Deck 11: Queueing Models

Question 1

The number of customers in a system is the number in the queue plus one.

Answer 1

False

Question 2

Waiting lines occur even in systems that are less that 100% utilized because of variability in service rates and/or arrival rates.

Answer 2

True

Question 3

Most queueing models assume that the form of the probability distribution of interarrival times is an exponential distribution.

Answer 3

True

Question 4

Queueing models conventionally assume that the queue can hold an unlimited number of customers.

Question 5

The utilization factor is the ratio of the arrival rate to the service rate.

Question 6

A loading dock with two servers who work together as a team would be an example of a multiple-server system.

Question 7

The cost of customer waiting is easy to estimate.

Question 8

The most commonly used queueing models assume a service rate that is exponential.

Question 9

The goal of queuing analysis is to minimize customer waiting lines.

Question 10

The lack-of-memory property refers to a customer's willingness to wait in line even though there are other customers that will be served first.

Question 11

The expected waiting time in line is equal to the expected number of customers in line divided by the arrival rate.

Question 12

The exponential distribution will always provide a reasonably close approximation of the true service-time distribution.

Question 13

Queueing models enable finding an appropriate balance between the cost of service and the amount of waiting.

Question 14

The standard deviation for the degenerative distribution equals zero.

Question 15

Managers who oversee queueing systems are usually concerned with how many customers are waiting and how long they will have to wait.

Question 16

In a single-server system, the utilization factor is equal to the mean arrival rate divided by the mean service rate.

Question 17

A queueing system is said to be in a "steady state" when customers arrive at a constant rate, that is, without any variability.

Question 18

All single-server queueing models require the utilization factor to be less than 1.

Question 19

The only distribution of interarrival times that fits having random arrivals is the exponential distribution.

Question 20

Queue discipline refers to the willingness of customers to wait in line for service.

Question 21

As the ratio of arrival rate to service rate is increased, which of the following is likely?

A) Customers move through the system in less time because utilization is increased.
B) Customers move through the system more slowly because utilization is increased.
C) Utilization is decreased because of the added strain on the system.
D) The average number in the system decreases.
E) None of the answer choices is correct.

Question 22

In a nonpreemptive priority system, customers are served in the order in which they arrive in the queue.

Question 23

Multiple-server queueing systems can perform satisfactorily with somewhat higher utilization factors than can single-server queueing systems.

Question 24

Which of the following is not generally considered as a measure of performance in queueing analysis?

A) The average number waiting in line
B) The average number in the system
C) The system utilization factor
D) The cost of servers plus customer waiting cost
E) Service time

Question 25

Applying nonpreemptive priorities improves the measures of performance in the top priority class even more than applying preemptive priorities.

Question 26

In a preemptive priority system, the lowest-priority customer being served is ejected back into the queue whenever a higher-priority customer enters the queueing system.

Question 27

A queueing system has four crews with three members each. The number of "servers" is:

A) 3.
B) 4.
C) 7.
D) 12.
E) 1.

Question 28

The term queue discipline refers to:

A) the willingness of customers to wait in line for service.
B) having multiple waiting lines without customers switching from line to line.
C) the order in which customers are processed.
D) the reason waiting occurs in underutilized systems.
E) None of the answer choices is correct.

Question 29

The goal of queueing analysis is to minimize:

A) the sum of customer waiting costs and service costs.
B) the sum of customer waiting time and service time.
C) service costs.
D) customer waiting time.
E) None of the answer choices is correct.

Question 30

Which of the following will equal the average time that a customer is in the system?
I) The average number in the system divided by the arrival rate.
II) The average number in the system multiplied by the arrival rate.
III) The average time in line plus the average service time.

A) I only.
B) II only.
C) III only.
D) II and III only.
E) I and III only.

Question 31

If a manager increases the system utilization standard (assuming no change in the customer arrival rate) what happens to the customer waiting time?

A) It increases exponentially.
B) It increases proportionally.
C) It decreases proportionally.
D) It decreases exponentially.
E) No change.

Question 32

A system has one service facility that can service 10 customers per hour. The customers arrive at an average rate of 6 per hour. In this case, no waiting line will form.

