Deck 19: Supplement B Waiting Lines

Question 1

The mean of the Poisson distribution is equal to its standard deviation.

Answer 1

False

Question 2

The best example of a finite customer population is the:

A) car-buying public of an automotive manufacturer.
B) constituents in a precinct lining up to vote.
C) e-mail messages arriving at a major ISP mail server.
D) members of the Management department at your university waiting to speak to the Dean about their department chairman.

Answer 2

D

Question 3

A bank lobby with six teller windows, each with a separate line, is an example of a:

A) single-channel, single-phase arrangement.
B) single-channel, multiple-phase arrangement.
C) multiple-channel, single-phase arrangement.
D) multiple-channel, multiple-phase arrangement.

Answer 3

C

Question 4

India Sisson wants to grab a latte before heading to her marketing class, knowing that the jolt of a double tall mocha is the only thing that can possibly keep her eyes open during today's presentation on the four P's. The server is slower than molasses in January and India notes that the pace of the line won't permit her to grab her favorite seat in the back row of her class. She decides to risk marketing without a latte and leaves the line before getting served. India's behavior is best described as:

A) balking.
B) blocking.
C) reneging.
D) queuing.

Question 5

Which statement about queue structure is best?

A) Customers are more likely to feel a sense of fairness when waiting in the multiple line system than in a single line system.
B) When similarly skilled, multiple servers are available, a single line is best.
C) Customers that are in the same line must be colocated.
D) Machines needing repair are left in place and repair techs come to them; thus, the repair techs are technically the customers since they must travel to the machine.

Question 6

The calling population in a queuing problem must go to the server, that is servers do not go to the calling population.

Question 7

The owner of a desktop publishing company exclusively caters to seven loyal clients who periodically require his services. The owner has:

A) an infinite customer population of patient customers.
B) an infinite population of impatient customers.
C) a finite customer population.
D) a finite customer population with balking customers.

Question 8

A homemade-ice cream shop owner has noticed that, often, potential customers will stop outside the store, assess the wait in line, and then pass by. The shop has a(n):

A) infinite customer population with balking customers.
B) infinite customer population with reneging customers.
C) finite customer population with balking customers.
D) finite customer population with reneging customers.

Question 9

The distinction between an infinite customer population and a finite customer population is whether the:

A) potential number of customers is appreciably affected by the number of customers already in the system.
B) number of potential customers exceeds the square of the number of servers.
C) number of potential customers exceeds the number of servers raised to the power of the number of channels.
D) number of customers exceeds infinity.

Question 10

An automatic, one-lane, drive-through car wash is an example of a:

A) single-channel, single-phase arrangement.
B) single-channel, multiple-phase arrangement.
C) multiple-channel, single-phase arrangement.
D) multiple-channel, multiple-phase arrangement.

Question 11

The single, multiple, and finite waiting line models all assume that the:

A) arrival rate exceeds the service rate.
B) number of servers exceeds the number of customers.
C) number of customers exceeds the number of servers.
D) customers are patient.

Question 12

A drive-through system with one lane at a fast food restaurant where the first facility takes the order, the second takes the money, and the third provides the food is an example of a:

A) single-channel, single-phase arrangement.
B) single-channel, multiple-phase arrangement.
C) multiple-channel, single-phase arrangement.
D) multiple-channel, multiple-phase arrangement.

Question 13

Under the assumptions of waiting line models, it is impossible for management to affect the rate of customer arrivals.

Question 14

The four elements common to all waiting-line situations are a customer population, a waiting line of customers, the service facility, and a priority rule.

Question 15

A bank that dedicates one window for commercial account customers and one window for personal account channel has two channels.

Question 16

A Laundromat where there are washing machines and dryers is an example of a:

A) single-channel, single-phase arrangement.
B) single-channel, multiple-phase arrangement.
C) multiple-channel, single-phase arrangement.
D) multiple-channel, multiple-phase arrangement.

Question 17

A phase represents a single step in providing a service.

Question 18

Ed Deadbeat races to the Bursar's Office on the first day of class and notes that the line is four students long. Ed figures that the wait will be at least ten minutes and, having better uses of his time, he decides to proceed to the next item on his to-do list. Ed's behavior is best described as:

A) reneging.
B) balking.
C) blocking.
D) queuing.

