Exam 16: Appendix: Queuing Analysis

If the probability of a number of people waiting is 0.10, the probability of one person waiting is 0.09, and the probability of two people waiting is 0.08, what is the probability of three or more people waiting?

The manner in which new arrivals are ordered or prioritized for service is known as _____.

Which of the following is NOT a key assumption of the multiple-server queuing model?

The multiple-server queuing model assumes that the mean service rate, $\mu$ , varies from server to server.

The arrival rate in queuing formulas is expressed as:

Compare and contrast wait cost with server cost. Which is harder to estimate?

For the multiple-server queuing model to apply, the overall mean service rate should be greater than the mean arrival rate.

Describe at least four queue disciplines.

A local hamburger chain is considering adding a drive-through window. They estimate that during the dinner hour, customer arrival rate will average 18 per hour and follow a Poisson distribution. Service times during this same period are estimated to follow an exponential distribution with a mean of 24 customers per hour. a. Determine the probability that the service facility (drive-through window) is idle. b. Determine the probability of four vehicles in the system. c. Determine the average number of vehicles waiting for service. d. Determine the average number of vehicles in the system. e. Determine the average time a vehicle spends waiting for service. f. Determine the average time a vehicle spends in the system. g. Determine the probability that an arriving vehicle has to wait for service.

Which of the following variables is ordinarily NOT an output of waiting-line analysis?

Many analytical queuing models exist, each based upon unique assumptions about the nature of arrivals.

What are the seven key assumptions for the multiple-server waiting line model?

A local bank has two drive-through teller windows with an essentially unlimited queue length. They estimate that the arrival rate during their most busy time will average about 40 cars per hour. They also estimate they can serve an average of 50 cars per hour. Management wants to make sure that the system is operating efficiently. a. What is the probability that there will be no cars in the system? b. On average, how many cars are in the system? c. How long would a car be waiting (in seconds) in the drive-through, on average?

For a single-server queuing model, which of the following is NOT a key assumption?

In queuing models, what are channels?

A university bookstore opens a booth and buys back used books during the final exam week. From 9 to 12 in the morning, students arrive at the rate of 35 per hour, on average. The bookstore employee can service an average of 40 students per hour. a. What is the average length of the line? b. What is the average time (in minutes) a student spends in the bookstore (system)? c. What is the chance that the bookstore employee will be idle?

Since most service times follow an exponential distribution, there is no need to collect data on actual service times.

Arrival distributions for queuing models:

The mean arrival rate is used to express demand; the mean service rate is used to express a system's capacity.

An ice cream shop is quite busy after the neighborhood high school lets out each day. From 3 pm to 5 pm customers arrive at the rate of 50 per hour, on average. Currently, the clerk can serve one customer per minute, on average. The store manager can buy an electrically heated scoop with an automatic ice cream ejector which will decrease the serving time to one custom-er per 45 seconds, on average. a. What is the current time (in minutes) spent waiting in line? b. What will the waiting time (in minutes) become using the automatic ice cream ejector? c. What fraction of time is the clerk currently idle? d. What fraction of time will the clerk be idle using the automatic ice cream ejector? e. How many customers, on average, are in the shop under the current system? f. How many customers would be in the shop, on average, using the automatic ice cream ejector?