Question 33

Decreasing the variability of service times, without any change in the mean, improves the performance of a single-server queueing system substantially.

Question 34

For a system that has a high utilization factor, decreasing the service rate will have only a negligible effect on customer waiting time.

Question 35

When designing a single-server queueing system, giving a relatively high utilization factor to the server ensures that the system is working efficiently.

Question 36

Which of the following is not an example of a commercial service system?

A) ATM cash machine
B) Brokerage service
C) Travel agency
D) Tool crib
E) Call center

Question 37

Choosing the number of servers in a system involves finding an appropriate trade-off between the cost of the servers and the amount of waiting.

Question 38

The reason for using priorities is to decrease the waiting times for high-priority customers.

Question 39

The assumption of constant service times cannot be used with human servers because of the inevitable variability.

Question 40

A single server queueing system has an average service time of 8 minutes and an average time between arrivals of 10 minutes. The arrival rate is:

A) 6 per hour.
B) 7.5 per hour.
C) 8 per hour.
D) 10 per hour.
E) 12.5 per hour.

Question 41

A single-server queueing system has an average service time of 16 minutes per customer, which is exponentially distributed. The manager is thinking of converting to a system with a constant service time of 16 minutes. The arrival rate will remain the same. The effect will be to:

A) increase the utilization factor.
B) decrease the utilization factor.
C) increase the average waiting time.
D) decrease the average waiting time.
E) not have any effect since the service time is unchanged.

Question 42

Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays.
What is the system utilization?

A) 0.6
B) 0.7
C) 0.8
D) 0.9
E) 1

Question 43

Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays.
What is the average number of customers waiting in line?

A) 1.633
B) 2.333
C) 2.5
D) 3.966
E) 4

Question 44

There are 5 servers in a system with an arrival rate of 6 per hour and a service time of 20 minutes. What is the system utilization?

A) 0.1
B) 0.3
C) 0.4
D) 1.2
E) 2.0

Question 45

Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times).
What is the minimum number of servers needed to keep the average time in the system under 6 minutes?

A) 2
B) 3
C) 4
D) 5
E) 6

Question 46

A multiple-server system has customers arriving at an average rate of five per hour and an average service time of forty minutes. The minimum number of servers for this system to have a utilization factor under 1 is:

A) 2.
B) 3.
C) 4.
D) 5.
E) None of the answer choices is correct.

Question 47

Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 0.4 customers per minute (exponential service times).
If there are 4 servers, what is the probability of three or fewer customers in the system?

A) 0.19
B) 0.23
C) 0.63
D) 0.68
E) 0.79

Question 48

During the early morning hours, customers arrive at a branch post office at the average rate of 45 per hour (exponential interarrival times), while clerks can handle transactions on an average of 4 minutes each (exponential).
If clerk cost is $30 per hour and customer waiting time represents a cost of $20 per hour, how many clerks can be justified on a cost basis?

A) 2.
B) 3.
C) 4.
D) 5.
E) 6.

Question 49

Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays.
How many minutes does the average customer spend in the system?

A) 7.
B) 8.
C) 9.
D) 10.
E) 11.

Question 50

Customers arrive at a suburban ticket outlet at the rate of 14 per hour on Monday mornings (exponential interarrival times). Selling the tickets and providing general information takes an average of 3 minutes per customer, and varies exponentially. There is 1 ticket agent on duty on Mondays.
How many minutes does the average customer wait in line?

A) 7
B) 8
C) 9
D) 10
E) 11

Question 51

Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times).
What is the average number of customers in the system with 8 servers?

A) 2
B) 3
C) 4
D) 5
E) 6

Question 52

During the early morning hours, customers arrive at a branch post office at the average rate of 45 per hour (exponential interarrival times), while clerks can handle transactions on an average of 4 minutes each (exponential).
What is the minimum number of clerks needed to keep the average time in the system under 5 minutes?

A) 2
B) 3
C) 4
D) 5
E) 6

Question 53

Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 0.4 customers per minute (exponential service times).
What is the minimum number of servers needed to achieve an average time in the system of less than three minutes?

