2.6. Customers arrive at a service facility according to a Poisson process of rate A. There is...

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2.6. Customers arrive at a service facility according to a Poisson process of rate A. There is a single server, whose service times are exponentially distributed with parameter μ. Suppose that "gridlock" occurs whenever the total number of customers in the system exceeds a capacity C. What is the smallest capacity C that will keep the probability of gridlock, under the limiting distributing of queue length, below 0.001? Express your answer in terms of the traffic intensity p = A/μ.

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An Introduction To Stochastic Modeling

ISBN: 9780126848878

3rd Edition

Authors: Samuel Karlin, Howard M. Taylor

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