Exam 21: Waiting-Line Models

A small hair styling salon has several operators. While customers do not have appointments, each is waiting to be served by a specific operator. This scenario provides an example of a

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, which are

What does it mean to have a patient customer in a waiting line?

A(n) ________ occurs when an arrival refuses to enter a waiting line; a(n) ________ occurs when an arrival joins a waiting line, then leaves it.

What is queue discipline? State three rules for queue discipline. Which of these rules appears most frequently in the four main models?

A finite population waiting line model with a single server has an average service time T of 200 minutes and an average time between service requirements U of 300 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 in the text.

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

A waiting-line system has three parts: the size of the arrival population, the behaviour of arrivals, and the statistical distribution of arrivals.

A waiting-line system that meets the assumptions of M/M/S has λ = 5, μ = 4, and M = 2. For these values, P_o is approximately 0.23077 and L_s is approximately 2.05128. The average time a unit spends in this system

In queuing problems, the term "renege" refers to the fact that some customers leave the queue before service is completed.

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

An M/M/1 model and an M/D/1 model each have an arrival rate of 1 per minute and a service rate of 3 per minute; the average queue length of the M/M/1 will be twice that of the M/D/1.

What are the components in a waiting-line system?

On a typical Friday, an average of 12 customers per hour arrive at the bank to transact business. There is one teller at the bank, and the average time required to transact business is four minutes. It is assumed that service times may be described by the exponential distribution. A single line would be used, and the customer at the front of the line would go to the first available bank teller. If a single teller is used, find: a) The average time in the line. b) The average number in the line. c) The average time in the system. d) The average number in the system. e) The probability that the bank is empty. f) If the business is considering adding a second teller (who would work at the same rate as the first) to reduce the waiting time for customers. She assumes that this will cut the waiting time in half. If a second teller is added, find the new answers to parts (a) to (e).

Which of the following is an example of a finite arrival population?

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

In the analysis of queuing models, the Poisson distribution often describes arrival rates and service times are often described by the negative exponential distribution.

Which of the following is a measure of queue performance?

A dental clinic at which only one dentist works is open only two days a week. During those two days, the traffic is uniformly busy with patients arriving at the rate of three per hour. The doctor serves patients at the rate of one every 15 minutes. a. What is the probability that the clinic is empty (except for the dentist)? b. What percentage of the time is the dentist busy? c. What is the average number of patients in the waiting room? d. What is the average time a patient spends in the office (wait plus service)? e. What is the average time a patient waits for service?

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