Stability conditions for multiclass fluid queueing networks

Author

Bertsimas, Dimitris ; Gamarnik, David ; Tsitsiklis, John N.

Author_Institution

Sloan Sch. of Manage., MIT, Cambridge, MA, USA

Volume

41

Issue

11

fYear

1996

fDate

11/1/1996 12:00:00 AM

Firstpage

1618

Lastpage

1631

Abstract

We introduce a new method to investigate stability of work-conserving policies in multiclass queueing networks. The method decomposes feasible trajectories and uses linear programming to test stability. We show that this linear program is a necessary and sufficient condition for the stability of all work-conserving policies for multiclass fluid queueing networks with two stations. Furthermore, we find new sufficient conditions for the stability of multiclass queueing networks involving any number of stations and conjecture that these conditions are also necessary. Previous research had identified sufficient conditions through the use of a particular class of (piecewise linear convex) Lyapunov functions. Using linear programming duality, we show that for two-station systems the Lyapunov function approach is equivalent to ours and therefore characterizes stability exactly

Keywords

Lyapunov methods; duality (mathematics); linear programming; queueing theory; scheduling; stability; duality; linear programming; multiclass fluid queueing networks; necessary condition; scheduling; stability conditions; sufficient condition; two-station systems; work-conserving policies; Laboratories; Linear programming; Lyapunov method; Operations research; Piecewise linear techniques; Stability; Stochastic processes; Sufficient conditions; Telecommunication traffic; Traffic control;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/9.543999

Filename

543999