Problem

Suppose that we want to estimate the expected average delay in queue of the first 100 cust...

Suppose that we want to estimate the expected average delay in queue of the first 100 customers in a FIFO M/G/1 queue where the initial conditions are empty and idle, the mean interarrival time is 1 minute, and service times have a Weibull distribution with shape parameter α = 2 and scale parameter minutes. Thus, the mean service time is minute (see Sec. 6.2.2), and the utilization factor is ρ = 0.9. (See Sec. 8.3.5 for Weibull-variate generation, which is easily done by the inverse-transform method.) As an external control variate, we could use CRN to simulate the M/M/1 queue for 100 customers with the same mean interarrival and service times, which is precisely the model of Example 11.13, and use the fact that the known expected average delay in queue for this M/M/1 queue is 4.13. Use the estimation technique given in Sec. 11.4 to estimate the optimal weight a* from n = 10 replications, and repeat the whole process 100 times to estimate the variance reduction in comparison with straightforward simulation of this M/G/1 queue. Is the variance reduction worthwhile, or should the computing time needed to simulate the M/M/1 queue be devoted instead to making additional direct replications of this M/G/1 queue?