Question 19

A super computer-accessory discount store often has customers who leave the checkout line before being served because of excessive waiting times. The store has a(n):

A) infinite customer population with balking customers.
B) infinite customer population with reneging customers.
C) finite customer population with balking customers.
D) finite customer population with reneging customers.

Question 20

If the customer population of a service system generates customers according to a Poisson distribution, the exponential distribution describes the probability that the next customer will arrive in the next T time periods.

Question 21

A ________ is a single step in the service process.

Question 22

Customers arrive according to a Poisson distribution. The average number of customer arrivals per hour is four. The probability that three customers will arrive in the next two hours is:

A) less than or equal to 0.015.
B) greater than 0.015 but less than or equal to 0.020.
C) greater than 0.020 but less than or equal to 0.025.
D) greater than 0.025.

Question 23

A(n) ________ selects the next customer to be served at the service facility.

Question 24

A(n) ________ is a single step in providing a service.

Question 25

Twelve customers arrive at the lunch counter at George's Happy Hog per hour and select the hickory smoked meat du jour along with a side and soda for $5. The server doubles as the cashier and can take and fill an order in three minutes on average. What is the likelihood that there is one customer in the system at the George's Happy Hog if the times can be assumed as exponentially distributed?

A) 0.24
B) 0.19
C) 0.81
D) 0.75

Question 26

Customers arrive and wait in one line single file as their documents are checked. Then they load their carry-on items on the conveyor belt for inspection. Finally, they walk through a metal detector before retrieving their carry-on items and proceeding to their departure gate. This facility is ________ channel, ________ phase.

Question 27

Customers arrive according to a Poisson distribution. The average number of customer arrivals per hour is six. The probability that four customers will arrive in the next three hours is:

A) less than or equal to 0.01.
B) greater than 0.01 but less than or equal to 0.02.
C) greater than 0.02 but less than or equal to 0.03.
D) greater than 0.03.

Question 28

Twelve customers arrive at the lunch counter at George's Happy Hog per hour and select the hickory smoked meat du jour along with a side and soda for $5. The server doubles as the cashier and can take and fill an order in three minutes on average. What is the likelihood that there are zero customers in the system at the George's Happy Hog if the times can be assumed as exponentially distributed?

A) 0.40
B) 0.25
C) 0.19
D) 0.81

Question 29

Twelve customers arrive at the lunch counter at George's Happy Hog per hour and select the hickory smoked meat du jour along with a side and soda for $5. The server doubles as the cashier and can take and fill an order in three minutes on average. What is the lowest number n such that the likelihood of n or more customers in line and receiving service is 0? Assume that the arrival and service times can be assumed as exponentially distributed.

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

Question 30

Customers are serviced at a rate of six customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than 20 minutes?

A) less than or equal to 0.70
B) greater than 0.70 but less than or equal to 0.80
C) greater than 0.80 but less than or equal to 0.90
D) greater than 0.90

Question 31

The exponential distribution is based on the assumption that each service time is ________ of those that preceded it.

Question 32

A ________ is one or more facilities required to perform a given service.

Question 33

A(n) ________ is a rule that allows a customer of higher priority to interrupt the service of another customer.

Question 34

Explain how waiting lines can develop even when the service time is a constant.

Question 35

Twelve customers arrive at the lunch counter at George's Happy Hog per hour and select the hickory smoked meat du jour along with a side and soda for $5. The server doubles as the cashier and can take and fill an order in three minutes on average. What is the likelihood that there are two customers in the system at the George's Happy Hog if the times can be assumed as exponentially distributed?

A) )33
B) )25
C) )144
D) )05

Question 36

What are the assumptions of the exponential distribution applied to the single server queuing situation? Provide examples of when these assumptions might be violated.

Question 37

The ________ distribution specifies the probability that n customers will arrive in T time periods.

Question 38

Customers are serviced at a rate of four customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than 30 minutes?

A) less than or equal to 0.50
B) greater than 0.50 but less than or equal to 0.60
C) greater than 0.60 but less than or equal to 0.70
D) greater than 0.70

Question 39

Customers are serviced at a rate of five customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than 20 minutes?

