Deck 26: Waiting Line Models

Question 1

11)High level of service often results in ______.

A)higher capacity related costs and lower waiting time costs
B)lower capacity related costs and higher waiting time costs
C)lower capacity related costs and lower waiting time costs
D)higher capacity related costs and higher waiting time costs

Answer 1

A

Question 2

17)The number of patients assigned to a doctor is an example of ______.

A)limited population source
B)constant population source
C)infinite population source
D)discrete population source

Answer 2

A

Question 3

5)Which of the following is one of the components of total costs involved with managing waiting lines?

A)Costs related to raw materials
B)Costs related to work-in-process inventory
C)Costs related to customer waiting time
D)Costs related to customer arrival rate

Answer 3

C

Question 4

9)In waiting line systems,the cost of service levels provided are ______ to capacity-related costs.

A)directly related
B)linear
C)inversely related
D)proportional

Question 5

2)The primary objective of managing waiting lines is to ______ throughout any service or manufacturing facility.

A)maximize total costs
B)minimize total costs
C)maximize total time
D)minimize production volume

Question 6

14)In ______,a mathematical model of a waiting line system is constructed so that the length of the queues and their associated waiting times can be predicted.

A)queuing theory
B)waiting line theory
C)queue analysis
D)game theory

Question 7

16)Toll booths on expressways,banks on busy streets,and theme parks are examples of ______.

A)finite population source
B)infinite population source
C)limited population source
D)constant population source

Question 8

6)Consider a scenario in which customers decide not to wait and receive service from a competitor.The lost sales are an example of ______.

A)tangible costs
B)fixed costs
C)recurring costs
D)intangible costs

Question 9

7)Wages paid to workers while the facility remains idle because of machine repair or lack of parts in an example of ______.

A)recurring costs
B)maintenance costs
C)intangible costs
D)tangible costs

Question 10

3)The total cost throughout any service or manufacturing facility consists of ______ components.

A)two
B)three
C)four
D)five

Question 11

18)______ population source theoretically represents systems that potentially have a large number of possible customers.

A)Limited
B)Constant
C)Infinite
D)Discrete

Question 12

13)______ represents a certain number of customers waiting for service at a facility.

A)Queue
B)Service level
C)Service capacity
D)Arrival rate

Question 13

15)In queuing theory models,the customers that potentially need service can be considered as arriving from ______.

A)finite population only
B)infinite population only
C)finite and infinite population
D)limited population only

Question 14

19)______ describes the way customers arrive at the service system.

A)Arrival pattern
B)Arrival rate
C)Interarrival time
D)Service time

Question 15

20)Which of the following statements is FALSE about random arrivals?

A)The exact time when a customer will arrive cannot be predicted.
B)Arrivals of customers are independent of each other.
C)Arrivals at most service facilities are random.
D)Arrivals of customers are dependent on each other.

Question 16

4)Waiting lines cause ______ and ______ costs.

A)fixed and variable
B)fixed and recurring
C)tangible and intangible
D)capacity and demand

Question 17

8)______ costs are incurred in order to maintain existing facility capacity or add additional capacity to provide the required service.

A)Customer waiting time-related
B)Capacity related
C)Manufacturing
D)Service

Question 18

1)Which of the following statements is FALSE about customer waiting lines?

A)A waiting line occurs when customers arrive at a service facility at random rather than at predictable intervals.
B)A waiting time for a customer is dependent on the number of people waiting for service ahead of that customer.
C)Waiting lines can only be physical,with customers waiting in line for service.
D)The time it takes to service a customer varies,as each customer's need for service is often unique.

Question 19

10)Low level of service often results in ______.

A)higher customer satisfaction
B)longer waiting lines
C)lower waiting time cost
D)higher capacity-related costs

Question 20

12)The branch of mathematics that deals with the study and analysis of waiting lines is known as ______.

A)queuing theory
B)waiting line theory
C)queue analysis
D)game theory

Question 21

29)In waiting line problems,the interarrival time is assumed to follow a probability distribution known as ______.

A)Poisson distribution
B)binomial distribution
C)normal distribution
D)negative exponential distribution

Question 22

32)______ refers to the order in which customers waiting in line receive service at the facility.

A)Queue discipline
B)Queue size
C)Service pattern
D)Interarrival rate

Question 23

34)______ is the design or structure of the service system.

A)Service pattern
B)Queue discipline
C)Service system structure
D)Phase design

Question 24

38)An airport check-in and security-service system is an example of ______ structure.

A)single channel,single-phase
B)single channel,multiphase
C)multichannel,multiphase
D)multichannel,single-phase

Question 25

37)There are ______ basic service system structures based on the number of channels and phases.

