9.2.7 Let X.t/ be the number of customers in an M=M=1 queueing system at time t. Suppose

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9.2.7 Let X.t/ be the number of customers in an M=M=1 queueing system at time t.

Suppose that X.0/ D 0.

(a) Derive the forward equations that are appropriate for this process by substituting the birth and death parameters into Chapter 6, equation (6.24).

(b) Show that M.t/ D E[X.t/] satisfies the differential equation M0.t/ D ????

M.t/ by multiplying the jth forward equation by j and summing.

(c) Solve for M.t/.

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An Introduction To Stochastic Modeling

ISBN: 9780233814162

4th Edition

Authors: Mark A. Pinsky, Samuel Karlin

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9.2.7 Let X.t/ be the number of customers in an M=M=1 queueing system at time t. Suppose

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An Introduction To Stochastic Modeling

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