Exam 16: Appendix: Queuing Analysis

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

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.

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 alls 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.

Queuing models:

Which of the following is NOT a psychological strategy for dealing with a long wait time?

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

What are five key assumptions for the basic, single-channel waiting line model?

According to the single-server queuing model, when $\lambda$ = $\mu$ , the operating characteristics are not defined, which means that these times and numbers of items grow infinitely large.

Which of the following CANNOT be found by queuing formulas?

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

List the seven operating characteristics of a single-channel waiting line (no formulas).

A flower shop has one employee in the front of the store to sell flowers out of a cooler. On Saturdays customers arrive every six minutes, on average. The employee can serve a customer every five minutes, on average. The owner of the store feels that if there are more than four customers in the store at one time, additional customers may not come in because the wait appears too long. a. What is the chance of four or more customers being in the store at one time? b. What is the total time (in minutes) a customer spends in the store? c. What is the average number of customers in the store?

Discuss three categories of information necessary to develop a queuing model.

Triage is a form of preemption.

_____ is the process of a customer evaluating the waiting line and server system and deciding not to join the queue.

A sandwich shop near a college 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?

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