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June 2016 Jackson networks in nonautonomous random environments
Ruslan Krenzler, Hans Daduna, Sonja Otten
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Adv. in Appl. Probab. 48(2): 315-331 (June 2016).

Abstract

We investigate queueing networks in a random environment. The impact of the evolving environment on the network is by changing service capacities (upgrading and/or degrading, breakdown, repair) when the environment changes its state. On the other side, customers departing from the network may enforce the environment to jump immediately. This means that the environment is nonautonomous and therefore results in a rather complex two-way interaction, especially if the environment is not itself Markov. To react to the changes of the capacities we implement randomised versions of the well-known deterministic rerouteing schemes 'skipping' (jump-over protocol) and `reflection' (repeated service, random direction). Our main result is an explicit expression for the joint stationary distribution of the queue-lengths vector and the environment which is of product form.

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Ruslan Krenzler. Hans Daduna. Sonja Otten. "Jackson networks in nonautonomous random environments." Adv. in Appl. Probab. 48 (2) 315 - 331, June 2016.

Information

Published: June 2016
First available in Project Euclid: 9 June 2016

zbMATH: 1343.60133
MathSciNet: MR3511763

Subjects:
Primary: 60K37
Secondary: 60K25 , 90B22 , 90B25

Keywords: breakdown of nodes , degrading service , Jackson network , processes in random environment , product form steady state , Randomised random walk , reflection , skipping , speed-up of service

Rights: Copyright © 2016 Applied Probability Trust

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Vol.48 • No. 2 • June 2016
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