Jackson networks in nonautonomous random environments
Research output: Journal contributions › Journal articles › Research › peer-review
Standard
Jackson networks in nonautonomous random environments. / Krenzler, Ruslan; Daduna, Hans; Otten, Sonja.
In: Advances in Applied Probability, Vol. 48, No. 2, 06.2016, p. 315–331.Research output: Journal contributions › Journal articles › Research › peer-review
Harvard
APA
Vancouver
Bibtex
}
RIS
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 -