Deck 12: Queues and Process Simulation Modeling

Question 1

The formula that is used to determine the average waiting time in the queue (W_q)is ________.

A) =
B) =
C) =
D) =

Answer 1

=

Question 2

Use the data given below to answer the following question(s).
In an FCFS single server queuing discipline,the mean arrival rate is 12 customers/minute and the mean service rate is 14.5 customers/minute.
Calculate the average number of customers in the queue.

A)0.17
B)0.40
C)4.80
D)3.97

Answer 2

3.97

Question 3

Identify the formula that is used to determine the average time a customer spends in the system (W).

A)_{W =}
B)W =
C)W =
D)W =

Answer 3

W =

Question 4

When the arrival pattern is described by a Poisson process,a mean arrival time of λ implies that the mean interarrival time,t,is ________.

A)1/λ
B)1 + λ
C)1 - λ
D)also λ

Question 5

Which of the following is an example of a probabilistic arrival?

A)parts feeding from an automated machine to an assembly line
B)people visiting a hair salon
C)counseling sessions in allotted time frames
D)teaching sessions at a university

Question 6

In queuing systems with multiple queues,customers switch lines if they perceive another to be moving faster.This kind of behavior is called ________.

A)balking
B)jockeying
C)reneging
D)straddling

Question 7

In the context of efficiency evaluation of a service operation,what does throughput mean?

A)It is the percentage of servers that are busy.
B)It is the percentage of customers who balk.
C)It is the rate at which customers are served.
D)It is the rate at which customers jockey from one queue to another.

Question 8

In queuing theory,what is the calling population?

A)It is the number of servers providing the service.
B)It is the set of potential customers.
C)It is the number of repair bays available.
D)It is the number of technically qualified people handling customer queries.

Question 9

Which of the following is an assumption of the Poisson process?

A)The probability of an arrival varies over time.
B)The arrival rate is not stationary.
C)Past arrivals do not influence future arrivals.
D)Customers do not arrive independently of each other.

Question 10

Use the model assumptions given below to answer the following question(s).
Assume Poisson arrivals with a mean arrival rate λ,exponential service times with mean service rate μ,a single server,and an FCFS queue discipline.
The formula that is used to determine the average number of customers in the system (L)is ________.

A)L =
B)L =
C)L =
D)L =

Question 11

Use the case given below to answer the following question(s).
Reuben went to a diner to have a hamburger and French fries.The person at the cash counter assigned the number 27 to Reuben and told him he would have to wait for his turn.
Which of the following is an example of balking?

A)While waiting in the queue to buy concert tickets,Elizabeth gave up her turn to an old lady who was standing right behind her.
B)Elizabeth got tired of waiting in the queue and decided she would come back later to buy the concert tickets.
C)Elizabeth chose the shortest queue when she arrived to buy concert tickets for herself and a friend.
D)When Elizabeth arrived at the booking counter and saw the length of all the queues,she decided she would try booking the tickets online instead.

Question 12

In queuing systems,some customers may arrive at the system,determine that the line is too long,and decide not to join the queue.This kind of behavior is called ________.

A)balking
B)jockeying
C)reneging
D)straddling

Question 13

It is common for customers to leave a queue before being served.This kind of behavior is known as ________.

A)balking
B)jockeying
C)reneging
D)ratifying

Question 14

Identify the formula that is used to determine the probability that the system is empty (P₀).

A)P₀ = 1 - μ/λ
B)P₀ = 1 - λ/μ
C)P₀ = λ/μ
D)P₀ = μ/λ

Question 15

Use the model assumptions given below to answer the following question(s).
Assume Poisson arrivals with a mean arrival rate λ,exponential service times with mean service rate μ,a single server,and an FCFS queue discipline.
Identify the formula that is used to determine the average number of customers in the queue (L_q).

A) =
B) =
C) =
D) =

Question 16

Consider a situation where service times follow an exponential distribution.If the probability of the average service time,t,exceeding the mean is low at 0.368,which of the following is likely to be true?

A)There are a large number of long service times and a few short ones.
B)There are a large number of short service times and a few long ones.
C)There are a large number of balking scenarios and a few jockeying scenarios.
D)There are a large number of jockeying scenarios and a few balking scenarios.

Question 17

Process simulation ________.

A)analyzes sample statistics empirically by repeatedly sampling the data and creating distributions of the statistics
B)is the process of modeling chronological data
C)is the process of changing key model inputs to determine their effect on the outputs
D)is an approach for modeling the logical sequence of events as they take place

Question 18

Which of the following is an example of a deterministic arrival?

