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Decomposition and Customer Streams of Feedback Queueing Networks in Equilibrium,
MICHIGAN UNIV ANN ARBOR DEPT OF INDUSTRIAL AND OPERATIONS ENGINEERING
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P. J. Burke and E. Reich independently showed the output of a MM1 queue in equilibrium to be a Poisson process. Consequently, analysis of tandem exponential servers with a Poisson input stream can be reduced to consideration of a series of MM1 queues. This work generalizes the above results to so-called Jackson networks, which consists of exponential servers with mutually independent Poisson exogenous inputs and random customer routings permitting customer feedback. The authors prove that traffic on all exit arcs is Poisson moreover, the customer streams leaving any exit set are mutually independent.
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