AMS 553: Program Set 1
We wish to analyze the following two singleserver queueing systems:
(i) An M/M/1 queue, where the interarrival times and service times are independent exponen
tially distributed random variables
(ii) An M/D/1 queue, where the interarrival times are i.i.d. exponential random variables but
the service times are deterministic
In both cases, assume that the mean interarrival time is 5 minutes, and mean service time is 4
minutes (in case (ii), this implies that the service time is exactly 4 minutes).
Write a computer simulation program to simulated the above systems (or two separate pro
grams, one for each of the two systems). Your program should be able to calculate the following
performance measures:
•
average time that a customer waits in queue
•
average number of customers in the queue
•
fraction of customers that spent more than 4
.
5 minutes in the system
•
fraction of time that the system is busy
In your program, use the LCG
Z
i
+1
= 16807
Z
i
mod
2147483647
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 Spring '08
 Badr,H
 Probability theory, Randomness, Monte Carlo method

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