A)patients arriving at appointed times to a medical facility
B)people visiting the emergency room
C)tweets transmitted during a live event
D)people visiting a supermarket for their monthly groceries

Question 19

Use the case given below to answer the following question(s).
Reuben went to a diner to have a hamburger and French fries.The person at the cash counter assigned the number 27 to Reuben and told him he would have to wait for his turn.
Which of the following,if true,would suggest that Reuben reneged?

A)He chose the counter with the least number of customers to place his order.
B)He canceled his order and decided to find another food joint where he would not have to wait long.
C)He exchanged his turn with an old gentleman after him who had been assigned the waiting number 28.
D)He tried to exchange his turn with a lady who would be serviced ahead of him,citing a personal emergency.

Question 20

Use the case given below to answer the following question(s).
Reuben went to a diner to have a hamburger and French fries.The person at the cash counter assigned the number 27 to Reuben and told him he would have to wait for his turn.
Which of the following,if true,would suggest that Reuben jockeyed?

A)He moved to the next counter when he realized it had fewer people.
B)He left the diner and decided to eat somewhere else.
C)He exchanged his turn with an old gentleman after him who had been assigned the waiting number 28.
D)He tried to exchange his turn with a lady who would be serviced ahead of him,citing a personal emergency.

Question 21

If the number of customers in the system is 10,the number of customers in the queue is 9,and the arrival rate is 2 customers per minute,determine the average customer service rate.

A)2 customers per minute
B)1 customer per minute
C)1.25 customers per minute
D)1.5 customers per minute

Question 22

Use the scenario given below to answer the following question(s).
You arrive at a queue and spend 10 minutes in the system (waiting plus service).During this time,customers arrive at the rate of 15 per minute.The mean service rate is 20 per minute.
Assuming Little's law,calculate the number of customers that remain in the queue when you leave the system.

A)approximately 149 customers
B)approximately 140 customers
C)approximately 145 customers
D)approximately 143 customers

Question 23

If the average arrival rate increases to 14,what is the probability that the system is empty?

A)0.034
B)0.34
C)0.057
D)0.57

Question 24

If the average arrival rate increases to 13,the average number of customers in the system ________.

A)reduces by 3.87
B)reduces by 8.67
C)increases by 8.67
D)increases by 3.87

Question 25

What is the probability that the system is empty?

A)0.75
B)0.25
C)0.55
D)0.45

Question 26

What is the expected number of customers in service?

A)0.40
B)0.60
C)0.17
D)0.83

Question 27

What is the probability that the system contains at least one customer?

A)0.25
B)0.55
C)0.75
D)0.45

Question 28

In queuing theory,Little's law states that the ________.

A)average number of customers in a system is equal to the sum of the average time in the queue and the average time in the system
B)average number of customers in a system is equal to the difference of the average time in the queue and the average time in the system
C)average number of customers in a system is equal to the mean arrival rate times the average time in the system
D)average number of customers is equal to the ratio of the mean arrival rate over the average time in the system

Question 29

Use the scenario given below to answer the following question(s).
You arrive at a queue and spend 10 minutes in the system (waiting plus service).During this time,customers arrive at the rate of 15 per minute.The mean service rate is 20 per minute.
Assuming Little's law,determine the number of customers that remain in the system when you leave.

A)250
B)25
C)150
D)100

Question 30

If the servicing rate falls to 11,which of the following will occur?

A)The average service time will increase by 60 seconds.
B)The number of customers in the system will reduce to one.
C)The length of the queue will become infinitely long.
D)The average time that a customer has to spend in the queue will increase by 120 seconds.

Question 31

What is the average time a customer has to spend in the system?

A)20 seconds
B)60 seconds
C)24 seconds
D)30 seconds

Question 32

Use the data given below to answer the following question(s).
In an FCFS single server queuing discipline,the mean arrival rate is 12 customers/minute and the mean service rate is 14.5 customers/minute.
What is the average number of customers in the system?

A)0.17
B)0.40
C)4.80
D)3.97

Question 33

Determine the probability that the system is empty.

A)0.60
B)0.40
C)0.83
D)0.17

Question 34

If the average arrival rate increases to 14,the probability that the system contains at least one customer is ________.

A)0.66
B)0.34
C)0.03
D)0.97

Question 35

Determine the time that you had to spend in the queue.

A)9 minutes 20 seconds
B)10 minutes 57 seconds
C)9 minutes 57 seconds
D)10 minutes 20 seconds

Question 36

What is the probability that the system is not empty?

