Exam 25: Queuing Models

A crew of mechanics at the Highway Department Garage repair vehicles that break down at an average of λ = 7 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. 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 waiting for service at any one time?

A(n)________ is a discrete probability distribution that often describes the arrival rate in queuing theory.

What are the six assumptions underlying the M/M/1 waiting line model? Which of these also hold for the M/D/1 model?

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?

In the M/M/1 waiting line model with an arrival rate of 2 per hour and a service rate of 6 per hour,the utilization factor for the system is approximately 0.333.

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?

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 three characteristics: Poisson arrivals,FIFO discipline,and exponential service times.

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

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?

A waiting-line system that meets the assumptions of M/M/S has λ = 5,μ = 4,and M = 2.For these values,Po is approximately 0.23077,and Ls is approximately 2.05128.What is the average time a unit spends in 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 fewer than two units in the system?

Suppose that a service facility has an average line of 2 customers that must wait,on average,5 minutes for service.How many customers are arriving per hour?

A waiting-line system that meets the assumptions of M/M/1 has λ = 1,μ = 4.For this system,Po is ________ and utilization is ________.

A finite population waiting line model has an average service time T of 100 minutes and an average time between service requirements U of 400 minutes;the service factor X is 0.25.

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 waiting-line system that meets the assumptions of M/M/S has λ = 5,μ = 4,and M = 2.For these values,Po is approximately 0.23077,and Ls is approximately 2.05128.What is the average number of units waiting in the queue?

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

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 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)?

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