This problem is intended to illustrate the nonlinear nature of the queuing theory models.
a. For a given number of servers, there are only two ways that the utilization factor can be altered. What are they?
b. For 5 servers, a service rate of 2 and the appropriate arrival rates, calculate the average number waiting for the utilization factor of 0.1, 0.3, 0.5, 0.7, 0.8, and 0.9. Plot Lq against utilization. Create a similar plot for a service rate of 4.
c. Interpret what you see in your plots.
d. A 5-server system currently has a workload that keeps the servers occupied 70% of the time. Suppose that the workload increased so that the utilization became 90%. From your answer to part (b), what is the percent increase in the average waiting line?
Compare that to the percent increase in the workload, and comment. e. What might a fast-food restaurant do to increase the service rate?