Stationary increments of accumulation processes in queues and generalized semi-Markov schemes
Keyword(s):
Let Tx be the length of time to accumulate x units of a resource. In queueing, the resource could be service. We derive a sufficient condition for the process to have stationary increments where Tx is an additive functional of a Markov process. This condition is satisfied in symmetric queues and generalized semi-Markov schemes with insensitive components. As a corollary, we show that the conditional expected response time in a symmetric queue is linear in the service requirement. A similar result holds for the conditional average residence time of an insensitive component in a GSMS.
1991 ◽
Vol 28
(04)
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pp. 864-872
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2004 ◽
Vol 61
(1)
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pp. 25-35
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2017 ◽
Vol 21
(2)
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pp. 779-790
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2020 ◽
pp. 1-25
2008 ◽
Vol 31
(2)
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pp. 224-230
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Keyword(s):
1993 ◽
Vol 27
(2)
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pp. 109-119
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