Open Access
Translator Disclaimer
2012 Stability and Probability 1 Convergence for Queueing Networks via Lyapunov Optimization
Michael J. Neely
J. Appl. Math. 2012: 1-35 (2012). DOI: 10.1155/2012/831909


Lyapunov drift is a powerful tool for optimizing stochastic queueing networks subject to stability. However, the most convenient drift conditions often provide results in terms of a time average expectation, rather than a pure time average. This paper provides an extended drift-plus-penalty result that ensures stability with desired time averages with probability 1. The analysis uses the law of large numbers for martingale differences. This is applied to quadratic and subquadratic Lyapunov methods for minimizing the time average of a network penalty function subject to stability and to additional time average constraints. Similar to known results for time average expectations, this paper shows that pure time average penalties can be pushed arbitrarily close to optimality, with a corresponding tradeoff in average queue size. Further, in the special case of quadratic Lyapunov functions, the basic drift condition is shown to imply all major forms of queue stability.


Download Citation

Michael J. Neely. "Stability and Probability 1 Convergence for Queueing Networks via Lyapunov Optimization." J. Appl. Math. 2012 1 - 35, 2012.


Published: 2012
First available in Project Euclid: 17 October 2012

zbMATH: 1251.90096
MathSciNet: MR2948168
Digital Object Identifier: 10.1155/2012/831909

Rights: Copyright © 2012 Hindawi


Vol.2012 • 2012
Back to Top