Exam 25: 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 L_q and W_q be if the service rate were exponential,not constant?

In a finite or limited population waiting line,the ________ is calculated from the average service time and average time between service requirements before the problem can be completed.

A(n)________ queuing system has one waiting line,but several servers;a(n)________ queuing system is one in which the customer receives services from several stations before exiting the system

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

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

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?

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?

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

Identify the seven major measures of a queue system's performance.

Describe the difference between FIFO and LIFO queue disciplines.

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

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?

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

A finite population waiting line model with a single server has an average service time T of 50 minutes and an average time between service requirements U of 350 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.

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.

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

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 utilization factor?

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?

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

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