A) less than or equal to 0.75
B) greater than 0.75 but less than or equal to 0.80
C) greater than 0.80 but less than or equal to 0.85
D) greater than 0.85

Question 40

You drive your car into the parking lot of your favorite fast food establishment and get in the line for drive through service. After placing your order into the speaker, you proceed to the first window to pay, and then to the second window to pick up your meal. Since you just studied waiting lines that day in your Operations Management class, you quickly realize as you drive away that this was an example of a ________ channel ________ phase queuing system.

Question 41

With a finite-source model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in a(n):

A) increase in the utilization of the server.
B) increase in the average number of customers in the service system.
C) decrease in the average time spent in the system, including service.
D) increase in the waiting time in line.

Question 42

With a single-server model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in a(n):

A) increase in the utilization of the server.
B) increase in the average number of customers in the system.
C) decrease in the average time spent in the system, including service.
D) increase in the waiting-line time.

Question 43

The best method for analyzing a waiting-line problem is to relate the five operating characteristics and their alternatives to dollars.

Question 44

With a multiple-server model, increasing the arrival rate by 10 percent and also increasing the service rate of each server by 10 percent will result in:

A) a decrease in the utilization of the system.
B) no change in the average number of customers in the waiting line.
C) a decrease in the average number of customers in the waiting line.
D) an increase in the waiting time in line.

Question 45

With a single-server model, increasing the service rate while holding all other factors constant will:

A) increase the utilization of the server.
B) increase the time spent per customer.
C) decrease the probability that there are two customers in the system at any time.
D) decrease the arrival rate of customers.

Question 46

Comment on the tension between cost management and customer satisfaction management in a call center situation.

Question 47

Your employer is considering a choice between a single-line and a multiple-line arrangement. The operation involves multiple servers and a single-phase service. When would each arrangement be ideal?

Question 48

The standard assumption in the single-server model is that there is an infinite number of customers and that customers will wait in line as long as it takes to get served.

Question 49

What is a finite-source model? Give an example of its appropriate use.

Question 50

Customers are serviced at a rate of 10 customers per hour according to an exponential distribution. What is the probability that customer service will require fewer than two minutes?

A) less than or equal to 0.25
B) greater than 0.25 but less than or equal to 0.30
C) greater than 0.30 but less than or equal to 0.35
D) greater than 0.35

Question 51

With a single-server model, increasing the promotions for a service through advertising will most likely:

A) increase the utilization of the server.
B) decrease the average number of customers in the service system.
C) decrease the average time a customer spends in the system.
D) increase the probability that the server will be idle.

Question 52

The standard assumption in the single-server model is that customers are served according to the earliest due date, i.e., which customer needs to be finished first.

Question 53

With a single-server model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in:

A) a decrease in the utilization of the server.
B) no change in the average number of customers in the service system.
C) an increase in the average number of customers in the waiting line.
D) an increase in the waiting time in line.

Question 54

The number of customers in line and being served also relates to service efficiency and capacity.

Question 55

With a single-server model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in:

A) no change in the probability that there are n customers in the system.
B) a decrease in the average waiting time in line.
C) an increase in the average time spent in the system, including service.
D) an increase in the average number of customers in the system.

Question 56

With a single-server model, increasing the capital-to-labor ratio will most likely:

A) increase the utilization of the server.
B) have no effect on the operating characteristics because they are affected only by work-methods changes.
C) decrease the probability that there are zero customers in the system at any time.
D) decrease the average number of customers in the waiting line.

Question 57

With a finite-source model, increasing the arrival rate by 10 percent and also increasing the service rate by 10 percent will result in:

A) a decrease in the utilization of the server.
B) no change in the average number of customers in the system.
C) an increase in the average number of customers in the waiting line.
D) an increase in the waiting time in line.

Question 58

In the single-server model, the:

A) customers are assumed to arrive at constant intervals of time.
B) variability of customer arrivals is most often described by a Poisson distribution.
C) mean of the distribution of customer arrivals must be greater than the variance of customer arrivals to get meaningful results.
D) probability of n arrivals in T time periods comes from a normal distribution.

Question 59

In the single-server model, the:

A) service time of a customer is most often described by an exponential distribution.
B) service time depends on the number of customers in the system as long as there is at least one customer in the waiting line.
C) mean of the service-time distribution must be as great as the target service time for a feasible solution.
D) service times are always constant to avoid large waiting lines.

Question 60

What are priority rules? Provide examples and indicate why a manager would choose to adopt one over another.

