An Intuitive Condition for Stability and Performance Analysis of Multiclass Queueing Networks

Univ. Pompeu Fabra, Economics and Business Working Paper No. 429

16 Pages Posted: 1 May 2000

See all articles by Kevin D. Glazebrook

Kevin D. Glazebrook

Newcastle University

José Niño Mora

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Abstract

We present an intuitive stability condition for open multiclass queueing networks with Bernoulli routing: if each station has enough service capacity to cope with its peak traffic intensity, then the network is stable under any stationary nonidling scheduling policy. The condition is close to sharp for networks with light traffic between stations. Under this peak-rate condition, in the case of Markovian networks, we derive a closed-form upper bound on the time-average number of customers in the system, which is uniformly valid under all stationary nonidling policies. Our proof combines two recent results concerning (1) the relation between stability and performance via linear programming developed by Kumar and Meyn (1996); and (2) the work decomposition laws for multiclass queueing networks of Bertsimas and Ni?o-Mora (1999). The stability condition is tested on a generalization of the Lu-Kumar network, which shows how its quality depends on the degree of network connectivity.

JEL Classification: C60, C61

Suggested Citation

Glazebrook, Kevin D. and Niño Mora, José, An Intuitive Condition for Stability and Performance Analysis of Multiclass Queueing Networks. Univ. Pompeu Fabra, Economics and Business Working Paper No. 429. Available at SSRN: https://ssrn.com/abstract=224555 or http://dx.doi.org/10.2139/ssrn.224555

Kevin D. Glazebrook (Contact Author)

Newcastle University ( email )

5 Barrack Road
Devonshire Building
NE1 7RU Newcastle upon Tyne, NE1 7RU
United Kingdom

José Niño Mora

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
(34-3) 542 26 73 (Phone)
(34-3) 542 17 46 (Fax)

Register to save articles to
your library

Register

Paper statistics

Downloads
48
Abstract Views
1,446
PlumX Metrics