Consider the M/M/1 queueing theory model that was discussed in Sec. 17.6 and Example 2, Sec. 22.1. Suppose that the mean arrival rate is 5 per hour, the mean service rate is 10 per hour, and you are required to estimate the expected waiting time before service begins by using simulation.

R

(a) Starting with the system empty, use next-event incrementing to perform the simulation by hand until two service completions have occurred.

R

(b) Starting with the system empty, use fixed-time incrementing (with 2 minutes as the time unit) to perform the simulation by hand until two service completions have occurred.

D,I

(c) Use the interactive routine for simulation in your OR Courseware (which incorporates next-event incrementing)

to interactively execute a simulation run until 20 service completions have occurred.

Q

(d) Use the Queueing Simulator to execute a simulation run with 10,000 customer arrivals.

E

(e) Use the Excel template for this model in the Excel file for Chap. 17 to obtain the usual measures of performance for this queueing system. Then compare these exact results with the corresponding point estimates and 95 percent confidence intervals obtained from the simulation run in part (d). Identify any measure whose exact result falls outside the 95 percent confidence interval.