Further Results on the M/M/1 Queue with Randomly Varying Rates.

Marcel F. Neuts

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Advanced Queuing Theory Analysis Probability and Statistical Research Probability and Risk Models

Abstract

The M/M/c queue, with arrival and service rates which vary according to the state of a Markov process, has a steady-state probability vector of a modified matrix-geometric form. The rate matrix R is the unique positive solution to a quadratic matrix equation, which may be solved numerically by successive substitutions. A theorem which provides an accuracy check on that computation is proved. Finally a numerical example is discussed and its results are interpreted.

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