TY - JOUR

T1 - Jackson networks in nonautonomous random environments

AU - Krenzler, Ruslan

AU - Daduna, Hans

AU - Otten, Sonja

PY - 2016/6

Y1 - 2016/6

N2 - 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.

AB - 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.

KW - Mathematics

KW - Randomised random walks

KW - Jackson network

KW - skipping

KW - processes in random environment

KW - reflection

KW - product form steady state

KW - breakdown of nodes

KW - degrading services

KW - speed-up of service

KW - Informatics

KW - Jackson network

KW - breakdown of nodes

UR - http://www.scopus.com/inward/record.url?scp=84976420385&partnerID=8YFLogxK

U2 - 10.1017/apr.2016.2

DO - 10.1017/apr.2016.2

M3 - Journal articles

VL - 48

SP - 315

EP - 331

JO - Advances in Applied Probability

JF - Advances in Applied Probability

SN - 0001-8678

IS - 2

ER -