A)0.60
B)0.40
C)0.83
D)0.17

Question 37

If the average arrival rate increases to 14,the average number of customers in the queue ________.

A)reduces by 27.03
B)reduces by 23.06
C)increases by 23.06
D)increases by 27.03

Question 38

What is the average time a customer has to spend in the queue?

A)approximately 240 seconds
B)approximately 20 seconds
C)approximately 90 seconds
D)approximately 5 seconds

Question 39

If the average arrival rate falls to 11,the average time a customer spends in the queue ________.

A)reduces by 14 seconds
B)reduces by 7 seconds
C)increases by 7 seconds
D)increases by 14 seconds

Question 40

If the servicing rate increases to 16,the ________.

A)average number of customers in the system decreases by 1.8
B)average number of customers in the queue increases by 1.7
C)probability of the system being empty will reduce to 0.75
D)probability that the system contains at least one customer will increase to 0.25

Question 41

If the number of customers in a queue is 6,the number of customers in the system is 10,and the arrival rate is 2 customers per minute,the customer service rate is ________.

A)0.75 customers per minute
B)1.75 customers per minute
C)2 customers per minute
D)0.5 customers per minute

Question 42

The mean time that an object spends in the waiting line is ________.

A)21.53 minutes
B)60.33 minutes
C)0.95 minutes
D)35.19 minutes

Question 43

Compute the probability that the system has at least one customer.

A)0.47
B)0.53
C)0.95
D)0.05

Question 44

Determine the probability that the system is empty.

A)0.47
B)0.53
C)0.95
D)0.05

Question 45

Determine the average time for which the workstation is used.

A)75 seconds
B)57 seconds
C)45 seconds
D)30 seconds

Question 46

What is the fraction of time that the work station was waiting to pass a customer on to the next element?

A)0.00 minutes
B)0.95 minutes
C)1.00 minutes
D)0.50 minutes

Question 47

If the average number of customers in a queue is 9.6,the number of customers in the system is 10,and the arrival rate is 2 customers per minute,what is the probability that at least one customer is in the system?

A)0.8
B)0.2
C)0.6
D)0.4

Question 48

Determine the number of customers that left the buffer.

A)21.53
B)60.33
C)0.95
D)38.80

Question 49

Use the following scenario to answer the question(s)below.
Solomon operates a drive-in restaurant and is in charge of marketing and analysis; his son is in charge of delivery.The restaurant works as a single queue FCFS system.During the "lunch hour," which Solomon defines as the period from 12.30 p.m.to 2.30 p.m.,customers arrive randomly at an average of 30 customers per hour (or one customer every two minutes).A customer takes an average of three minutes to receive his order (or 20 customers per hour),but this fluctuates quite a bit due to variations in customer preferences.Solomon doesn't understand how a line could possibly pile up when his son can work faster than the rate at which customers arrive.Although customers complain a bit,they do not leave even if they have to wait.Solomon is particularly interested in understanding the waiting time,the number waiting,and how long his son is actually busy before considering improving his facility.
(Hint: Use SimQuick)
The percentage of customers entering the process divided by the total number that tried to enter is ________.

A)21.53
B)18.02
C)1.00
D)0.95

Question 50

In SimQuick,service level is defined as the ________.

A)mean time an object spends in the buffer
B)number of objects in the buffer
C)fraction of time that the work station was waiting to pass an object on to the next element
D)percentage of objects entering the process divided by the total number that tried to enter

Question 51

Based on the simulation results,determine the average number of customers in the system.

A)18.95
B)23.28
C)35.23
D)11.85

Question 52

If the average waiting time for a customer in a system is 30 minutes and the customer service rate is 5 customers per minute,the average time a customer spends in the queue is ________.

A)35 minutes 48 seconds
B)25 minutes
C)29 minutes 48 seconds
D)30 minutes

Question 53

If the average waiting time for a customer in a queue is 25 minutes and the customer service rate is 5 customers per minute,calculate the average time a customer spends in the system.

