Deck 13: Queuing Analysis

Question 1

Utilization of 100% is necessary for a queuing system to reach a steady state.

Answer 1

False

Question 2

Providing quick service is an important aspect of quality customer service.

Answer 2

True

Question 3

Queuing models provide optimal solutions to waiting line problems.

Answer 3

False

Question 4

The service rate is the average time it takes to serve a customer.

Question 5

Operating characteristics describe the methods used by the service process.

Question 6

The calling population is the source of customers.

Question 7

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

Question 8

Components of a waiting line system include arrivals, servers, and the calling population.

Question 9

Queuing system operating statistics are constant over time.

Question 10

The arrival rate is most frequently described by a negative exponential distribution.

Question 11

The arrival rate is the frequency at which customers arrive at a waiting line according to a probability distribution.

Question 12

The basic single-server queuing model assumes an infinite calling population.

Question 13

Calling populations are always finite.

Question 14

Waiting lines form because people or things arrive at the servicing function, or server, faster than they can be served.

Question 15

The queue discipline is the order in which waiting customers are served.

Question 16

Queue discipline describes customers' behavior in the queue.

Question 17

As the level of service improves, the cost of service decreases.

Question 18

The most important factors to consider in analyzing a queuing system are queuing discipline, arrival and service rate, and the nature of the calling population.

Question 19

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

Question 20

The service time can often be described by the Poisson distribution.

Question 21

The ________ is the source of the customers or objects being simulated.

Question 22

If λ = 24 and μ = 30, then utilization is equal to ________.

Question 23

The arrival rate can generally be described by a(n) ________ distribution.

Question 24

The ________ is the frequency at which the customers arrive at a waiting line according to a probability distribution.

Question 25

The ________ is the average number of customers who can be served during a given time period.

Question 26

In systems with finite queue length, the service rate does not have to exceed the arrival rate.

Question 27

Server utilization in a multiple-server system is calculated the same as in a single-server system.

Question 28

Customers arrive at a candy shop every 8 minutes on average. The arrival rate is ________.

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. Utilization is ________.

Question 30

In a multiple-server system, the ratio of the mean effective service rate for the system to the arrival rate to the system must be greater than 1 for customers to be served in a reasonable time.

Question 31

A car wash with two attendants who work together as a team would be an example of a multiple-server system.

Question 32

The basic single-server model assumes that customers who arrive first are served first.

Question 33

A situation in which a mechanic is responsible for repairing a pool of fleet vehicles should be analyzed for a waiting line system with a ________ calling population

Question 34

In real-world queuing applications, the multiple-server system analysis techniques are the same whether customers wait in one line or in separate lines due to customer balking.

Question 35

The multiple-server system models have been developed on the assumption that the service times are normally distributed.

Question 36

The number of servers, c, in a multiple-server queuing system must be greater than the average queue length.

Question 37

The service time can most often be described by the ________ distribution.

Question 38

In multiple-server models, two or more servers work as a team to serve a single waiting line.

Question 39

If it takes 5 minutes to serve a customer at a fast food restaurant the service rate is ________.

Question 40

The basic single-server model assumes that arrival rates are normally distributed.

Question 41

At Joe's Pool Hall they rent tables by the hour and also rent Balabushka pool cues for purists that can't afford their own. The rental process for these cues is exhaustive and takes an hour and a half for each application. There are three leasing agents that conduct these interviews, and on average, it is one hour between customer arrivals.

-On average, how busy are the servers and how likely is it that they have nothing to do?

Question 42

Lenny, a graduate research assistant, "moonlights" at the short order counter in the student union snack bar in the evenings. He is the only one on duty at the counter during the hours he works. Arrivals to the counter seem to follow the Poisson distribution with a mean of 8 per hour. Each customer is served one at a time and the service time follows an exponential distribution with a mean of 5 minutes.
How long will a student wait in line, on average?

Question 43

A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day.
What is the average time that a snowplow is out of service?

Question 44

Lenny, a graduate research assistant, "moonlights" at the short order counter in the student union snack bar in the evenings. He is the only one on duty at the counter during the hours he works. Arrivals to the counter seem to follow the Poisson distribution with a mean of 8 per hour. Each customer is served one at a time and the service time follows an exponential distribution with a mean of 5 minutes.

-Instead of having another student help Lenny, the manager is thinking of having two lines instead. Customers will equally divide themselves between the two lines. How long will students wait in line if there's a second server? (Assume that the service time is 5 minutes.)

