Consider the queueing model in Fig. 11.9. Customers arrive according to a Poisson process...

Consider the queueing model in Fig. 11.9. Customers arrive according to a Poisson process at rate 1 per minute and face a FIFO queue for server 1, who provides exponential service with mean 0.7 minute. Upon exiting server 1, customers leave with probability p, and go to server 2 with probability 1 – p. Server 2 is also fed by a FIFO queue, and provides exponential service with mean 0.9 minute. All service times, interarrival times, and routing decisions are independent, the system is initially empty and idle, and it runs until 100 customers have finished their total delay in queue(s); the total delay in queues of a customer visiting server 2 is the sum of his or her delays in the two queues. The performance measure is the expected average total delay in queue(s) of the first 100 customers to complete their total delay in queue(s).

FIGURE 11.9 The queueing model of Prob. 11.4.

(a) Suppose there are two configurations of this system, with p being either 0.3 or 0.8. Make 10 replications of each system using both independent sampling and CRN, and compare the estimated variances of the resulting estimate of the difference between the performance measures. Take care to maintain proper synchronization when using CRN.

---

(b) For p = 0.3, make five pairs of runs using both independent sampling and AV within a pair, and compare the estimated variances of the estimated performance measure. Again, pay attention to synchronization.