Exam 20: Queuing Analysis

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

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

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

Many analytical queuing models exist, each based upon unique assumptions.

Discuss the seven key assumptions for the multiple-server waiting line model.

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 ejector?

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?

A small software company hired a Customer Service Representative (CSR) to handle technical support questions.It is estimated that during peak periods, the CSR would receive four (4) calls per hour and follow a Poisson distribution.Based on past experience, a CSR can handle an average of five (5) calls per hour during the same time period and follow an exponential distribution. a.Determine the probability that the CSR is idle. b.Determine the probability that three customers are in the system, waiting or being served c.Determine the average number of callers waiting for service (on hold). d.Determine the average number of callers in the system. e.Determine the average time a caller spends waiting for service (on hold). f.Determine the average time a caller spends in the system (waiting time plus service time). g.Determine the probability that an arriving call will have to wait for service.

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

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

Rules that determine the order in which arrivals are sequenced through the service system are called

For the multiple-server queuing model to apply, k $\mu$ > $\lambda$ .

Describe at least four queue disciplines.

Triage is a form of preemption.

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?

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

The multiple-server queuing model assumes jockeying can take place.

Discuss three categories of information necessary to analyze a waiting line.