A)three
B)four
C)five
D)six

Question 26

39)In ______,______ structure,the customer joins a single waiting line but receives service in multiple phases.

A)single channel,single-phase
B)single channel,multiphase
C)multichannel,multiphase
D)multichannel,single-phase

Question 27

22)When a variable's outcomes take on numerical values that can be counted ,the variable is known as a(n)______.

A)discrete random variable
B)random variable
C)continuous random variable
D)independent variable

Question 28

35)______ refers to the total number of counters,service bays,or other providers that are part of the system.

A)Number of phases
B)Number of channels
C)Number of queues
D)Number of service systems

Question 29

30)______ is a probability distribution that describes the time between events in a process in which events occur continuously and independently at a constant average rate.

A)Poisson distribution
B)binomial distribution
C)normal distribution
D)negative exponential distribution

Question 30

26)The mathematical expression for the Poisson distribution is shown as P(x)= e⁻λλˣ/x! The term λ stands for ______.

A)probability of arrivals
B)number of arrivals per unit of time
C)expected or average arrival rate
D)total arrival time

Question 31

28)______ is the elapsed time between one customer arrival and the next.

A)Arrival pattern
B)Arrival rate
C)Interarrival time
D)Service time

Question 32

25)The mathematical expression for the Poisson distribution is shown as P(x)= e⁻λλˣ/x! The term x stands for ______.

A)probability of arrivals
B)number of arrivals per unit of time
C)expected or average arrival rate
D)total arrival time

Question 33

27)Assume the average arrival rate at a service center is five customers per hour.Determine the probability of three customers arriving in any random hour.

A)4%
B)5%
C)10%
D)14%

Question 34

21)______ is the number of customer arrivals per unit of time.

A)Arrival pattern
B)Arrival rate
C)Interarrival time
D)Service time

Question 35

24)In waiting line problems,the arrival rate is typically described by a discrete probability distribution known as ______.

A)Poisson distribution
B)binomial distribution
C)normal distribution
D)positive exponential distribution

Question 36

23)If 50 customers arrive at a teller window in a bank during a 5-hour period,then the arrival rate is ______.

A)250 customers per hour
B)10 customers per hour
C)five customers per hour
D)50 customers per hour

Question 37

40)The number of customers served per unit of time is called ______.

A)service rate
B)service time
C)arrival rate
D)interarrival rate

Question 38

31)______ limit the size or length of a finite queue.

A)Capacity constraints
B)Demand constraints
C)Service constraints
D)Time constraints

Question 39

36)______ refers to the number of service stops that each customer must make in sequential servers to complete the required service.

A)Number of phases
B)Number of channels
C)Number of queues
D)Number of service systems

Question 40

33)Which of the following is the most commonly used queue disciplines?

A)last in,first out
B)first in,first out
C)random order
D)alphabetical order of last names

Question 41

54)Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.Determine the probability of exactly five customers in the system.

A)4.50%
B)6.70%
C)5.60%
D)3.80%

Question 42

43)A waiting line grows infinitely long when ______.

A)service rate is greater than arrival rate
B)arrival rate is greater than service rate
C)service rate is equal to arrival rate
D)arrival rate is stable

Question 43

49)In queuing models,if the service rate forms a Poisson distribution,then the service times have a ______.

A)binomial distribution
B)positive exponential distribution
C)Poisson distribution
D)negative exponential distribution

Question 44

51)Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.Determine the percentage of time the employee at the service booth will be idle.

A)17%
B)44%
C)12%
D)43%

Question 45

41)In waiting line problems,the service rate is assumed to follow a probability distribution known as ______.

A)discrete Poisson distribution
B)binomial distribution
C)normal distribution
D)negative exponential distribution

Question 46

46)Which of the following is NOT one of the commonly used measures of the queuing model?

A)average number of customers waiting in line
B)average time a customer spends waiting in line for service
C)average value of transaction by the customer
D)capacity utilization factor for the system

Question 47

57)Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.It is estimated that the cost of customer waiting time associated with dissatisfied customers and loss of goodwill is $15 per hour.The employee at the service booth is paid $10 an hour.Determine the capacity related cost per day for the waiting line system.Assume total hours of operation as 10 hours per day.

A)$725
B)$625
C)$500
D)$100

Question 48

52)Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.Determine the average number of customers waiting in line.

A)3.23 customers
B)4.17 customers
C)8 customers
D)7.65 customers

Question 49

60)An automatic car wash with a single bay takes a constant 3 minutes to wash.The arrival rate is 10 cars per hour.Determine the average time a car spends in the system.The arrival rate of cars tends to follow a Poisson distribution.

