Stability of queueing networks and scheduling policies

Author

Kumar, P.R. ; Meyn, Sean P.

Author_Institution

Dept. of Electr. & Comput. Eng., Illinois Univ., Urbana, IL, USA

Volume

40

Issue

2

fYear

1995

fDate

2/1/1995 12:00:00 AM

Firstpage

251

Lastpage

260

Abstract

We develop 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

Keywords

Lyapunov methods; Markov processes; convergence of numerical methods; mathematical programming; probability; production control; queueing theory; stability; Lyapunov function; Markovian system; exponential moment; geometric convergence; linear programming; machine scheduling; nonlinear programming; probability distribution; production control; quadratic functional; queueing networks; stability; Convergence; Functional programming; Linear programming; Lyapunov method; Quadratic programming; Stability; Steady-state; Stochastic processes; Telecommunication traffic; Traffic control;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.341782

Filename

341782