A)25 minutes 12 seconds
B)25 minutes
C)5 minutes
D)5 minutes 12 seconds

Question 54

Use the following scenario to answer the question(s)below.
Solomon operates a drive-in restaurant and is in charge of marketing and analysis; his son is in charge of delivery.The restaurant works as a single queue FCFS system.During the "lunch hour," which Solomon defines as the period from 12.30 p.m.to 2.30 p.m.,customers arrive randomly at an average of 30 customers per hour (or one customer every two minutes).A customer takes an average of three minutes to receive his order (or 20 customers per hour),but this fluctuates quite a bit due to variations in customer preferences.Solomon doesn't understand how a line could possibly pile up when his son can work faster than the rate at which customers arrive.Although customers complain a bit,they do not leave even if they have to wait.Solomon is particularly interested in understanding the waiting time,the number waiting,and how long his son is actually busy before considering improving his facility.
(Hint: Use SimQuick)
The number of work cycles started in the work station is ________.

A)21.53
B)18.02
C)60.33
D)38.80

Question 55

The inventory remaining at the end of the simulation is ________.

A)37.80
B)60.33
C)0.95
D)21.53

Question 56

What is the expected number of customers in service?

A)0.47
B)0.95
C)0.53
D)0.05

Question 57

If the average number of customers in a queue is 9.6,the number of customers in the system is 10,and the arrival rate is 2 customers per minute,what is the probability that the system is empty?

A)0.8
B)0.2
C)0.6
D)0.4

Question 58

If the number of customers in a queue is 8,the arrival rate is 2 customers per minute,and the customer service rate is 4 customers per minute,what is the average number of customers in the system?

A)10 customers
B)12 customers
C)8.5 customers
D)10.5 customers

Question 59

Based on the simulation results,what is the average number of customers in the queue?

A)18.90
B)23.23
C)35.19
D)10.90

Question 60

Typically,the first step in process simulation is to ________.

A)enter key inputs such as how long it takes to perform each step of the process
B)create a graphical flowchart that describes all process steps and logical decisions that route entities to different locations
C)identify the resources that are needed to perform process tasks
D)run samples from the probability distributions of the input variables that drive the flow of entities

Question 61

Some customers may arrive at the system,determine that the line is too long,and decide not to join the queue.This kind of behavior is called jockeying.

Question 62

Use the scenario given below to answer the following question.
Consider the flow process map given below.Assume that orders enter the system with a time between arrivals that is exponentially distributed with a mean of 0.8 minutes.The processing time at work station 1 is exponential with a mean of 0.50 minutes,and at work station 2,it is exponential with a mean of 1 minute.The queue for work station 1 has a capacity of 6,while the queue for work station 2 has a capacity of 4.
Run the simulations for 30 replications of a 24-hour.
The percentage of customers entering the process divided by the total number that tried to enter is ________.

A)2.87
B)0.49
C)0.79
D)0.42

Question 63

Use the scenario given below to answer the following question.
Consider the flow process map given below.Assume that orders enter the system with a time between arrivals that is exponentially distributed with a mean of 0.8 minutes.The processing time at work station 1 is exponential with a mean of 0.50 minutes,and at work station 2,it is exponential with a mean of 1 minute.The queue for work station 1 has a capacity of 6,while the queue for work station 2 has a capacity of 4.
Run the simulations for 30 replications of a 24-hour.
The fraction time working for work station 2 is ________.

A)0.00 minutes
B)0.97 minutes
C)0.42 minutes
D)0.49 minutes

Question 64

Use the scenario given below to answer the following question.
Consider the flow process map given below.Assume that orders enter the system with a time between arrivals that is exponentially distributed with a mean of 0.8 minutes.The processing time at work station 1 is exponential with a mean of 0.50 minutes,and at work station 2,it is exponential with a mean of 1 minute.The queue for work station 1 has a capacity of 6,while the queue for work station 2 has a capacity of 4.
Run the simulations for 30 replications of a 24-hour.
The number of work cycles started in work station 1 is ________.

A)3.39
B)1406.87
C)700.69
D)1410.90

Question 65

Determine the average time a customer spends in queue 1.

A)3 minutes 28 seconds
B)4 minutes 42 seconds
C)5 minutes 5 seconds
D)2 minutes 58 seconds

Question 66

Use the scenario given below to answer the following question.
Consider the flow process map given below.Assume that orders enter the system with a time between arrivals that is exponentially distributed with a mean of 0.8 minutes.The processing time at work station 1 is exponential with a mean of 0.50 minutes,and at work station 2,it is exponential with a mean of 1 minute.The queue for work station 1 has a capacity of 6,while the queue for work station 2 has a capacity of 4.
Run the simulations for 30 replications of a 24-hour.
The fraction time working for work station 1 is ________.

