Question: . Suppose that a queueing system has m service channels. The demand for service arises in accordance with a Poisson process with rate a, and

. Suppose that a queueing system has m service channels. The demand for service arises in accordance with a Poisson process with rate

a, and the service time distribution has exponential distribution with parameter b.

Suppose that the service system has no storage facility-that is, a demand that arises when all m channels are busy is rejected and is lost to the system.

Let X(t) be the number of busy service channels (number of demands)

at time t. Show that { X(t), t ≥ 0} is a continuous-time Markov chain.

Determine the infinitesimal generator. (See problem 1.8 for the same queue with discrete service time.)

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