Exam 21: Waiting-Line Models

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?

In a repetitive focus factory, the number of channels available for the processing of a certain part would likely refer to

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

A Car Wash takes a constant time of 9.1 minutes in its automated car wash cycle. Autos arrive following a Poisson distribution at the rate of 6 per hour. The owner wants to know: a) The average waiting time in line. b) The average length of the line. c) The average utilization rate. d) The average time in the system. e) The average number of customers in the system.

A large discount store and supermarket has a hair styling salon on its premises. The salon has several operators. Salon customers can shop in other parts of the store until their name is called for salon service, at which time the customer will be served by the next available stylist. This scenario provides an example of a

In the basic queuing model (M/M/1), service times are described by

A finite population waiting line model has an average service time T of 200 minutes and an average time between service requirements U of 300 minutes; the service factor X is

In queuing problems, which of the following probability distributions is typically used to describe the time to perform the service?

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.

A Car Wash takes a constant time of 5.2 minutes in its automated car wash cycle. Autos arrive following a Poisson distribution at the rate of 8 per hour. The owner wants to know: a) The average waiting time in line. b) The average length of the line. c) The average utilization rate. d) The average time in the system. e) The average number of customers in the system.

A university has several technicians in the repair station to care for the computers in the student labs. This system is most likely

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?

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

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 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

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

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.

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 university has only one technician in the repair station to care for the computers in the student labs. This system is most likely

The registration area has just opened at a large convention of building contractors in Banff. There are 300 people arriving per hour (Poisson distributed), and the cost of their waiting time in the queue is valued at $120 per person per hour. The local convention bureau provides servers to register guests at a fee of $20 per person per hour. It takes about 1.5 minutes to register an attendee (exponentially distributed). A single waiting line, with multiple servers, is set up. a) What is the minimum number of servers for this system? b) What is the optimal number of servers for this system? c) What is the cost for the system, per hour, at the optimum number of servers? d) What is the server utilization rate with the minimum number of servers?