Deck 25: Waiting-Line Analysis

Question 1

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

Answer 1

True

Question 2

The most commonly used queuing models assume a service rate that follows an exponential distribution.

Answer 2

True

Question 3

The cost of customers waiting is always greater than the cost of increasing service capacity.

Answer 3

False

Question 4

Waiting lines occur even in underloaded systems because of variability in service rates and/or arrival rates.

Question 5

The goal of queuing analysis is to minimize the cost of customers having to wait.

Question 6

In an infinite source model,the server utilization is the ratio of the average arrival rate to the service capacity.

Question 7

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

Question 8

Average service rate is the reciprocal of the average service time.

Question 9

A system has one service facility that on an average can service 10 customers per hour.The customers arrive at a variable rate,which averages 6 per hour.In this circumstance,no waiting lines will form.

Question 10

In waiting-line analysis,queue discipline refers to the willingness of customers to wait in line for service.

Question 11

In an infinite source model,the average number being served is equal to the ratio of the average arrival rate to the average service rate.

Question 12

Queuing models discussed in the text pertain only to stable conditions.Stable conditions exist only when customers arrive at a constant rate; that is,without any variability.

Question 13

Typically customers will perceive waiting times to be less if the line continues to move.

Question 14

A multiple server system assumes that each server will have its own waiting line.

Question 15

Total queuing system costs are always minimized at the point where the costs of customers waiting are equal to the service capacity costs.

Question 16

The cost of having customers wait has to be balanced with the cost of providing service capacity.

Question 17

If customers are homogeneous (similar needs),then separate waiting lines for each server are preferable.

Question 18

For a server that already has a high utilization ratio,decreasing service capacity will only have a negligible effect on customer waiting time.

Question 19

Having separate lines for customers that are heterogeneous (different needs)can reduce the variability of service times.

Question 20

The most commonly used queuing models assume an arrival rate can be described by a Poisson distribution.

Question 21

All infinite source queuing models require the server utilization to be less than 1.0.

Question 22

A multiple server queuing system has a Poisson arrival rate of 16 per hour and exponential service time averaging 8 per hour.Server cost is $25 per hour and the cost of waiting is $40 per hour.Based on total cost,how many servers should be staffed?

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

Question 23

Infinite source queuing models basically apply only to underloaded systems in which waiting lines can form.

Question 24

In a single server,exponential service durations,and finite number in system model there are 4 customers in the system three in line and one being served.What is the probability no new customer will join the line? The probability of zero customers in the system is .40,arrival rate is 16 per hour and the service rate is 18 per hour.

A)0.1156
B)0.1987
C)0.2115
D)0.2497
E)0.3655

Question 25

All of the following are constraint management options,EXCEPT:

A)use temporary workers
B)increase waiting space
C)shift demand
D)standardize the service
E)look for a bottleneck

Question 26

The finite-source queuing model is appropriate when the potential calling population is relatively small.

Question 27

A multiple server queuing system has a Poisson arrival rate of 9 per hour and exponential service time averaging 5 per hour.Server cost is $100 per hour and the cost of waiting is $360 per hour.Based on total cost,how many servers should be staffed?

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

Question 28

In a single server,exponential service durations,and finite number in system model there are 4 customers in the system three in line and one being served.What is the probability no new customer will join the line? The probability of zero customers in the system is .375,arrival rate is 18 per hour and the service rate is 24 per hour.

A)0.093
B)0.1187
C)0.256
D)0.289
E)0.311

Question 29

Compared to a single server system with exponential service time,the same system with a constant service time will have an average of one-half the number of customers waiting in the system.

Question 30

Compared to a single server system with exponential service time,a single server system with a constant service time causes a reduction of 50 percent in the average number waiting in line.

Question 31

A queuing system has four work stations with three workers to staff each station.To analyze this system,the number of "servers" is:

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

Question 32

A major difference between the finite and infinite source queuing models is that the customer arrival rate in a finite situation is dependent on the length of the waiting line.

Question 33

In an infinite source model,the average time in line is equal to the average number of customers in line divided by the average arrival rate.

Question 34

If wait times are too long managers can relegate some customers to lower priority classes.

Question 35

Studies have shown a difference between the actual time customers spend waiting and their perceived time.

Question 36

In waiting lines,reneging occurs when a customer does not join the line because it is too long.

Question 37

Infinite-source queuing models assume average arrival and service rates are stable.