Question 45

As customers move through a processing center line they first wait in the reception room, then they fill in some personal information on a tablet PC once one becomes available. Finally, they head to another waiting area before submitting a sample. This queuing system is ________.

Question 46

A single-bay car wash with a Poisson arrival rate and an exponential service time has cars arriving an average of 15 minutes apart. It takes approximately 9 minutes to wash a car. What is the system utilization?

Question 47

In a single-server system, if λ = 24 and μ = 30, then W is equal to ________ minutes.

Question 48

A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day.

-Approximately how many vehicles are in the garage, waiting for repairs or being repaired?

Question 49

In a single-server system, if λ = 24 and μ = 30, then L is equal to ________.

Question 50

The number of servers multiplied by the service rate is the ________ for a multiple-server system.

Question 51

A single-channel queuing system has an average service time of 10 minutes and an average time between arrivals of 15 minutes. What is the arrival rate?

Question 52

A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day.

-On average, how long does a snowplow wait before the mechanic can begin his repair?

Question 53

In the ________ queuing system, which is a variation of the single-phase single-channel model, the service rate does not have to exceed the arrival rate.

Question 54

Movement by customers between two or more queues in a system is called ________.

Question 55

Lenny, a graduate research assistant, "moonlights" at the short order counter in the student union snack bar in the evenings. He is the only one on duty at the counter during the hours he works. Arrivals to the counter seem to follow the Poisson distribution with a mean of 8 per hour. Each customer is served one at a time and the service time follows an exponential distribution with a mean of 5 minutes.
The manager thinks that students will go elsewhere for lunch if they have to wait more than 5 minutes. Therefore he's thinking of hiring another server to help Lenny, reducing the customer service time to 4 minutes. How long will students wait in line if Lenny gets help?

Question 56

Poultry Processing processes chickens for fast food restaurants. The Majestic chickens arrive from the farms on trucks, in cages, at a rate of 8 trucks per hour according to the Poisson distribution. The quality standards of Poultry Processing require that the chickens be processed within 30 minutes, which includes the time from when the trucks arrive until the chickens are finished processing. Determine the maximum average processing rate (in truckloads per hour) that must be designed for the machine, in order to ensure that the cages will be processed, on the average, in 30 minutes or less. Assume processing time is exponentially distributed.

Question 57

________ is the act of a customer refusing to enter a service system because the wait is too lengthy.

Question 58

At Joe's Pool Hall they rent tables by the hour and also rent Balabushka pool cues for purists that can't afford their own. The rental process for these cues is exhaustive and takes an hour and a half for each application. There are three leasing agents that conduct these interviews, and on average, it is one hour between customer arrivals.

-On average how many people are waiting in line at any time and what is the average wait?

Question 59

A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 4 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 7 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day.
What is the utilization rate for the mechanic?

Question 60

In a single-server queuing system, if 10 customers arrive per hour, and 20 customers are served per hour, what is the probability that there are no customers in the system?

Question 61

In a factory, machines breakdown at an average of 6 machines per hour according to a Poisson distribution. The time a repair person takes to repair the machine is not defined by any probability distribution, but has a mean of 8 minutes and a standard deviation of 3 minutes.

-What is the probability that no machine is being fixed?

Question 62

The local grocery store consists of two cashiers. The customers arrive at the checkout according to the Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is 4 minutes and the average time between the arrivals of successive customers is 3 minutes. Assume that customers equally divide themselves between the two cashiers.
On average, how many customers are waiting in line to be served?

Question 63

The local grocery store consists of two cashiers. The customers arrive at the checkout according to the Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is 4 minutes and the average time between the arrivals of successive customers is 3 minutes. Assume that customers equally divide themselves between the two cashiers.
What is the average number of customers waiting in each line and being checked out?

Question 64

An aggressive advertising campaign increases demand for the service by 50%. By what percentage do the average queue length and average time in queue increase?

Question 65

In a bank drive-through, there is a single service window and room only for two cars to line-up to wait for service. The mean time between arrivals for drive through customers is 5 minutes. The mean time to complete a customer transaction is 3 minutes. The number of arrivals is distributed according to a Poisson distribution and the service times are exponentially distributed.

-On average, how many cars are in the system?

Question 66

In a factory, machines breakdown at an average of 6 machines per hour according to a Poisson distribution. The time a repair person takes to repair the machine is not defined by any probability distribution, but has a mean of 8 minutes and a standard deviation of 3 minutes.

-On average, how long will a machine have to wait before it is fixed?

