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On regenerative and ergodic properties of the k-server queue with non-stationary Poisson arrivals

Published online by Cambridge University Press:  14 July 2016

Hermann Thorisson
Hermann Thorisson*
Affiliation:
Chalmers University of Technology and the University of Göteborg
*
∗ Postal address: Department of Mathematics, Chalmers University of Technology and University of Göteborg, S 412 96 Göteborg, Sweden.
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Abstract

We consider the stable k-server queue with non-stationary Poisson arrivals and i.i.d. service times and show that the non-time-homogeneous Markov process Zt = (the queue length and residual service times at time t) can be subordinated to a stable time-homogeneous regenerative process. As an application we show that if the system starts from given conditions at time s then the distribution of Zt stabilizes (but depends on t) as s tends backwards to –∞. Also moment and stochastic domination results are established for the delay and recurrence times of the regenerative process leading to results on uniform rates of convergence.

Keywords

NON-TIME-HOMOGENEOUS MARKOV PROCESSREGENERATIVE PROCESSBACKWARD LIMITS
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 4 , December 1985 , pp. 893 - 902
Copyright
Copyright © Applied Probability Trust 1985 

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Footnotes

Supported by the Swedish Natural Science Research Council and by the Icelandic Science Foundation.

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