Question 61

Scenario B.1
A single volunteer octogenarian usher can scan tickets with a handheld device and direct theater patrons to their seats at a rate of 30 per hour with an accuracy rate approaching 23%. On average, about twenty-five customers arrive every hour for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.
How many theater patrons from Scenario B.1 are either waiting in line to be seated or being seated by the volunteer octogenarian usher?

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

Question 62

Scenario B.1
A single volunteer octogenarian usher can scan tickets with a handheld device and direct theater patrons to their seats at a rate of 30 per hour with an accuracy rate approaching 23%. On average, about twenty-five customers arrive every hour for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.
When not directing patrons to their seats, the octogenarian usher in Scenario B.1 sneaks in a little knitting. If she can knit one stitch every two seconds, how many stitches can she knit in an average hour of seating patrons?

A) 200
B) 300
C) 400
D) 500

Question 63

Scenario B.4
Customers arrive at an airline ticket counter at the rate of 50 customers per hour, according to a Poisson distribution. There are three ticket agents. Customers select the first available agent from one line. Each agent can process 20 customers per hour with exponential service times.
Use the information in Scenario B.4. What is the average waiting time in line?

A) fewer than or equal to 3.5 minutes
B) greater than 3.5 minutes but fewer than or equal to 4.5 minutes
C) greater than 4.5 minutes but fewer than or equal to 5.5 minutes
D) greater than 5.5 minutes

Question 64

Scenario B.2
Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson distribution.
Use the information in Scenario B.2. What is the average number of customers in line?

A) fewer than or equal to 1.0
B) greater than 1.0 but fewer than or equal to 2.0
C) greater than 2.0 but fewer than or equal to 3.0
D) greater than 3.0

Question 65

Scenario B.6
The Jackson Machine Company has four cutting tools that need to be refurbished after an average of 30 hours, according to an exponential distribution. The single machine that refurbishes the tools needs 15 hours for each tool on the average, with exponential service times.
Use the information in Scenario B.6. What is the average utilization of the refurbishing machine?

A) less than or equal to 40 percent
B) greater than 40 percent but less than or equal to 50 percent
C) greater than 50 percent but less than or equal to 60 percent
D) greater than 60 percent

Question 66

Scenario B.1
A single volunteer octogenarian usher can scan tickets with a handheld device and direct theater patrons to their seats at a rate of 30 per hour with an accuracy rate approaching 23%. On average, about twenty-five customers arrive every hour for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.
What is the likelihood that two patrons are in the system?

A) )12
B) )17
C) )83
D) )50

Question 67

Scenario B.2
Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson distribution.
Use the information in Scenario B.2. What is the average time a customer spends in line?

A) less than or equal to 1.0 minute
B) greater than 1.0 but fewer than or equal to 2.0 minutes
C) greater than 2.0 but fewer than or equal to 3.0 minutes
D) greater than 3.0 minutes

Question 68

Scenario B.4
Customers arrive at an airline ticket counter at the rate of 50 customers per hour, according to a Poisson distribution. There are three ticket agents. Customers select the first available agent from one line. Each agent can process 20 customers per hour with exponential service times.
Use the information in Scenario B.4. What is the average time spent in the system?

A) fewer than or equal to 6.5 minutes
B) greater than 6.5 minutes but fewer than or equal to 7.5 minutes
C) greater than 7.5 minutes but fewer than or equal to 8.5 minutes
D) greater than 8.5 minutes

Question 69

Scenario B.1
A single volunteer octogenarian usher can scan tickets with a handheld device and direct theater patrons to their seats at a rate of 30 per hour with an accuracy rate approaching 23%. On average, about twenty-five customers arrive every hour for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.
The curtain goes up at 8 pm for the play "The Life and Times of A.K. Erlang." If the parameters in Scenario B.1 are at work, what's the latest a patron of the theater would want to arrive in order to be seated before the light dims, the curtain rises, and the actor playing A.K. Erlang takes his rightful place at center stage?

A) 7:58 pm
B) 7:54 pm
C) 7:50 pm
D) 7:48 pm

Question 70

Scenario B.4
Customers arrive at an airline ticket counter at the rate of 50 customers per hour, according to a Poisson distribution. There are three ticket agents. Customers select the first available agent from one line. Each agent can process 20 customers per hour with exponential service times.
Use the information in Scenario B.4. What is the average utilization of the three-agent system?

