AMS 553: Program Set 1 We wish to analyze the following two single-server 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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