Question 38

In waiting lines,what is the term used when customers become impatient from waiting and leave the line?

A)balking
B)premature exit
C)failure
D)reneging
E)service failure

Question 39

The reciprocal of the average rate of arrivals is the average interarrival time.

Question 40

The multiple server queuing table cannot be applied to single server systems.

Question 41

When the cost incurred by all customers is not the same,an appropriate queuing model is:

A)single server,single phase.
B)single server,two phases.
C)multiple server,single priority.
D)multiple server,multiple phase.
E)multiple server,with priority.

Question 42

Which of the following is not an assumption of an infinite source,multiple servers with priority queuing model?

A)Poisson arrival rates
B)Poisson service rates
C)Customers are processed in order of arrival.
D)Customers wait in a single line.
E)A unit with a low priority could conceivably wait a rather long time for processing.

Question 43

Why is there waiting in a queue even if the service capacity exceeds the average demand on the system?

A)Poor scheduling
B)Slow service
C)Low utilization
D)Variability in arrival and service rates
E)Multiple phase processing

Question 44

Which of these would increase server utilization?

A)An increase in the average service rate.
B)An increase in average arrival rate.
C)An increase in the number of servers.
D)A decrease in service time.
E)An increase in server cost.

Question 45

Which of the following is not a disadvantage of a single line for a multiple server queuing system?

A)It might appear too long for customers.
B)It increases average wait time for customers.
C)It may take up too much space.
D)Customers can't choose their favourite server.
E)Servers may not work as fast as if they were responsible for their own line.

Question 46

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 served.
D)the reason waiting occurs in underutilized systems.
E)an overloaded system.

Question 47

A multiple server queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 4 customers per hour and an average service time of 18 minutes per customer.The minimum number of servers required to avoid an overloaded system is:

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

Question 48

The basic multiple-server-with-priority queuing model assumes that:

A)arrival rates are exponentially distributed.
B)service times are Poisson distributed.
C)items are serviced in order of arrival.
D)items are serviced in order of priority class.
E)service activities are pre-emptive.

Question 49

The goal of queuing analysis is to minimize:

A)the sum of customer waiting costs and costs of providing capacity.
B)the sum of customer waiting time and service time.
C)costs of providing capacity.
D)customer waiting time.
E)the number of servers,service cost.

Question 50

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 be underloaded is:

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

Question 51

A single server queuing 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 average arrival rate will remain the same.The effect will be to:

A)increase utilization.
B)decrease utilization.
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

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)The arrival rate decreases.

Question 53

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

A)24
B)40
C)67
D)2.50
E)60

Question 54

All of the following are characteristics of the waiting line system that affect the choice of the queuing model EXCEPT:

A)potential number of customers.
B)order of service (queue discipline).
C)cost of service.
D)arrival and service patterns.
E)number of servers.

Question 55

If a manager increases server utilization (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)There is no change in the time.

Question 56

A basic difference between infinite source and finite source queuing models is:

A)the number of servers.
B)the average waiting time.
C)the average arrival rate.
D)the potential number of customers.
E)the processing rate.

Question 57

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

A)The average number waiting in line
B)The average number in the system
C)Server utilization
D)The probability that an arriving customer will have to wait for service
E)The average service time

Question 58

A single server queuing system has an average service time of eight minutes and an average time between arrivals of 10 minutes.The average 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 59

Which one of the following measures of system performance is a key measure?

A)The average number of customers waiting in line.
B)The average time customers wait in line.
C)The average time customers are in the system.
D)The average number of customers in the system.
E)The probability that an arrival will have to wait for service.

Question 60

A single phase queuing system is one which has a single:

A)type of customer (homogeneous).
B)server.
C)customer being served.
D)operational step.
E)time all customers wait.

Question 61

The following questions refer to this data for a multiple server,priority service queuing model:
What is average time in the system for a low priority item?

Question 62

A bank is designing a new branch office and needs to determine how much driveway space to allow for cars waiting for drive up teller service.The drive up service will have three tellers and a single waiting line.At another branch of the bank in a similar setting,the average service time for drive up tellers is 4 minutes per customer and average arrival rate is 36 customers per hour.It is expected that the new bank will have similar characteristics. How many spaces should be provided to have a 96% probability of accommodating all of the waiting cars?

