Exam 25: Waiting-Line Models

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 average time a unit spends in the system and the average time a unit spends waiting (in hours)?

Of the three types of queue discipline,only ________ is assumed by the four primary waiting line models.

Describe the difference between FIFO and LIFO queue disciplines.

A finite population waiting line model with a single server has an average service time T of 200 minutes and an average time between service requirements U of 300 minutes.Calculate the service factor X.If the population consists of 5 elements,what are the average number waiting,the average number being serviced,and the average number running? Refer to Table D.8.

LIFS (last-in,first-served)is a common queue discipline,most often seen where people,not objects,form the waiting line.

A queuing model that follows the M/M/1 assumptions has λ = 10 and μ = 12.What is the average number of units in the system?

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?

Which part of a waiting line has characteristics that involve a statistical 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).What is the expected cost of this system?

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?

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.How many students,on average,will be waiting in line at any one time?

The potential restaurant customer who says to her husband,"The line looks too long; let's eat somewhere else," is an illustration of which element of arrival behavior?

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 waiting line meeting the M/M/1 assumptions has an arrival rate of 4 per hour and a service rate of 12 per hour.What is the average time a unit spends in the system and the average time a unit spends waiting (in hours)?

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

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 ________.

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 100 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? e.What would Lq and Wq be if the service rate were exponential,not constant?

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?

A concert hall,employing both ticket takers and ushers to seat patrons,behaves typically as which of the following?