Multiple waiting lines, multiple service stations.

Question 39

Exhibit 12.5
The following questions use the information below.
The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem.
The number of arrivals to a store follows a Poisson distribution with mean λ = 10/hour. What is the mean inter-arrival time?

A) 6 seconds
B) 6 minutes
C) 10 minutes
D) 10 hours

Question 40

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
A jockey refers to

A) a customer who refuses to join the queue.
B) a customer who refuses service by a specific server.
C) a customer who joins the queue but leaves before service is complete.
D) a customer who switches between queues in the system.

Question 41

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
A doctor's office only has 8 chairs. The doctor's service times and customer inter-arrival times are exponentially distributed. What type of system is it?

A) M/M/1
B) M/M/8
C) M/M/1 with Finite Queue
D) M/M/1 with Finite Population

Question 42

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
The M/M/s model with finite capacity queue can be used to model

A) a machine breakdown process in a shop with 10 identical machines
B) traffic in a dentist's office
C) a process of patient departure from a dentist's office
D) a process of installing new machines in a shop

Question 43

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
Which type of queuing system are you likely to encounter at a grocery store?

A) Single waiting line, single service station.
B) Multiple waiting lines, single service station.
C) Single waiting line, multiple service stations.
D) Multiple waiting lines, multiple service stations.

Question 44

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
In the Kendall notation M/G/4, M stands for

A) memoryless arrival distribution
B) memoryless departure distribution
C) memoryless arrival and departure distributions
D) none of the above

Question 45

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
A renege refers to

A) a customer who refuses to join the queue.
B) a customer who refuses service by a specific server.
C) a customer who joins the queue but leaves before service is complete.
D) a customer who requires extra service time.

Question 46

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
Refer to Exhibit 13.1. What is the probability that a customer can go directly into service without waiting in line?

A) 0.00
B) 0.25
C) 0.75
D) 1.00

Question 47

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
If a service system has a constant service time, Poisson arrival rates and 2 servers its Kendall notation is

A) P/D/2
B) M/D/2
C) M/D/1
D) G/D/2

Question 48

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
Joe's Copy Center has 10 copiers. They break down at a rate of 0.02 copiers per hour and are sent to the service facility. What is the average arrival rate of broken copiers to the service facility?

A) 0.02
B) 0.2
C) 10
D) It cannot be determined from the information provided.

Question 49

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
A common queue discipline used in practice is

A) first-in-first-out
B) random
C) last-in-first-out
D) group arrival

Question 50

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
Which of the following is the typical operating characteristic for the probability an arriving unit has to wait for service?

A) W_p
B) P₀
C) P_w
D) P_n

Question 51

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
Refer to Exhibit 13.1. How many customers will be in the store on average at any one time?

A) 0.375
B) 0.50
C) 2.25
D) 3.00

Question 52

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
If the number of arrivals in a time period follow a Poisson distribution with mean λ then the inter-arrival times follow a(n) ____ distribution with mean ____.

A) normal; μ
B) constant; λ
C) exponential; λ
D) exponential; 1/λ

Question 53

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
A company has recorded the following list of service rates (customers/hour) for one of its servers. What is the mean service time for this server? ​
Customers / hour: 4, 4, 5, 6, 5, 4, 3, 4, 3, 5, 5, 6
​

A) 0.22 min
B) 1.11 min
C) 4.5 min
D) 13.3 min

Question 54

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
The M/M/s model with finite population can be used to model

A) a machine breakdown process in a shop with 10 identical machines
B) a process of patient arrival to a dentist's office
C) a process of patient departure from a dentist's office
D) a process of installing new machines in a shop

Question 55

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
The M/D/1 model results can be derived from which of the following systems?

A) M/M/1 with λ = 0
B) M/G/1 with μ = 0
C) M/G/1 with σ = 0
D) M/M/2 with finite queue length.

Question 56

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
What is the probability that it will take less than or equal to 0.25 hours to service any call based on the following exponential probability distribution with rate μ = 5? ​

A) 0.00
B) 0.71
C) 0.92
D) 1.00

Question 57

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
Refer to Exhibit 13.1. What is the average amount of time spent waiting in line?

A) 0.375
B) 0.50
C) 2.25
D) 3.00

Question 58

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
To find steady-state values for the M/M/S queuing system, which of the following statements must be true about the arrival rate?

