Advances in Applied Probability

Jackson networks in nonautonomous random environments

Ruslan Krenzler, Hans Daduna, and Sonja Otten

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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.

Article information

Adv. in Appl. Probab., Volume 48, Number 2 (2016), 315-331.

First available in Project Euclid: 9 June 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K37: Processes in random environments
Secondary: 60K25: Queueing theory [See also 68M20, 90B22] 90B22: Queues and service [See also 60K25, 68M20] 90B25: Reliability, availability, maintenance, inspection [See also 60K10, 62N05]

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


Krenzler, Ruslan; Daduna, Hans; Otten, Sonja. Jackson networks in nonautonomous random environments. Adv. in Appl. Probab. 48 (2016), no. 2, 315--331.

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