A)5 minutes
B)6 minutes
C)3.5 minutes
D)4.5 minutes

Question 50

42)In waiting line problems,the service time is assumed to follow a probability distribution known as ______.

A)discrete Poisson distribution
B)binomial distribution
C)normal distribution
D)negative exponential distribution

Question 51

48)In the notation used to identify the single-channel queuing model (M/M/1),the second M refers to ______.

A)Poisson distribution of arrival rates
B)Poisson distribution of service rates
C)single channel or server
D)constant service rate

Question 52

47)Which of the following assumptions is FALSE about the single-server queuing model?

A)The size of the queue is infinite.
B)Average arrival rates remain constant over time.
C)Arrival rates follow a negative exponential distribution.
D)It uses first-in,first-out (FIFO)queue discipline.

Question 53

50)Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.Determine the capacity utilization for the system.

A)56%
B)78%
C)83%
D)98%

Question 54

44)Let us assume the average number of customers served per hour is five customers.What is the probability that the service exceeds 15 minutes for any customer?

A)29%
B)76%
C)45%
D)13%

Question 55

55)Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.It is estimated that the cost of customer waiting time associated with dissatisfied customers and loss of goodwill is $12 per hour.The employee at the service booth is paid $8 an hour.Determine the average customer waiting time cost per day in the queue.Assume total hours of operation as 10 hours per day.

A)$599
B)$625
C)$500
D)$700

Question 56

56)Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.It is estimated that the cost of customer waiting time associated with dissatisfied customers and loss of goodwill is $15 per hour.The employee at the service booth is paid $10 an hour.Determine the total expected cost per day for the waiting line system.Assume total hours of operation as 10 hours per day.

A)$725
B)$625
C)$500
D)$100

Question 57

58)In the notation used to identify the single-channel,constant service rate queuing model M/D/1,the letter D refers to ______.

A)Poisson distribution of arrival rates
B)Poisson distribution of service rates
C)single channel or server
D)constant service rate

Question 58

59)An automatic car wash with a single bay takes a constant 3 minutes to wash.The arrival rate is 10 cars per hour.Determine the average number of cars waiting in line for the car wash.The arrival rate of cars tends to follow a Poisson distribution.

A)0.25 cars
B)0.5 cars
C)1 car
D)1.5 cars

Question 59

45)Let us assume the average number of customers served per hour is five customers.What is the probability that the service exceeds 1 hour for any customer?

A)0.67%
B)1.23%
C)0.98%
D)9.00%

Question 60

53)Customers at an amusement park arrive at the rate of 10 customers per hour.The entry booth is staffed by one employee.The mean service time at the booth to provide service to each customer is 5 minutes.The arrival rate follows a Poisson distribution,and the service time at the booth follows a negative exponential distribution.Determine the average time a customer spends in the system.

A)30 minutes
B)20 minutes
C)45 minutes
D)15 minutes

Question 61

80)ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the cost savings of having two technicians as compared to one technician.

A)$320.50
B)$100.50
C)$162.50
D)$175.00

Question 62

76)ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the average cost per hour of downtime.

A)$500.34
B)$532.50
C)$234.50
D)$675.50

Question 63

71)Let us consider that customers arrive at the rate of seven per hour and wait for an average 0.25 hour in a shop.Using Little's law,determine the average number of customers in the queuing system.

A)2
B)2.4
C)1.25
D)1.75

Question 64

78)ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the average number of machines working if the number of technicians is equal to two.

A)3.72
B)3.21
C)2.32
D)1.32

Question 65

66)The owner of an amusement park has decided to open a second entry booth and hire another employee to service customers entering the park.Customers arrive at the rate of 20 per hour and will wait in a single line until one of the two employees is available to provide service.The average service time of both employees is 2 minutes to provide service.The arrival rate follows Poisson distribution,and the service time follows a negative exponential distribution.Determine the average time the customer spends in the system.

A)2.25 minutes
B)3 minutes
C)0.25 minutes
D)1 minute

Question 66

64)The owner of an amusement park has decided to open a second entry booth and hire another employee to service customers entering the park.Customers arrive at the rate of 20 per hour and will wait in a single line until one of the two employees is available to provide service.The average service time of both employees is 2 minutes to provide service.The arrival rate follows Poisson distribution,and the service time follows a negative exponential distribution.Determine the average number of customers waiting in line.

A)0.75
B)0.89
C)0.08
D)0.98

Question 67

73)Which of the following statements is FALSE about finite population queuing model?

A)Arrival rates have a Poisson distribution.
B)Services time has a negative exponential distribution.
C)Length of the queue has an impact on the arrival rate.
D)Arrival rate is independent of the length of the queue.

