Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
invited-talk

Bounds Implied by Drift with Applications

Published:15 June 2015Publication History
Skip Abstract Section

Abstract

A recurring theme in the design of control schemes for computer communication networks has been to identify the drift of critical quantities such as queue lengths, and then devise control strategies that close the loop. A useful tool for the performance analysis of such strategies are bounds on deviations from the expected trajectory. This talk identifies an incomplete list of such tools that have been used in a broad class of applications, for both stochastic and deterministically constrained models of load.

References

  1. A. Eryilmaz and R. Srikant. Asymptotically tight steady-state queue length bounds implied by drift conditions. Queueing Systems, 72(3-4):311--359, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  2. D. Gamarnik. Using fluid models to prove stability of adversarial queueing networks. IEEE Trans Automatic Control, 45(4):741--746, 2000.Google ScholarGoogle ScholarCross RefCross Ref
  3. B. Hajek. Hitting-time and occupation-time bounds implied by drift analysis with applications. Advances in Applied probability, 14:502--525, 1982.Google ScholarGoogle ScholarCross RefCross Ref
  4. B. Hajek. Mean stochastic comparison of diffusions. Zeitschrift für Wahrscheinlichkeitstheorie und verwandte Gebiete, 68(3):315--329, 1985.Google ScholarGoogle Scholar
  5. B. Hajek. Cooling schedules for optimal annealing. Math Operations Research, 13(2):311--329, 1988. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. B. Hajek. Large bursts do not cause instability. IEEE Trans Automatic Control, 45(1):116--118, 2000.Google ScholarGoogle ScholarCross RefCross Ref
  7. B. Hajek. A maximal inequality for supermartingales. Elect. Commun. Probability, 19:1--10, 2014.Google ScholarGoogle Scholar
  8. J. Kingman. Some inequalities for the queue GI/G/1. Biometrika, 49(3/4):315--324, December 1962.Google ScholarGoogle ScholarCross RefCross Ref
  9. J. Kingman. A martingale inequality in the theory of queues. Cambridge Phiolos. Soc., 59:359--361, 1964.Google ScholarGoogle ScholarCross RefCross Ref
  10. A. L. Stolyar. On the stability of multiclass queueing networks: A relaxed sufficient condition via limiting fluid processes. Markov Processes and Related Fields, 1(4):491--512, 1995.Google ScholarGoogle Scholar
  11. L. Tassiulas and A. Ephremides. Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE Trans Automatic Control, 37(12):1936--1948, 1992.Google ScholarGoogle ScholarCross RefCross Ref

Index Terms

  1. Bounds Implied by Drift with Applications

        Recommendations

        Comments

        Login options

        Check if you have access through your login credentials or your institution to get full access on this article.

        Sign in

        Full Access

        • Published in

          cover image ACM SIGMETRICS Performance Evaluation Review
          ACM SIGMETRICS Performance Evaluation Review  Volume 43, Issue 1
          Performance evaluation review
          June 2015
          468 pages
          ISSN:0163-5999
          DOI:10.1145/2796314
          Issue’s Table of Contents
          • cover image ACM Conferences
            SIGMETRICS '15: Proceedings of the 2015 ACM SIGMETRICS International Conference on Measurement and Modeling of Computer Systems
            June 2015
            488 pages
            ISBN:9781450334860
            DOI:10.1145/2745844

          Copyright © 2015 Owner/Author

          Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

          Publisher

          Association for Computing Machinery

          New York, NY, United States

          Publication History

          • Published: 15 June 2015

          Check for updates

          Qualifiers

          • invited-talk
        • Article Metrics

          • Downloads (Last 12 months)3
          • Downloads (Last 6 weeks)0

          Other Metrics

        PDF Format

        View or Download as a PDF file.

        PDF

        eReader

        View online with eReader.

        eReader