Stationary increments of accumulation processes in queues and generalized semi-Markov schemes

Stationary increments of accumulation processes in queues and generalized semi-Markov schemes

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Article ID: iaor19932430
Country: Israel
Volume: 28
Issue: 4
Start Page Number: 864
End Page Number: 872
Publication Date: Dec 1991
Journal: Journal of Applied Probability
Authors: , ,
Keywords: markov processes
Abstract:

Let Tx be the length of time to accumulate x units of a resource. In queueing, the resource could be service. The authors derive a sufficient condition for the process (Tx,x≥0) 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, the authors 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.

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