Question

Consider a single-server queueing system with arrival and service details as: Interarrival times: 3, 2, 6, 2, 4, 5 Service times: 2, 5, 5, 8, 4, 5 Prepare a table show below for the given data. Stop simulation when the clock reaches 20. Write a Java program, to implement this single-server queueing system, print out the table shown below： You should create a future event list in your Java code, and print out the contents of FE list in each loop. Clock LQ(t) LS(t) B MQ Future Event List B: total server busy time MQ: maximum queue length LS(t): the number of customers being served (0 or 1) at time t. LQ(t): the number of customers in the waiting queue Also, output the following statistics information when simulation stops: 1.average number of customers in queue 2.average delay in queue 3.Server utilization The answer should look like: Single-server queueing system simulation Interarrival times: 3, 2, 6, 2, 4, 5 Service times: 2, 5, 5, 8, 4, 5 Simulation Ending Time: 20 Clock LQ LS B MQ FE List 0 0 0 0.0 0 (1,3) (3,20) 3 0 1 0.0 0 (2,5) (1,5) (3,20) 5 0 0 2.0 0 (1,5) (3,20) 5 0 1 2.0 0 (2,10) (1,11) (3,20) 10 0 0 7.0 0 (1,11) (3,20) 11 0 1 7.0 0 (1,13) (2,16) (3,20) 13 1 1 9.0 1 (2,16) (1,17) (3,20) 16 0 1 12.0 1 (1,17) (3,20) 17 1 1 13.0 1 (3,20) Average delay in queue 0.75 minutes Average number in queue 0.30 Server utilization 0.80 Number of delays completed 4

Answer 1

Queueing networks have been used to model the performance of a variety of complex systems. Since exact results exist for only a limited class of networks, the decomposition methodology has been used extensively to obtain approximate results. In this paper, we consider open queueing networks with multiple product classes, deterministic routings and general arrival and service distributions. We examine the decomposition method for such systems and show that it provides estimates of key parameters with an accuracy that is not acceptable in many practical settings. Recognizing this weakness, we enrich the approach by modeling a phenomenon previously ignored. We consider interference among products and describe its effect on the variance of the departure streams. The recognition of this effect significantly improves the performance of this methodology. We provide extensive experimental results based on the data of a manufacturer of semiconductor devices.