Instability conditions of open regenerative queueing networks
Department of Mathematical Statistics,
Lund Institute of Technology,
We establish the so-called instability conditions for Jackson-type (single-class)
and for multiclass open networks with Markovian switching between classes,
where the basic network processes are regenerative. In fact, our results
imply that the known stability condition (traffic intensity less than 1 for
each network node) is also necessary for stability of a wide class of open
networks. We separate two cases: strong instability and weak instability.
In the first case queueing process increases infinitely with probability
1 when time increases. In the second it increases generally, in probability.
The proofs are based on the characterization of the embedded renewal process
of the regeneration points by the limit behaviour of the residual renewal
Jackson-type network, multiclass network, non-homogeneous nodes, regenerative
process, queue-size process, waiting time process, instability condition