A) less than or equal to 80 percent
B) greater than 80 percent but less than or equal to 85 percent
C) greater than 85 percent but less than or equal to 90 percent
D) greater than 90 percent

Question 71

Scenario B.2
Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson distribution.
Use the information in Scenario B.2. What is the average number of customers in the system?

A) fewer than or equal to 3.0
B) greater than 3.0 but fewer than or equal to 5.0
C) greater than 5.0 but fewer than or equal to 7.0
D) greater than 7.0

Question 72

Scenario B.4
Customers arrive at an airline ticket counter at the rate of 50 customers per hour, according to a Poisson distribution. There are three ticket agents. Customers select the first available agent from one line. Each agent can process 20 customers per hour with exponential service times.
Use the information in Scenario B.4. What is the average number of customers waiting in line for service?

A) fewer than or equal to 4.0
B) greater than 4.0 but fewer than or equal to 4.5
C) greater than 4.5 but fewer than or equal to 5.0
D) greater than 5.0

Question 73

Scenario B.2
Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson distribution.
Use the information in Scenario B.2. What is the probability that a traveler will pull up to the attendant's service window without having to wait for another customer?

A) less than or equal to 0.15
B) greater than 0.15 but less than or equal to 0.25
C) greater than 0.25 but less than or equal to 0.35
D) greater than 0.35

Question 74

Scenario B.2
Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson distribution.
Use the information in Scenario B.2. How many minutes per hour is the attendant not serving customers?

A) fewer than or equal to 13
B) greater than 13 but fewer than or equal to 17
C) greater than 17 but fewer than or equal to 21
D) greater than 21

Question 75

Scenario B.6
The Jackson Machine Company has four cutting tools that need to be refurbished after an average of 30 hours, according to an exponential distribution. The single machine that refurbishes the tools needs 15 hours for each tool on the average, with exponential service times.
Use the information in Scenario B.6. What is the average waiting time of tools in line?

A) fewer than or equal to 15 hours
B) greater than 15 hours but fewer than or equal to 25 hours
C) greater than 25 hours but fewer than or equal to 35 hours
D) greater than 35 hours

Question 76

The average lead time of a unit of product through a manufacturing station is 10 minutes. The production rate has been steady at five units per hour. The average work-in-process inventory at this station is:

A) 50 units.
B) 10 units.
C) 5 units.
D) 0.83 units.

Question 77

Scenario B.1
A single volunteer octogenarian usher can scan tickets with a handheld device and direct theater patrons to their seats at a rate of 30 per hour with an accuracy rate approaching 23%. On average, about twenty-five customers arrive every hour for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.
How many theater patrons are waiting for their favorite octogenarian usher in Scenario B.1?

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

Question 78

Scenario B.2
Weary travelers arrive at Will Rogers International Airport, pick up their luggage, stumble to their cars, and proceed to the parking lot attendant to pay for their parking. Traveler interarrival times are exponentially distributed, as are the service times of the attendant. On average, travelers arrive every 25 seconds. The attendant can process three travelers per minute, and processing rates follow a Poisson distribution.
Use the information in Scenario B.2. What is the average amount of time a customer spends waiting in line and being served?

A) less than or equal to 1.0 minutes
B) greater than 1.0 minutes but fewer than or equal to 1.50 minutes
C) greater than 1.5 minutes but fewer than or equal to 2.0 minutes
D) greater than 2.0 minutes

Question 79

Scenario B.6
The Jackson Machine Company has four cutting tools that need to be refurbished after an average of 30 hours, according to an exponential distribution. The single machine that refurbishes the tools needs 15 hours for each tool on the average, with exponential service times.
Use the information in Scenario B.6. What is the probability that there will be no tools in the system?

A) less than or equal to 0.16
B) greater than 0.16 but less than or equal to 0.19
C) greater than 0.19 but less than or equal to 0.22
D) greater than 0.22

Question 80

Scenario B.1
A single volunteer octogenarian usher can scan tickets with a handheld device and direct theater patrons to their seats at a rate of 30 per hour with an accuracy rate approaching 23%. On average, about twenty-five customers arrive every hour for assistance and always wait, regardless of how long the line gets. Arrivals are governed by the Poisson distribution and service is governed by the exponential distribution.
How busy is the octogenarian usher described in Scenario B.1?

A) 74% busy
B) 83% busy
C) 91% busy
D) 100% busy