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Stability Of Queueing Networks And Scheduling Policies (1995)
| Venue: | IEEE Transactions on Automatic Control |
| Citations: | 132 - 16 self |
BibTeX
@ARTICLE{Kumar95stabilityof,
author = {P. R. Kumar and Sean P. Meyn},
title = {Stability Of Queueing Networks And Scheduling Policies},
journal = {IEEE Transactions on Automatic Control},
year = {1995},
volume = {40},
pages = {251--260}
}
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Abstract
Usually, the stability of queueing networks is established by explicitly determining the invariant distribution. However, outside of the narrow class of queueing networks possessing a product form solution, such explicit solutions are rare, and consequently little is known concerning stability too. We develop here a programmatic procedure for establishing the stability of queueing networks and scheduling policies. The method uses linear or nonlinear programming to determine what is an appropriate quadratic functional to use as a Lyapunov function. If the underlying system is Markovian, our method establishes not only positive recurrence and the existence of a steady--state probability distribution, but also the geometric convergence of an exponential moment. We illustrate this method on several example problems. For an example of an open re-entrant line, we show that all stationary non-idling policies are stable for all load factors less than one. This includes the well known First Com...
Keyphrases
scheduling policy explicit solution lyapunov function stationary non-idling policy geometric convergence open re-entrant line appropriate quadratic functional steady state probability distribution invariant distribution first com programmatic procedure product form solution several example problem narrow class positive recurrence exponential moment load factor
