Deck 11: Queuing models

Question 1

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

Answer 1

True

Question 2

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

Answer 2

False

Question 3

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

Answer 3

True

Question 4

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

Question 5

The goal of queuing analysis is to minimize customer waiting lines

Question 6

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

Question 7

The cost of customer waiting is easy to estimate

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

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

Question 13

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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 18

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

Question 19

The standard deviation for the degenerative distribution equals zero

Question 20

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

Question 21

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

Question 22

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 23

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 above

Question 24

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 above

Question 25

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

Question 26

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 27

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

Question 28

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

Question 29

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 30

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

Question 31

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 above

Question 32

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

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

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

Question 35

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 36

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 above

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

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 39

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 40

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

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

Question 41

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 42

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 43

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 44

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 45

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 above are assumptions

Question 46

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 47

How many minutes does the average customer spend in the system?

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

Question 48

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 49

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 above

Question 50

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 51

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 52

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 53

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 above

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 average number of customers in the system with 8 servers?

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

Question 55

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 56

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 57

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 58

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 59

How many minutes does the average customer wait in line?

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

Question 60

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 61

Priority :Average Arrival Rate (exponential interarrival times)
High : 3 per hour
Low : 5 per hour
Number of servers: 5
Service rate: 2 per hour (exponential service times)
What is the overall arrival rate per hour?

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

Question 62

Priority :Average Arrival Rate (exponential interarrival times)
High : 3 per hour
Low : 5 per hour
Number of servers: 5
Service rate: 2 per hour (exponential service times)
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 63

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 64

Priority :Average Arrival Rate (exponential interarrival times)
High : 3 per hour
Low : 5 per hour
Number of servers: 5
Service rate: 2 per hour (exponential service times)
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 65

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 66

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 67

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 68

Priority :Average Arrival Rate (exponential interarrival times)
High : 3 per hour
Low : 5 per hour
Number of servers: 5
Service rate: 2 per hour (exponential service times)
What is the system utilization factor?

A)0 45
B)0 50
C)0 55
D)0 65
E)0 80

Question 69

Priority :Average Arrival Rate (exponential interarrival times)
High : 3 per hour
Low : 5 per hour
Number of servers: 5
Service rate: 2 per hour (exponential service times)
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 70

Priority :Average Arrival Rate (exponential interarrival times)
High : 3 per hour
Low : 5 per hour
Number of servers: 5
Service rate: 2 per hour (exponential service times)
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 71

Priority :Average Arrival Rate (exponential interarrival times)
High : 3 per hour
Low : 5 per hour
Number of servers: 5
Service rate: 2 per hour (exponential service times)
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 72

Priority :Average Arrival Rate (exponential interarrival times)
High : 3 per hour
Low : 5 per hour
Number of servers: 5
Service rate: 2 per hour (exponential service times)
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 73

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 74

Priority :Average Arrival Rate (exponential interarrival times)
High : 3 per hour
Low : 5 per hour
Number of servers: 5
Service rate: 2 per hour (exponential service times)
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