Stability and Probability 1 Convergence for Queueing Networks via Lyapunov Optimization
Author
Source
Journal of Applied Mathematics
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-35, 35 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-06-26
Country of Publication
Egypt
No. of Pages
35
Main Subjects
Abstract EN
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.
American Psychological Association (APA)
Neely, Michael J.. 2012. Stability and Probability 1 Convergence for Queueing Networks via Lyapunov Optimization. Journal of Applied Mathematics،Vol. 2012, no. 2012, pp.1-35.
https://search.emarefa.net/detail/BIM-993742
Modern Language Association (MLA)
Neely, Michael J.. Stability and Probability 1 Convergence for Queueing Networks via Lyapunov Optimization. Journal of Applied Mathematics No. 2012 (2012), pp.1-35.
https://search.emarefa.net/detail/BIM-993742
American Medical Association (AMA)
Neely, Michael J.. Stability and Probability 1 Convergence for Queueing Networks via Lyapunov Optimization. Journal of Applied Mathematics. 2012. Vol. 2012, no. 2012, pp.1-35.
https://search.emarefa.net/detail/BIM-993742
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-993742