Exam 20: Queuing Analysis

Queuing models

Discuss the five key assumptions for the basic, single-channel waiting line model.

Which of the following cannot be found by queuing formulas?

Describe at least four queue disciplines.

Triage is a form of preemption.

____ is the use of a criterion that allows new arrivals to displace members of the current queue and become the first to receive service.

For a single-server queuing model, the utilization factor $\lambda$ / $\mu$ has to be

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

Generally for queuing models, the slower the rate of arrivals, the shorter the time period chosen.

A sandwich shop near campus has a special counter, open from 11 am to 1 pm, which is used exclusively for selling pre-made sandwiches. This is much faster than making sandwiches to order at lunch time. The clerk can handle a customer in about one minute. Customers arrive at a rate of 40 per hour on average. a. How long in minutes) does a customer have to wait? b. What percentage of the time is the employee working? c. What is the average number of customers waiting in line? d. What is the probability of there being 3 or more customers in the system?

The arrival rate in queuing formulas is expressed as:

A local bank has two drive-thru 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 driveway, on average?

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

The process of customers leaving one waiting line to join another in a multiple-server channel) configuration is called

A multiple-server queuing model has three servers with a mean service time of five customers per server per hour. It has been determined that arrivals will average 12 per hour. Arrivals follow a Poisson distribution and service times follow an exponential distribution. a. Calculate the probability that all three service channels are idle. b. Determine the probability of five customers in the system. c. Determine the average number of customers waiting for service. d. Determine the average number of customers in the system. e. Determine the average time a customer spends waiting for service. f. Determine the average time a customer spends in the system. g. Determine the probability an arriving customer will wait for service.

Contrast wait cost with server cost. Which is harder to estimate?

By using two-servers for airport check-ins instead of one, the imputed cost of waiting goes up.

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 customer 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 ejec-tor?

A university bookstore opens a booth and buys back used books during 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?