Question 67

At Joe's Pool Hall they rent tables by the hour and also rent Balabushka pool cues for purists that can't afford their own. The rental process for these cues is exhaustive and takes an hour and a half for each application. There are three leasing agents that conduct these interviews, and on average, it is one hour between customer arrivals.

-What is the likelihood that there are three or fewer customers in the entire system? How does this compare with the likelihood of three or fewer customers in a system with the same arrival and service rates but staffed by four servers?

Question 68

A hotel is considering changing its waiting line system. In the current system, hotel guests divide themselves equally between the lines that form in front of 4 hotel clerks. The manager is considering having hotel guests wait in one line and then proceed to the next available clerk. If average service time is 10 minutes and the average number of arrivals per hour is 12 guests, determine which system results in the lowest customer waiting time.

Question 69

In a factory, machines breakdown at an average of 6 machines per hour according to a Poisson distribution. The time a repair person takes to repair the machine is not defined by any probability distribution, but has a mean of 8 minutes and a standard deviation of 3 minutes.

-On average, how many machines are waiting in line to be fixed?

Question 70

The local grocery store consists of two cashiers. The customers arrive at the checkout according to the Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is 4 minutes and the average time between the arrivals of successive customers is 3 minutes. Assume that customers equally divide themselves between the two cashiers.
How much time is a customer expected to spend waiting in line and being checked out?

Question 71

In a bank drive-through, there is a single service window and room only for two cars to line-up to wait for service. The mean time between arrivals for drive through customers is 5 minutes. The mean time to complete a customer transaction is 3 minutes. The number of arrivals is distributed according to a Poisson distribution and the service times are exponentially distributed.

-What is the probability that the system is full and new arrival must drive on?

Question 72

In a bank drive-through, there is a single service window and room only for two cars to line-up to wait for service. The mean time between arrivals for drive through customers is 5 minutes. The mean time to complete a customer transaction is 3 minutes. The number of arrivals is distributed according to a Poisson distribution and the service times are exponentially distributed.

-On average, how many customers are waiting to be served?

Question 73

A multiple channel queuing system with a Poisson arrival rate and exponential service time has an average arrival rate of 6 customers per hour and an average service time of 20 minutes per customer. What is the minimum number of servers required to avoid an overloaded system?

Question 74

The local grocery store consists of two cashiers. The customers arrive at the checkout according to the Poisson distribution and the service times are based on negative exponential distribution. The average customer service time is 4 minutes and the average time between the arrivals of successive customers is 3 minutes. Assume that customers equally divide themselves between the two cashiers.
On average, how much time will the customer spend in line waiting to be served?

Question 75

The local grocery store consists of two cashiers. The customers arrive according to a Poisson distribution and the service times are based on a negative exponential distribution. The average customer service time is 5 minutes and the average time between the arrivals of successive customers is 3 minutes. What is the probability that there are no customers in the grocery store?

Question 76

In a factory, machines breakdown at an average of 6 machines per hour according to a Poisson distribution. The time a repair person takes to repair the machine is not defined by any probability distribution, but has a mean of 8 minutes and a standard deviation of 3 minutes.

-On average, how long will a machine be down and out of service?

Question 77

In a bank drive-through, there is a single service window and room only for two cars to line-up to wait for service. The mean time between arrivals for drive through customers is 5 minutes. The mean time to complete a customer transaction is 3 minutes. The number of arrivals is distributed according to a Poisson distribution and the service times are exponentially distributed.

-What is the average time a customer spends in the system?

Question 78

In a factory, machines breakdown at an average of 6 machines per hour according to a Poisson distribution. The time a repair person takes to repair the machine is not defined by any probability distribution, but has a mean of 8 minutes and a standard deviation of 3 minutes.

-On average, how many machines are in the system either being repaired or waiting in line to be repaired?

Question 79

In a bank drive-through, there is a single service window and room only for two cars to line-up to wait for service. The mean time between arrivals for drive through customers is 5 minutes. The mean time to complete a customer transaction is 3 minutes. The number of arrivals is distributed according to a Poisson distribution and the service times are exponentially distributed.

-What is the probability that there are no vehicles in the system?

Question 80

At Joe's Pool Hall they rent tables by the hour and also rent Balabushka pool cues for purists that can't afford their own. The rental process for these cues is exhaustive and takes an hour and a half for each application. There are three leasing agents that conduct these interviews, and on average, it is one hour between customer arrivals.

-On average, how many people are either waiting in line or currently being served?