Exam 24: Waiting-Line Models

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

A hospital emergency room always follows a first-in,first-served queue discipline in the interest of fairness.

At the order fulfillment centre 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?

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?

Customers take a number as they join the waiting line of the customer service counter at a discount store.There are two customer service agents.Provide the most likely characteristics of this system. a.name of model b.number of channels c.number of phases d.arrival rate distribution e.service time distribution f.population size g.queue discipline

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

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?

What are Ls and Lq,as used in waiting line terminology? Which is larger,Ls or Lq? Explain.

As the average service rate μ grows larger,the slope of the distribution of service time probabilities grows larger and larger,eventually becoming positive.

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.The average length of the queue Lq is approximately

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.A student has just entered the system.How long is she expected to stay in the system?

"Women and children first!" declares the captain of a sinking ship.His directive employs which of the following queue disciplines in disembarking passengers?

What is the waiting-line problem? Why is it important to operations?

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?

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