Exam 24: Waiting-Line Models

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?

The greater the margin by which the arrival rate exceeds the service rate, the better the performance of the waiting line.

Provide an example of a limited or finite population for a queue.

A manufacturing plant is trying to determine how long the average line for a repair process will be. If 10 machines arrive each hour and must wait 6 minutes in the line, how long will the line be, on average?

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

The sign at the bank that reads "Wait here for the first available teller" suggests the use of a __________ waiting line system.

In the basic queuing model (M/M/1), arrival rates are distributed by

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. The average number of units waiting in the queue

Waiting-line models are useful to operations in such diverse settings as service systems, maintenance activities, and shop-floor control.

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 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

What are the components in a waiting-line system?

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

Describe the difference between FIFO and LIFO queue disciplines.

A queuing model which follows the M/M/1 assumptions has λ = 10 and μ = 12. The average number in the system is

A crew of mechanics at the Highway Department garage repair vehicles which break down at an average of λ = 5 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?

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.

Genco, Inc., a small manufacturer of diesel-generator sets has four shearing machines. Because of the age of these machines, they need minor repairs after 30 hours of use. Analysis of previous breakdowns indicates that breakdowns follow a Poisson distribution. The facility employs one repairman specifically to repair these machines. Average repair time is two hours following an exponential distribution. a. What is the service factor for this system? b. What is the average number of these machines in service? c. What is the impact of adding a second repairman?

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

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