A Characterization of M/G/1 Queues with Renewal Departure Processes

Ralph L. Disney, Robert L. Farrell and Paulo Renato De Morais
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Ralph L. Disney: Professor, Department of Industrial and Operations Engineering, University of Michigan, Ann Arbor, Michigan
Robert L. Farrell: Vector Research, Inc., Ann Arbor, Michigan
Paulo Renato De Morais: Auxiliar de Ensino, Instituto Tecnolögica de Aeronautica, S~ao Jose dos Campos, Brazil

Management Science, 1973, vol. 19, issue 11, 1222-1228

Abstract: Burke [Burke, P. J. 1956. The output of a queueing system. Oper. Res. 4 699-704.] showed that the departure process from an M/M/1 queue with infinite capacity was in fact a Poisson process. Using methods from semi-Markov process theory, this paper extends this result by determining that the departure process from an M/G/1 queue is a renewal process if and only if the queue is in steady state and one of the following four conditions holds: (1) the queue is the null queue--the service times are all 0; (2) the queue has capacity (excluding the server) 0; (3) the queue has capacity 1 and the service times are constant (deterministic); or (4) the queue has infinite capacity and the service times are negatively exponentially distributed (M/M/1/\infty queue).

Date: 1973
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