Question: Queuing Theory 8.2 Consider an M/M/1 queueing system where customers are discouraged from entering the queue in the following fashion: While the queue length is

Queuing Theory

Queuing Theory 8.2 Consider an M/M/1 queueing

8.2 Consider an M/M/1 queueing system where customers are discouraged from entering the queue in the following fashion: While the queue length is less than or equal to K for some K > 0, the arrival rate is fixed at l; when the queue length is greater than K, the arrival rate becomes In = \, n > K+ 1. The service rate is fixed at u > . (a) Find the stationary probability distribution of the queue length. (b) Determine the average queue length and system time at steady state. (c) How far can you reduce the service rate before the average queue length becomes infinite

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