A) λ < s μ
B) λ − s = μ
C) λ > s μ
D) λ = s μ

Question 59

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
Which of the following is the typical operating characteristic for average number of units in a queue?

A) W
B) W_q
C) L
D) L_q

Question 60

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
Which of the following is the typical operating characteristic for average time a unit spends waiting for service?

A) W
B) W_q
C) L
D) L_q

Question 61

Exhibit 13.6
The following questions refer to the information and output below.
The university computer lab has 10 computers which are constantly being used by students. Users need help from the one lab assistant fairly often. Students ask for help at a Poisson rate of with an average of 4 requests per hour for any one computer. The assistant answers questions as quickly as possible and the service time follows an exponential distribution with mean of 1 minute per help session. The following queuing analysis spreadsheet was developed from this information.
Refer to Exhibit 13.6. What is the Kendall notation for this system?

Question 62

Exhibit 13.6
The following questions refer to the information and output below.
The university computer lab has 10 computers which are constantly being used by students. Users need help from the one lab assistant fairly often. Students ask for help at a Poisson rate of with an average of 4 requests per hour for any one computer. The assistant answers questions as quickly as possible and the service time follows an exponential distribution with mean of 1 minute per help session. The following queuing analysis spreadsheet was developed from this information.
Refer to Exhibit 13.6. Based on this report what is the average number of students waiting to be helped?

Question 63

Exhibit 13.6
The following questions refer to the information and output below.
The university computer lab has 10 computers which are constantly being used by students. Users need help from the one lab assistant fairly often. Students ask for help at a Poisson rate of with an average of 4 requests per hour for any one computer. The assistant answers questions as quickly as possible and the service time follows an exponential distribution with mean of 1 minute per help session. The following queuing analysis spreadsheet was developed from this information.
The customer service desk at Joe's Discount Electronics store receives 5 customers per hour on average. On average, each customer requires 10 minutes for service. The customer service desk is staffed by a single person. What is the average time a customer spends in the customer service area if modeled as an M/M/1 queuing system?

Question 64

Exhibit 13.3
The following questions refer to the information below.
A company has recorded the following customer inter-arrival times and service times for 10 customers at one of its single teller service lines. Assume the data are exponentially distributed and the 10 data points represent a reasonable sample.
Refer to Exhibit 13.3. What is the average number of customers in the system?

Question 65

Exhibit 13.5
The following questions refer to the information and output below.
A computer printer in a large administrative office has a printer buffer (memory to store printing jobs) capacity of 3 jobs. If the buffer is full when a user wants to print a file the user is told that the job cannot be printed and to try again later. There are so many users in this office that we can assume that there is an infinite calling population. Jobs arrive at the printer at a Poisson rate of 55 jobs per hour and take an average of 1 minute to print. Printing times are exponentially distributed. The following queuing analysis spreadsheet was developed from this information.
Refer to Exhibit 13.5. Based on this report what is the probability that a computer user will be told to resubmit a print job at a later time?

Question 66

Exhibit 13.4
The following questions refer to the information and output below.
A grocery store can serve an average of 360 customers per hour. The service times are exponentially distributed. The store has 4 checkout lines each of which serves 90 customers per hour. Customers arrive at the store at a Poisson rate of 240 customers per hour. The following queuing analysis spreadsheet was developed from this information.
Refer to Exhibit 13.4. What is the Kendall notation for this system?

Question 67

A company has recorded the following list of service rates (customers/hour) for one of its servers. What is the mean service time for this server?

Question 68

Exhibit 13.7
The following questions refer to the information and output below.
A tax accountant has found that the time to serve a customer has a mean of 30 minutes (or 0.5 hours) and a standard deviation of 6 minutes (or 0.1 hours). Customer arrivals follow a Poisson distribution with an average of 60 minutes between arrivals. The following queuing analysis spreadsheet was developed from this information.
Refer to Exhibit 13.7. Based on this report how long does a customer spend at the tax accountant's office?

Question 69

Exhibit 13.4
The following questions refer to the information and output below.
A grocery store can serve an average of 360 customers per hour. The service times are exponentially distributed. The store has 4 checkout lines each of which serves 90 customers per hour. Customers arrive at the store at a Poisson rate of 240 customers per hour. The following queuing analysis spreadsheet was developed from this information.
Refer to Exhibit 13.4. Based on this report what percent of the time is a grocery clerk busy serving a customer?

