Instability conditions of open regenerative queueing networks

Evsey Morozov

Department of Mathematical Statistics,
Lund Institute of Technology,
Lund University,
1998

ISSN 0281-1944
ISRN LUNFD6/NFMS--3195--SE

Abstract:

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 time.

Key words:

Jackson-type network, multiclass network, non-homogeneous nodes, regenerative process, queue-size process, waiting time process, instability condition