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Exam 21: Waiting-Line Models

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Question 31

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Why must the service rate be greater than the arrival rate in a single-channel system?

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If the service rate is not gre...

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Question 32

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In queuing problems, which of the following probability distributions is typically used to describe the number of arrivals per unit of time?

A) binomial
B) normal
C) Poisson
D) exponential
E) lognormal

F) A) and C)
G) B) and E)

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Question 33

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A(n) ________ queuing system has one line and one server.

A waiting-line system with one waiting line and three sequential processing stages is a multichannel single-phase system.

A crew of mechanics at the Highway Department garage repair vehicles that break down at an average of λ = 7.5 vehicles per day (approximately Poisson in nature). The mechanic crew can service an average of μ = 10 vehicles per day with a repair time distribution that approximates an exponential distribution. a. What is the utilization rate for this service system? b. What is the average time before the facility can return a breakdown to service? c. How much of that time is spent waiting for service? d. How many vehicles are likely to be in the system at any one time?

"Women and children first!" declares the captain of a sinking ship. His directive employs which of the following queue disciplines in disembarking passengers?

A manufacturing plant is trying to determine how long the average line for a repair process will be. If 12 machines arrive each hour and must wait 8 minutes in the line, how long will the line be, on average?

What is the waiting-line problem? Why is it important to operations?

If the food service for the university operates a cafeteria with a single serving line, that system behaves most like a

Customers take a number as they join the waiting line of the customer service counter at a discount store. There are two customer service agents. Provide the most likely characteristics of this system. a. name of model b. number of channels c. number of phases d. arrival rate distribution e. service time distribution f. population size g. queue discipline

Students arrive randomly at the help desk of a computer lab. There is only one service agent, and the service time varies from one student to the other. Provide the most likely characteristics for this system. a. name of model b. number of channels c. number of phases d. arrival rate distribution e. service time distribution f. population size g. queue discipline

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 = 10 vehicles per day with a repair time distribution that approximates an exponential distribution. a. What is the probability that the system is empty? b. What is the probability that there is precisely one vehicle in the system? c. What is the probability that there is more than one vehicle in the system? d. What is the probability of 5 or more vehicles in the system?

If the service time within a queuing system is constant, the service rate can be easily described by a negative exponential distribution.

You have seen that, in an M/D/1 problem, the average queue length is exactly one-half the average queue length of an otherwise identical M/M/1 problem. Are all other performance statistics one-half as large also? Explain.

Students arrive randomly at the help desk of the computer lab. There is only one service agent, and the time required for inquiry varies from student to student. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 students per hour, and the average service rate is 20 students per hour. What is the average service time for this problem?

Why does it matter whether a population of arrivals is limited or unlimited? Compose your answer in a well-organized, convincing paragraph.

The study of waiting lines calculates the cost of providing good service but does not value the cost of customers' waiting time.

A waiting line or ________ is where items or people are in a line awaiting service; ________ is a body of knowledge about waiting lines.

A(n) ________ queuing system is one in which the customer receives service from only one station and then exits the system.

An airline ticket counter, with several agents for one line of customers, is an example of a