A) 2
B) 3
C) 4
D) 5
E) 6

Question 54

Customers filter into a record shop at an average of 1 per minute (exponential interarrivals) where the service rate is 15 per hour (exponential service times).
What is the system utilization factor if 5 servers are used?

A) 0.6.
B) 0.7.
C) 0.8.
D) 0.9.
E) 1.

Question 55

A multiple priority queueing model assumes that:

A) arrival rates are exponentially distributed.
B) service rate is exponentially distributed.
C) items are serviced in the order of arrival.
D) items are serviced in order of priority class.
E) service activities are preemptive.

Question 56

A single bay car wash with an exponential arrival rate and service time has cars arriving an average of 10 minutes apart, and an average service time of 4 minutes. The utilization factor is:

A) 0.24.
B) 0.4.
C) 0.67.
D) 2.5
E) None of the answer choices is correct.

Question 57

Customers arrive at a video rental desk at the rate of one per minute (exponential interarrival times). Each server can handle 0.4 customers per minute (exponential service times).
If there are 4 servers, what is the average time it takes in minutes to rent a videotape?

A) 2
B) 3
C) 4
D) 5
E) 6

Question 58

Which of these would increase system utilization?

A) An increase in the service rate
B) An increase in the arrival rate
C) An increase in the number of servers
D) A decrease in service time
E) All of the answers choices are correct

Question 59

During the early morning hours, customers arrive at a branch post office at the average rate of 45 per hour (exponential interarrival times), while clerks can handle transactions on an average of 4 minutes each (exponential).
What is the average number of customers waiting for service if 6 clerks are used?

A) 0
B) 0.01
C) 0.1
D) 1
E) 10

Question 60

A multiple-server queueing system with an exponential arrival rate and service time has a mean arrival rate of 4 customers per hour and a mean service time of 18 minutes per customer. The minimum number of servers required to keep the utilization factor under 1 is:

A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Question 61

A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers.
On average, how many parties of truckers are waiting to be seated?

A) 0.27.
B) 0.52.
C) 0.88.
D) 1.36.
E) 1.75.

Question 62

$\begin{array}{l}\begin{array}{|l|l|}\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\\\hline \text { High } & 3 \text { per hour } \\\hline \text { Low } & 5 \text { per hour } \\\hline\end{array}\end{array}$
$\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\\\hline \end{array}$
What is the average number of high priority items waiting in line for service?

A) 0
B) 0.24
C) 1.74
D) 1.98
E) 2.22

Question 63

$\begin{array}{l}\begin{array}{|l|l|}\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\\\hline \text { High } & 3 \text { per hour } \\\hline \text { Low } & 5 \text { per hour } \\\hline\end{array}\end{array}$
$\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\\\hline \end{array}$
What is the average time in line (in minutes) for a low priority item?

A) 2
B) 5
C) 24
D) 35
E) 54

Question 64

$\begin{array}{l}\begin{array}{|l|l|}\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\\\hline \text { High } & 3 \text { per hour } \\\hline \text { Low } & 5 \text { per hour } \\\hline\end{array}\end{array}$
$\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\\\hline \end{array}$
What is the system utilization factor?

A) 0.45
B) 0.50
C) 0.55
D) 0.65
E) 0.80

Question 65

Which of the following is not an assumption of a multiple priority queueing model?

A) Exponential interarrival times.
B) Exponential service times.
C) Customers are processed in the order of arrival.
D) Customers wait in a single line.
E) All of the answers choices are assumptions of a multiple priority queueing model.

Question 66

A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers.
On average, how much longer in minutes do parties of non-truckers spend in the system, compared to parties of truckers?

A) 4.
B) 7.
C) 11.
D) 15.
E) It is impossible to determine without more information.

Question 67

$\begin{array}{l}\begin{array}{|l|l|}\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\\\hline \text { High } & 3 \text { per hour } \\\hline \text { Low } & 5 \text { per hour } \\\hline\end{array}\end{array}$
$\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\\\hline \end{array}$
What is the average number of all items waiting in line for service?

