Consider the M/G/1queue with FIFO service. Assume that (1) the arrival rate is 5

Question

Consider the M/G/1queue with FIFO service. Assume that (1) the arrival rate is 5 messages per second, and (2) the service times are described by P(X=0.1) = 0.8 and P(X = 0.5) = 0.2 (measured in seconds).

1.) Find the server utilization

2.) Find the average value of the waiting time.

3.) Suppose that instead of the discrete service time distribution described above, the service times are assumed to be exponetially distributed, with the same average value. If an arriving customer finds the server busy, find the probability that he will wait in the queue for at least 2 seconds.

Explanation / Answer

Consider the M/G/1queue with FIFO service. Assume that (1) the arrival rate is 5

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