Exam 21: Waiting-Line Models

The registration area has just opened at a large convention of building contractors in Banff. There are 200 people arriving per hour (Poisson distributed), and the cost of their waiting time in the queue is valued at $100 per person per hour. The local convention bureau provides servers to register guests at a fee of $15 per person per hour. It takes about 0.8 minutes to register an attendee (exponentially distributed). A single waiting line, with multiple servers, is set up. a) What is the minimum number of servers for this system? b) What is the optimal number of servers for this system? c) What is the cost for the system, per hour, at the optimum number of servers? d) What is the server utilization rate with the minimum number of servers?

Little's Law is not applicable in which of the following situations?

In the M/M/1 waiting line model with an arrival rate of 2 per hour and a service rate of 6 per hour, the utilization factor for the system is approximately 0.333.

There is only one bay and one type of service at an automatic car wash. Provide the most likely characteristics of this system. a. name of model b. number of channels c. number of phases d. arrival rate distribution e. service time distribution f. population size g. queue discipline

A waiting line meeting the M/M/1 assumptions has an arrival rate of 4 per hour and a service rate of 12 per hour. What is the average time a unit spends in the system and the average time a unit spends waiting?