A)10
B)12
C)14
D)16
E)18

Question 63

The following questions refer to this data for a multiple server,priority service queuing model:

Question 64

A bank of ten machines requires regular periodic service.Machine running time and service time are both exponential.Machines run for an average of 44 minutes between service requirements,and service time averages 6 minutes per machine. What is the average machine downtime with two operators?

A)1.71 minutes
B)3.46 minutes
C)6.25 minutes
D)7.71 minutes
E)9.46 minutes

Question 65

The following questions refer to this data for a multiple server,priority service queuing model:
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Question 66

A bank of ten machines requires regular periodic service.Machine running time and service time are both exponential.Machines run for an average of 44 minutes between service requirements,and service time averages 6 minutes per machine. What is the average number of machines down with one operator?

A)1.49
B)3.35
C)4.40
D)6.65
E)8.51

Question 67

The following questions refer to this data for a multiple server,priority service queuing model:

Question 68

A bank is designing a new branch office and needs to determine how much driveway space to allow for cars waiting for drive up teller service.The drive up service will have three tellers and a single waiting line.At another branch of the bank in a similar setting,the average service time for drive up tellers is 4 minutes per customer and average arrival rate is 36 customers per hour.It is expected that the new bank will have similar characteristics. What is the expected average number of cars in the system?

A)approx.2.6
B)approx.5.0
C)approx.2.3
D)approx.1.8
E)approx.4.2

Question 69

The following questions refer to this data for a multiple server,priority service queuing model:
What is the average number of all items waiting in line for service?

Question 70

The following questions refer to this data for a multiple server,priority service queuing model:
What is the overall average arrival rate?

Question 71

A bank is designing a new branch office and needs to determine how much driveway space to allow for cars waiting for drive up teller service.The drive up service will have three tellers and a single waiting line.At another branch of the bank in a similar setting,the average service time for drive up tellers is 4 minutes per customer and average arrival rate is 36 customers per hour.It is expected that the new bank will have similar characteristics. What is the average time that a customer would have to wait in line before being served?

A)4.3 minutes
B)8.3 minutes
C)2.7 minutes
D)6.7 minutes
E)8.3 minutes

Question 72

A bank is designing a new branch office and needs to determine how much driveway space to allow for cars waiting for drive up teller service.The drive up service will have three tellers and a single waiting line.At another branch of the bank in a similar setting,the average service time for drive up tellers is 4 minutes per customer and average arrival rate is 36 customers per hour.It is expected that the new bank will have similar characteristics. By how much would the average time in the system increase if only two tellers were on duty?

A)approx.4 minutes
B)approx.10 minutes
C)approx.6 minutes
D)The lines would become infinitely long.
E)It is impossible to say without more information.

Question 73

A bank is designing a new branch office and needs to determine how much driveway space to allow for cars waiting for drive up teller service.The drive up service will have three tellers and a single waiting line.At another branch of the bank in a similar setting,the average service time for drive up tellers is 4 minutes per customer and average arrival rate is 36 customers per hour.It is expected that the new bank will have similar characteristics. For how many tellers should the system be designed if the managers want the average time a customer spends in the system to be no more than 5 minutes?

A)at least 3
B)at least 4
C)at least 5
D)at least 6
E)It is impossible to say without more information.

Question 74

The following questions refer to this data for a multiple server,priority service queuing model:
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Question 75

A manager assembled the following information about an infinite source waiting line system: 5 servers,an arrival rate of 6 per hour,and a service time of 20 minutes.The manager has determined that the average number of customers waiting for service is .04.Determine each of the following:
(i)the server utilization
(ii)the average waiting time in line in minutes
(iii)the average time in the system
(iv)the average number in the system

Question 76

The following questions refer to this data for a multiple server,priority service queuing model:
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Question 77

A bank of ten machines requires regular periodic service.Machine running time and service time are both exponential.Machines run for an average of 44 minutes between service requirements,and service time averages 6 minutes per machine. What is the probability that a machine will have to wait for service with two operators?

A)654
B)090
C)346
D)910
E)016

Question 78

The following questions refer to this data for a multiple server,priority service queuing model:
What is average time in line for a high priority item?

Question 79

A bank of ten machines requires regular periodic service.Machine running time and service time are both exponential.Machines run for an average of 44 minutes between service requirements,and service time averages 6 minutes per machine. If operators cost $15 per hour in wages and fringe benefits and machine downtime costs $75 per hour in lost production,what is the optimal number of operators for this bank of machines?

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