Abstract
We identify the large deviation rate function for a single server with multi-class arrivals in which the service priority is determined according to the weighted-serve-the-longest-queue policy. The problem setup falls into the general category of systems with discontinuous statistics. Our analysis, which is largely based on a weak convergence approach, does not require any symmetry or dimensional restrictions.
Paul Dupuis was supported in part by the National Science Foundation (NSF-DMS-0306070 and NSF-DMS-0404806) and the Army Research Office (W911NF-05-1-0289).
Kevin Leder was supported in part by the National Science Foundation (NSF-DMS-0404806). Hui Wang was supported in part by the National Science Foundation (NSF-DMS-0404806).
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
M. Alanyali and B. Hajek. On large deviations of Markov processes with discontinuous statistics. Ann. Appl. Probab., 8:45–66, 1998.
R. Atar and P. Dupuis. Large deviations and queueing networks: methods for rate function identification. Stoch. Proc. and Their Appl., 84:255–296, 1999.
P. Dupuis and R.S. Ellis. The large deviation principle for a general class of queueing systems, 1. Trans. Amer. Math. Soc., 347:2689–2751, 1996.
P. Dupuis and R. S. Ellis. A Weak Convergence Approach to the Theory of Large Deviations. John Wiley & Sons, New York, 1997.
P. Dupuis and R. S. Ellis. Large deviations for Markov processes with discontinuous statistics, II: Random walks. Probab. Th. Rel. Fields, 91:153–194, 1992.
P. Dupuis, R. S. Ellis, and A. Weiss. Large deviations for Markov processes with discontinuous statistics, I: General upper bounds. Annals of Probability, 19:1280–1297, 1991.
R. Foley and D. McDonald. Join the shortest queue: stability and exact asymptotics. Ann. Appl. Probab., 11:569–607, 2001.
I. Ignationk-Robert. Large deviations for processes with discontinuous statistics. Ann. Probab., 33:1479–1508, 2005.
K. Majewski. Large deviations of the steady-state distribution of reflected processes with applications to queueing systems. Queueing Systems, 29:351–381, 1998.
K. Ramanan and S. Stolyar. Largest weighted delay first scheduling: Large deviations and optimality. The Annals of Applied Probab., 11:1–49, 2001.
A. Shwartz and A. Weiss. Large Deviations for Performance Analysis: Queues, Communication and Computing. Chapman and Hall, New York, 1995.
L. Ying, R. Srikant, A. Eryilmaz, and G. E. Dullerud. A large deviation analysis of scheduling in wireless networks. Preprint, 2005.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Birkhäuser Verlag Basel/Switzerland
About this chapter
Cite this chapter
Dupuis, P., Leder, K., Wang, H. (2008). On the Large Deviations Properties of the Weighted-Serve-the-Longest-Queue Policy. In: Sidoravicius, V., Vares, M.E. (eds) In and Out of Equilibrium 2. Progress in Probability, vol 60. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8786-0_11
Download citation
DOI: https://doi.org/10.1007/978-3-7643-8786-0_11
Publisher Name: Birkhäuser Basel
Print ISBN: 978-3-7643-8785-3
Online ISBN: 978-3-7643-8786-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)