Question 70

Exhibit 13.1
The following questions are based on the output below.
A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system.
The M/D/1 model with infinite capacity queue can be used to model

A) a machine breakdown process in a shop with 10 identical machines
B) a process of washing a car in an automatic car wash
C) a process of patient departure from a dentist's office
D) a process of installing new machines in a shop

Question 71

Exhibit 13.2
The following questions refer to the information and output below.
A barber shop has one barber who can give 12 haircuts per hour. Customers arrive at a rate of 8 customers per hour. Customer inter-arrival times and service times are exponentially distributed. The following queuing analysis spreadsheet was developed from this information.
Refer to Exhibit 13.2. Based on this report what is the average number of customers waiting for a haircut?

Question 72

The customer service desk at Joe's Discount Electronics store receives 5 customers per hour on average. On average, each customer requires 10 minutes for service. The customer service desk is staffed by a single person. What is the average number of customers in the customer service area, if modeled as an M/M/1 queuing system?

Question 73

A grocery clerk can serve 20 customers per hour on average and the service time follows an exponential distribution. What is the probability that a customer's service time is less than 2 minutes?

Question 74

Exhibit 13.6
The following questions refer to the information and output below.
The university computer lab has 10 computers which are constantly being used by students. Users need help from the one lab assistant fairly often. Students ask for help at a Poisson rate of with an average of 4 requests per hour for any one computer. The assistant answers questions as quickly as possible and the service time follows an exponential distribution with mean of 1 minute per help session. The following queuing analysis spreadsheet was developed from this information.
Customers arrive at a store randomly, following a Poisson distribution at an average rate of 20 per hour. What is the probability of exactly 0, 1 2, and 3 arrivals in a 15 minute period?

Question 75

Exhibit 13.7
The following questions refer to the information and output below.
A tax accountant has found that the time to serve a customer has a mean of 30 minutes (or 0.5 hours) and a standard deviation of 6 minutes (or 0.1 hours). Customer arrivals follow a Poisson distribution with an average of 60 minutes between arrivals. The following queuing analysis spreadsheet was developed from this information.
Refer to Exhibit 13.7. What is the Kendall notation for this system?

Question 76

Exhibit 13.6
The following questions refer to the information and output below.
The university computer lab has 10 computers which are constantly being used by students. Users need help from the one lab assistant fairly often. Students ask for help at a Poisson rate of with an average of 4 requests per hour for any one computer. The assistant answers questions as quickly as possible and the service time follows an exponential distribution with mean of 1 minute per help session. The following queuing analysis spreadsheet was developed from this information.
Refer to Exhibit 13.6. Based on this report how much time do students spend getting help before they can resume work on their computers?

Question 77

Exhibit 13.2
The following questions refer to the information and output below.
A barber shop has one barber who can give 12 haircuts per hour. Customers arrive at a rate of 8 customers per hour. Customer inter-arrival times and service times are exponentially distributed. The following queuing analysis spreadsheet was developed from this information.
Customers arrive at a store randomly, following a Poisson distribution at an average rate of 90 per hour. How many customers arrive per minute, on average?

Question 78

Exhibit 13.5
The following questions refer to the information and output below.
A computer printer in a large administrative office has a printer buffer (memory to store printing jobs) capacity of 3 jobs. If the buffer is full when a user wants to print a file the user is told that the job cannot be printed and to try again later. There are so many users in this office that we can assume that there is an infinite calling population. Jobs arrive at the printer at a Poisson rate of 55 jobs per hour and take an average of 1 minute to print. Printing times are exponentially distributed. The following queuing analysis spreadsheet was developed from this information.
Refer to Exhibit 13.5. What is the Kendall notation for this system?

Question 79

Exhibit 13.4
The following questions refer to the information and output below.
A grocery store can serve an average of 360 customers per hour. The service times are exponentially distributed. The store has 4 checkout lines each of which serves 90 customers per hour. Customers arrive at the store at a Poisson rate of 240 customers per hour. The following queuing analysis spreadsheet was developed from this information.
Refer to Exhibit 13.4. Based on this report what is the average number of customers waiting for a checker?

Question 80

Exhibit 13.3
The following questions refer to the information below.
A company has recorded the following customer inter-arrival times and service times for 10 customers at one of its single teller service lines. Assume the data are exponentially distributed and the 10 data points represent a reasonable sample.
Refer to Exhibit 13.3. What is the mean service rate per hour?