In:
Management Science, Institute for Operations Research and the Management Sciences (INFORMS), Vol. 19, No. 11 ( 1973-07), p. 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/∞ queue).
Type of Medium:
Online Resource
ISSN:
0025-1909
,
1526-5501
DOI:
10.1287/mnsc.19.11.1222
Language:
English
Publisher:
Institute for Operations Research and the Management Sciences (INFORMS)
Publication Date:
1973
detail.hit.zdb_id:
206345-1
detail.hit.zdb_id:
2023019-9
SSG:
3,2
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