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Exam 25: Queuing Models

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Question 1

True/False

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A hospital emergency room always follows a FIFO queue discipline in the interest of fairness.

A) True
B) False

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Question 2

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Little's Law is not applicable in which of the following situations?

A) the opening of a toy store on Black Friday morning
B) a 24-hour supermarket
C) a gas station with 24-hour self-service pumps
D) B and C
E) It is applicable to A,B,and C.

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

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Question 3

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The ________ probability distribution is a continuous probability distribution often used to describe the service time in a queuing system.

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

A bank office with five tellers,each with a separate line of customers,exhibits the characteristics of a multiphase queuing system.

An M/M/1 model and an M/D/1 model each have an arrival rate of 1 per minute and a service rate of 3 per minute;the average queue length of the M/M/1 will be twice that of the M/D/1.

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 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 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?

A waiting-line system has three parts: the size of the arrival population,the behavior of arrivals,and the statistical distribution of arrivals.

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).What is the expected cost of this system?

At the order fulfillment center of a major mail-order firm,customer orders,already packaged for shipment,arrive at the sorting machine to be sorted for loading onto the appropriate truck for the parcel's address.The arrival rate at the sorting machine is at the rate of 140 per hour following a Poisson distribution.The machine sorts at the constant rate of 150 per hour. a.What is the utilization rate of the system? b.What is the average number of packages waiting to be sorted? c.What is the average number of packages in the sorting system? d.How long must the average package wait until it gets sorted?

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 waiting line meeting the M/M/1 assumptions has an arrival rate of 10 per hour and a service rate of 12 per hour.What is the probability that the waiting line is empty?

Which of the following represents an unlimited queue?

Which of the following is NOT a measure of a queue's performance?

A dental clinic at which only one dentist works is open only two days a week.During those two days,the traffic arrivals follow a Poisson distribution with patients arriving 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 is the probability that there are one or more patients in the system? c.What is the probability that there are four patients in the system? d.What is the probability that there are four or more patients in the system?

The source population is considered to be either ________ in its size.

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

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

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

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.