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Exam 25: Queuing Models

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Question 51

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Four of the most widely used waiting line models-M/M/1 or A,M/M/S or B,M/D/1 or C,and Limited population or D-all share which of the following three characteristics?

A) normal arrivals,FIFO discipline,and normal service times
B) Poisson arrivals,FIFO discipline,and a single-service phase
C) Poisson arrivals,FIFO discipline,and exponential service times
D) Poisson arrivals,no queue discipline,and exponential service times
E) Poisson arrivals,single-server,and FIFO discipline

F) C) and D)
G) A) and B)

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Question 52

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Service times in an automobile repair shop tend to follow which probability distribution?

A) exponential
B) normal
C) triangular
D) binomial
E) Erlang

F) All of the above
G) B) and D)

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Question 53

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Which of the following is a requirement for application of Little's Law to be valid?

The two characteristics of the waiting line itself are whether its length is limited or unlimited and the discipline of the people or items in it.

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 8.The average number in the system Ls is ________ and the utilization of the system is ________.

A(n)________ occurs when an arrival refuses to enter a waiting line;a(n)________ occurs when an arrival joins a waiting line,then leaves it before being served.

The greater the margin by which the arrival rate exceeds the service rate,the better the performance of the waiting line.

A waiting line,or queuing,system has three parts,which are:

A McDonald's single-lane drive-through that has one window for making the payment and a second window for receiving the food behaves most like which of the following?

A dental clinic at which only one dentist works is open only two days a week.During those two days,patients arrive at the rate of three per hour.The doctor serves patients at the rate of one every 15 minutes. a.What is the probability that the clinic is empty (except for the dentist and staff)? b.What percentage of the time is the dentist busy? c.What is the average number of patients in the waiting room? d.What is the average time a patient spends in the office (wait plus service)? e.What is the average time a patient waits for service?

In the analysis of queuing models,the Poisson distribution often describes arrival rates,while service times are often described by the negative exponential distribution.

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 8 vehicles per day (approximately Poisson in nature).The mechanic crew can service an average of μ= 11 vehicles per day with a repair time distribution that approximates an exponential distribution.The crew cost is approximately $300 per day.The cost associated with lost productivity from the breakdown is estimated at $150 per vehicle per day (or any fraction thereof).Which is cheaper,the existing system with one service crew,or a revised system with two service crews?

A manufacturing plant is trying to determine how long the average line for a repair process will be.If 10 machines arrive each hour and must wait 6 minutes in the line,how long will the line be,on average?

Which of the following occurs as the level of service decreases?

Which of the following is NOT an assumption of the M/M/1 model?

A waiting-line system that meets the assumptions of M/M/1 has λ = 1,μ = 4.For this system,what is the probability of more than two units in the system?

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1.Units arrive at this system every 12 minutes on average.Service takes a constant 8 minutes.What is the average number in the system Ls in units?

Which of the following is a measure of queue performance?

Suppose that 1 customer arrives each minute in a Poisson distribution.Is it more likely that 2 customers or 0 customers will arrive each minute?

Balk and renege are elements of queue discipline.