CS 5623 Simulation Techniques

Fall 2003
Instructor Dr. Turgay Korkmaz

Homework 6 - programming
Due by Nov 25, 2003 (5:30pm)

(80 points)

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You are asked to implement a simulation program using CSIM for the below system consisting of two M/M/1 queues in series, and analyze its steady-state (long-run) performance measure (assume we are just interested in the response time that a customer spends in the system).

System:

Assume that

• the arrival rate λ is 5 customers per hour
• the service rate μ is 5.4 customers per hour , and μ is the same for every server
• capacity of each waiting line is infinite

Initially all servers are idle and there are no customers in the system.

1. By making appropriate simulation runs (at least 10), determine the transient period and the deletion point to avoid the initialization bias in response time. (Justify your answers by computing and plotting ensample averages across replications, further smoothing that plot, and drawing cumulative averages after deleting different amount of data points etc.)

2. After choosing the deletion point in part (1),

1. use replication method to estimate the steady-state response time with 95% confidence.
2. If we want to reduce the half length of the confidence interval computed in part (2.a) 10%, how many more runs would be needed? (i.e., if h.l. was x in part (2.a) we want to know mow many more runs are needed to estimate response time within -+0.9 x)
3. Accordingly, conduct that many runs and give the new 95% confidence interval. Is the number of runs enough to accomplish the goal in (2.b).

3. Repeat part (2.a) by using batch means method.

4. Compare the results in parts (2.a) and (3), and explain the advantages and disadvantages of these two methods in analyzing output data.