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

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/∞ queue).

• 저널Management Science · 19(11) · 1222–1228
• 토픽Advanced Queuing Theory Analysis · Management Information Systems
• DOI10.1287/mnsc.19.11.1222
• 저자Ralph L. Disney, Robert L. Farrell, Paulo Renato de Morais