Question 68

70)In queuing theory,______ means that the number of customers or objects in a waiting line system is the same as the number of customers or objects leaving the system-the arrival rate is equal to the service rate.

A)equilibrium
B)steady state
C)FIFO state
D)stable state

Question 69

72)Suppose an item stays in an inventory system for an average of 8 days,and the demand rate for this item is 15 units per day.Determine the average inventory level for this item.

A)100
B)80
C)120
D)150

Question 70

61)The notation M/M/S is a representation of which of the following models?

A)single-channel or single-server queuing model
B)single-channel,constant service rate queuing model
C)multiple-channel or multiple-server queuing model
D)finite population queuing model

Question 71

62)The owner of an amusement park has decided to open a second entry booth and hire another employee to service customers entering the park.Customers arrive at the rate of 20 per hour and will wait in a single line until one of the two employees is available to provide service.The average service time of both employees is 2 minutes to provide service.The arrival rate follows Poisson distribution,and the service time follows a negative exponential distribution.Determine the probability that no customers are there in the system.

A)50%
B)60%
C)70%
D)45%

Question 72

77)ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the total cost per hour.

A)$550.34
B)$582.50
C)$284.50
D)$725.50

Question 73

65)The owner of an amusement park has decided to open a second entry booth and hire another employee to service customers entering the park.Customers arrive at the rate of 20 per hour and will wait in a single line until one of the two employees is available to provide service.The average service time of both employees is 2 minutes to provide service.The arrival rate follows Poisson distribution,and the service time follows a negative exponential distribution.Determine the average number of customers waiting in the system.

A)0.75
B)0.89
C)0.08
D)0.98

Question 74

68)The owner of an amusement park has decided to open a second entry booth and hire another employee to service customers entering the park.Customers arrive at the rate of 20 per hour and will wait in a single line until one of the two employees is available to provide service.The average service time of both employees is 2 minutes to provide service.T The arrival rate follows Poisson distribution,and the service time follows a negative exponential distribution.It is estimated that the cost of customer waiting time associated with dissatisfied customers and loss of goodwill is $20 per hour.The employee at the service booth is paid $10 an hour.Determine the customer waiting time cost per day for the waiting line system.Assume total hours of operation as 10 hours per day.

A)$16.67
B)$17.67
C)$15.67
D)$14.56

Question 75

67)The owner of an amusement park has decided to open a second entry booth and hire another employee to service customers entering the park.Customers arrive at the rate of 20 per hour and will wait in a single line until one of the two employees is available to provide service.The average service time of both employees is 2 minutes to provide service.T The arrival rate follows Poisson distribution,and the service time follows a negative exponential distribution.Determine the average time the customer spends in the queue.

A)2.25 minutes
B)3 minutes
C)0.25 minutes
D)1 minute

Question 76

79)ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the average cost per hour of downtime if number of technicians is equal to two.

A)$234
B)$432
C)$320
D)$345

Question 77

69)The owner of an amusement park has decided to open a second entry booth and hire another employee to service customers entering the park.Customers arrive at the rate of 20 per hour and will wait in a single line until one of the two employees is available to provide service.The average service time of both employees is 2 minutes to provide service.The arrival rate follows Poisson distribution,and the service time follows a negative exponential distribution.It is estimated that the cost of customer waiting time associated with dissatisfied customers and loss of goodwill is $20 per hour.The employee at the service booth is paid $10 an hour.Determine the total expected cost per day for the waiting line system.Assume total hours of operation as 10 hours per day.

A)$226.67
B)$245.67
C)$216.67
D)$234.21

Question 78

75)ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the average number of machines that will break down.

A)1.41
B)2.13
C)1.57
D)2.46

Question 79

74)ABS specializes in repair and maintenance of industrial machines.One repair technician has been assigned to five identical grinding machines for repair and maintenance.The machine breaks down after about 20 hours of use,and breakdowns have a Poisson probability distribution.It takes 6 hours to repair a machine,and repair times follow an exponential distribution.Machine downtime costs the company $250 an hour,and the technician is paid $50 an hour.Determine the average number of machines working.

A)3.59
B)2.87
C)3.43
D)2.54

Question 80

63)The owner of an amusement park has decided to open a second entry booth and hire another employee to service customers entering the park.Customers arrive at the rate of 20 per hour and will wait in a single line until one of the two employees is available to provide service.The average service time of both employees is 2 minutes to provide service.The arrival rate follows Poisson distribution,and the service time follows a negative exponential distribution.Determine the probability that an arriving customer will wait for service.

A)16.67%
B)34.54%
C)12.32%
D)11.56%