Piecewise Linear Test Functions for Stability and Instability of Queueing Networks (0)
| Venue: | Queueing Systems |
| Citations: | 33 - 3 self |
BibTeX
@INPROCEEDINGS{Down_piecewiselinear,
author = {D. Down and S.P. Meyn},
title = {Piecewise Linear Test Functions for Stability and Instability of Queueing Networks},
booktitle = {Queueing Systems},
year = {},
pages = {205--226}
}
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Abstract
We develop the use of piecewise linear test functions for the analysis of stability of multiclass queueing networks and their associated fluid limit models. It is found that if an associated LP admits a positive solution, then a Lyapunov function exists. This implies that the fluid limit model is stable and hence that the network model is positive Harris recurrent with a finite polynomial moment. Also, it is found that if a particular LP admits a solution, then the network model is transient. Running head : Stability and Instability of Queueing Networks Keywords : Multiclass queueing networks, ergodicity, stability, performance analysis. 1 Introduction It has generally been taken for granted in queueing theory that stability of a network is guaranteed so long as the overall traffic intensity is less than unity and in recent years there has been much analysis which supports this belief for special classes of systems, such as single class queueing networks (see Borovkov [2], Sig...
