Exam 25: Waiting-Line Models

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.On average,how long does it take to service each student?

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 3.What is the average time in the system?

A college registrar's office requires you to first visit with one of three advisors and then with one of two financial professionals.This system is best described as which of the following?

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?

The ________ of a waiting line and the probability that the queue is empty add to one.

In queuing problems,which of the following probability distributions is typically used to describe the time to perform the service?

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 3.What is the average number of units in the system?

What are the components in a waiting-line system?

Study of waiting-line models helps operations managers better understand:

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

Which of the following is most likely to violate a FIFO queue?

Provide an example of a limited or finite population for a queue.

Which of the following is most likely to be served in a last-in,first-served (LIFS)queue discipline?

Balk and renege are elements of queue discipline.

Which of the following represents an unlimited queue?

The shopper who says to himself,"I've waited too long in this line.I don't really need to buy this product today," and leaves the store is an illustration of which element of arrival behavior?

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?

What does it mean to have a patient customer in a waiting line?

A waiting line model meeting the assumptions of M/M/1 has an arrival rate of 2 per hour and a service rate of 6 per hour.What is the utilization factor for the system?

Waiting-line models are useful to operations in such diverse settings as service systems,maintenance activities,and shop-floor control.