### Jackson networks in nonautonomous random environments

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 9 June 2016

https://projecteuclid.org/euclid.aap/1465490750

Mathematical Reviews number (MathSciNet)
MR3511763

Zentralblatt MATH identifier
1343.60133

#### Citation

Krenzler, Ruslan; Daduna, Hans; Otten, Sonja. Jackson networks in nonautonomous random environments. Adv. in Appl. Probab. 48 (2016), no. 2, 315--331. https://projecteuclid.org/euclid.aap/1465490750

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