Exam 20: Waiting-Line Models

A single-phase waiting-line system meets the assumptions of constant service time or M/D/1. Units arrive at this system every 10 minutes on average. Service takes a constant 8 minutes. What is the average number in the system, L_s, in units?

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 before being served.

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

On average, 4 customers are waiting in line to be served in a local UPS store. The average waiting time is 5 minutes. The probability distributions that describe arrival and service times are unknown. What is the arrival rate per hour?

A dental clinic at which only one dentist works is open only two days per week. During those two days, patients arrive at the rate of four per hour. The doctor serves patients at the rate of one every 12 minutes. (a) What is the probability that the clinic is empty (except for the dentist and staff)? (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 finite population waiting line model with N = 5 has 5 arrivals per hour. Eight customers can be served per hour. The probability the system is empty is:

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

In queuing problems, arrival rates are generally described by the Poisson probability distribution.

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 ________.

Suppose that a fast-food restaurant wants the average line to be 4 customers and that 60 customers arrive each hour. How many minutes will the average customer be forced to wait in line?

The common measures of a queuing system's performance include:

A queuing model that follows the M/M/1 assumptions has λ = 2 and μ = 6. The average number in the system, L_s, is ________ and the utilization of 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/D/1 will be twice that of the M/M/1.

A copy center has five machines that serve many customers throughout the day. The waiting line for copy service has a finite population, while the waiting line for copier maintenance has an infinite population

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

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

What are the components in a waiting-line system?

A McDonald's single-lane drive-through that has one window for making the payment and a second window for receiving the food behaves most like which of the following?

Suppose that a coffee shop wants the average line length to be 5 customers and that 50 customers arrive each hour. The probability distributions that describe arrival and service times are unknown. How many minutes will the average customer wait in line?

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