A)0.00 minutes
B)0.97 minutes
C)0.42 minutes
D)0.49 minutes

Question 67

Use the scenario given below to answer the following question.
Consider the flow process map given below.Assume that orders enter the system with a time between arrivals that is exponentially distributed with a mean of 0.8 minutes.The processing time at work station 1 is exponential with a mean of 0.50 minutes,and at work station 2,it is exponential with a mean of 1 minute.The queue for work station 1 has a capacity of 6,while the queue for work station 2 has a capacity of 4.
Run the simulations for 30 replications of a 24-hour.
The number of work cycles started in work station 2 is ________.

A)3.39
B)1405.90
C)1410.90
D)1406.87

Question 68

Based on the simulation results,the average time a customer has to spend in the queue is ________.

A)18 minutes 54 seconds
B)23 minutes
C)35 minutes 11 seconds
D)10 minutes 54 seconds

Question 69

The inventory level that triggers an order is called the ________.

A)lot size
B)order quantity
C)reorder point
D)rate of return

Question 70

Use the scenario given below to answer the following question.
Consider the flow process map given below.Assume that orders enter the system with a time between arrivals that is exponentially distributed with a mean of 0.8 minutes.The processing time at work station 1 is exponential with a mean of 0.50 minutes,and at work station 2,it is exponential with a mean of 1 minute.The queue for work station 1 has a capacity of 6,while the queue for work station 2 has a capacity of 4.
Run the simulations for 30 replications of a 24-hour.
Determine the average number of customers in queue 2.

A)3.39
B)0.42
C)3.24
D)3.46

Question 71

According to the Poisson process,if the mean arrival rate is 2 customers per minute,the mean interval time is 4 minutes.

Question 72

According to the Poisson process in queuing systems,past arrivals do not influence future arrivals.

Question 73

Use the scenario given below to answer the following question.
Consider the flow process map given below.Assume that orders enter the system with a time between arrivals that is exponentially distributed with a mean of 0.8 minutes.The processing time at work station 1 is exponential with a mean of 0.50 minutes,and at work station 2,it is exponential with a mean of 1 minute.The queue for work station 1 has a capacity of 6,while the queue for work station 2 has a capacity of 4.
Run the simulations for 30 replications of a 24-hour.
Determine the average time a customer spends in queue 2.

A)3 minutes 19 seconds
B)4 minutes 24 seconds
C)5 minutes 50 seconds
D)2 minutes 29 seconds

Question 74

Use the scenario given below to answer the following question.
Consider the flow process map given below.Assume that orders enter the system with a time between arrivals that is exponentially distributed with a mean of 0.8 minutes.The processing time at work station 1 is exponential with a mean of 0.50 minutes,and at work station 2,it is exponential with a mean of 1 minute.The queue for work station 1 has a capacity of 6,while the queue for work station 2 has a capacity of 4.
Run the simulations for 30 replications of a 24-hour.
The fraction time blocked for work station 1 is ________.

A)0.00 minutes
B)0.97 minutes
C)0.42 minutes
D)0.49 minutes

Question 75

Use the scenario given below to answer the following question.
Consider the flow process map given below.Assume that orders enter the system with a time between arrivals that is exponentially distributed with a mean of 0.8 minutes.The processing time at work station 1 is exponential with a mean of 0.50 minutes,and at work station 2,it is exponential with a mean of 1 minute.The queue for work station 1 has a capacity of 6,while the queue for work station 2 has a capacity of 4.
Run the simulations for 30 replications of a 24-hour.
Identify the average number of customers in queue 1.

A)3.39
B)0.42
C)2.87
D)3.46

Question 76

Use the scenario given below to answer the following question.
Consider the flow process map given below.Assume that orders enter the system with a time between arrivals that is exponentially distributed with a mean of 0.8 minutes.The processing time at work station 1 is exponential with a mean of 0.50 minutes,and at work station 2,it is exponential with a mean of 1 minute.The queue for work station 1 has a capacity of 6,while the queue for work station 2 has a capacity of 4.
Run the simulations for 30 replications of a 24-hour.
What is the fraction time blocked for work station 2?

A)0.00 minutes
B)0.97 minutes
C)0.42 minutes
D)0.49 minutes

Question 77

Balking is the process of customers switching lines if they perceive another to be moving faster.

Question 78

What is the final number of customers remaining after simulation?

A)1580.80
B)1410.90
C)1406.87
D)1405.90

Question 79

Lot size is ________.

A)the inventory level that triggers an order
B)the number of units ordered
C)also known as the mean inventory level
D)the inventory remaining at the end of the simulation

Question 80

A queue may not even be visible or in one location.