A) 0
B) 0.24
C) 1.74
D) 1.98
E) 2.22

Question 68

$\begin{array}{l}\begin{array}{|l|l|}\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\\\hline \text { High } & 3 \text { per hour } \\\hline \text { Low } & 5 \text { per hour } \\\hline\end{array}\end{array}$
$\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\\\hline \end{array}$
What is the average time in the system (in minutes) for a high priority item?

A) 2
B) 5
C) 24
D) 35
E) 54

Question 69

For a single-server queueing system, which of the following is TRUE?
I) A high utilization factor will result in a system that performs well.
II) A high utilization factor will result in a system that performs poorly.
III) A low utilization factor will result in a system that performs efficiently.

A) I only.
B) II only.
C) III only.
D) I and II only.
E) I and III only.

Question 70

$\begin{array}{l}\begin{array}{|l|l|}\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\\\hline \text { High } & 3 \text { per hour } \\\hline \text { Low } & 5 \text { per hour } \\\hline\end{array}\end{array}$
$\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\\\hline \end{array}$
What is the overall arrival rate per hour?

A) 3
B) 4
C) 5
D) 8
E) 15

Question 71

A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers.
What is the approximate average time in minutes that truckers wait to be seated?

A) 2.7
B) 4.5
C) 8.4
D) 13.6
E) 15.8

Question 72

A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers.
What is the approximate average time in minutes that non-truckers wait to be seated?

A) 2.7
B) 4.5
C) 8.4
D) 13.6
E) 15.8

Question 73

$\begin{array}{l}\begin{array}{|l|l|}\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\\\hline \text { High } & 3 \text { per hour } \\\hline \text { Low } & 5 \text { per hour } \\\hline\end{array}\end{array}$
$\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\\\hline \end{array}$
What is the average time in the system (in minutes) for a low priority item?

A) 2
B) 5
C) 24
D) 35
E) 54

Question 74

For a single-server queueing system, which of the following is FALSE?
I) Decreasing the variability of service times improves the performance of the system.
II) Decreasing the variability of service times reduces the performance of the system.
III) Increasing the variability of arrival times improves the performance of the system.

A) I only
B) II only
C) III only
D) I and II only
E) I and III only

Question 75

A small popular restaurant at an interstate truck stop provides priority service to truckers. The restaurant has ten tables where customers may be seated. The service time averages 40 minutes once a party is seated. The customer arrival rate is 12 parties per hour, with the parties being equally divided between truckers and non-truckers.
On average, how many parties of non-truckers are waiting to be seated?

A) 0.27.
B) 0.52.
C) 0.88.
D) 1.36.
E) 1.75.

Question 76

A firm has two separate phone systems for customers to use when contacting the firm. A manager is considering combining the two systems into a single system (with the same number of total servers as the two existing systems). What is likely to be the result of this change?
I) The new system will have higher utilization of servers.
II) The new system will have longer wait times for customers.
III) The new system will have shorter wait times for customers.

A) I only.
B) II only.
C) III only.
D) I and II only.
E) II and III only.

Question 77

$\begin{array}{l}\begin{array}{|l|l|}\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\\\hline \text { High } & 3 \text { per hour } \\\hline \text { Low } & 5 \text { per hour } \\\hline\end{array}\end{array}$
$\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\\\hline \end{array}$
What is the average time in line (in minutes) for a high priority item?

A) 2
B) 5
C) 24
D) 35
E) 54

Question 78

$\begin{array}{l}\begin{array}{|l|l|}\hline \text { Priority }&\text { Average Arrival Rate (exponential interarrival times) }\\\hline \text { High } & 3 \text { per hour } \\\hline \text { Low } & 5 \text { per hour } \\\hline\end{array}\end{array}$
$\begin{array}{|l|l|}\hline Nurrber~ of~ servers:&5\\\hline Service~ rate:&2~ per~ hour ~(exponential ~service~ times)\\\hline \end{array}$
What is the average number of low priority items waiting in line for service?

A) 0
B) 0.24
C) 1.74
D) 1.98
E) 2.22