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

When heavy-tailed and light-tailed flows compete: the response time tail under generalized max-weight scheduling

Published: 01 April 2016 Publication History

Abstract

This paper focuses on the design and analysis of scheduling policies for multi-class queues, such as those found in wireless networks and high-speed switches. In this context, we study the response-time tail under generalized max-weight policies in settings where the traffic flows are highly asymmetric. Specifically, we consider a setting where a bursty flow, modeled using heavy-tailed statistics, competes with a more benign, light-tailed flow. In this setting, we prove that classical max-weight scheduling, which is known to be throughput optimal, results in the light-tailed flow having heavy-tailed response times. However, we show that via a careful design of inter-queue scheduling policy (from the class of generalized max-weight policies) and intra-queue scheduling policies, it is possible to maintain throughput optimality, and guarantee light-tailed delays for the light-tailed flow, without affecting the response-time tail for the heavy-tailed flow.

References

[1]
J. Nair, K. Jagannathan, and A. Wierman, "When heavy-tailed and lighttailed flows compete: The response time tail under generalized maxweight scheduling," in Proc. IEEE INFOCOM, 2013.
[2]
L. Tassiulas and A. Ephremides, "Dynamic server allocation to parallel queues with randomly varying connectivity," IEEE Trans. Inf. Theory, vol. 39, no. 2, pp. 466--478, 1993.
[3]
L. Tassiulas and A. Ephremides, "Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks," IEEE Trans. Autom. Contr., vol. 37, no. 12, pp. 1936--1948, 1992.
[4]
N. McKeown, A. Mekkittikul, V. Anantharam, and J. Walrand, "Achieving 100% throughput in an input-queued switch," IEEE Trans. Commun., vol. 47, no. 8, pp. 1260--1267, 1999.
[5]
M. Neely, E. Modiano, and C. Rohrs, "Power and server allocation in a multi-beam satellite with time varying channels," in Proc. IEEE INFOCOM, 2002.
[6]
A. Stolyar, "Maxweight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic," Annals Appl. Probab., vol. 14, no. 1, pp. 1--53, 2004.
[7]
A. Eryilmaz, R. Srikant, and J. R. Perkins, "Stable scheduling policies for fading wireless channels," IEEE/ACM Trans. Netw., vol. 13, no. 2, pp. 411--424, 2005.
[8]
A. Brzezinski and E. Modiano, "Dynamic reconfiguration and routing algorithms for IP-over-WDM networks with stochastic traffic," J. Lightw. Technol., vol. 23, no. 10, pp. 3188--3205, 2005.
[9]
M. Neely, "Delay analysis for max weight opportunistic scheduling in wireless systems," IEEE Trans. Autom. Contr., vol. 54, no. 9, pp. 2137--2150, 2009.
[10]
M. Neely, E. Modiano, and C. Rohrs, "Dynamic power allocation and routing for time varying wireless networks," in Proc. IEEE INFOCOM, 2003.
[11]
L. Le, K. Jagannathan, and E. Modiano, "Delay analysis of maximum weight scheduling in wireless ad hoc networks," in Proc. IEEE CISS, 2009.
[12]
A. Eryilmaz and R. Srikant, "Asymptotically tight steady-state queue length bounds implied by drift conditions," Queueing Syst., vol. 72, no. 3---4, pp. 311--359, 2012.
[13]
A. Ganti, E. Modiano, and J. Tsitsiklis, "Optimal transmission scheduling in symmetric communication models with intermittent connectivity," IEEE Trans. Inf. Theory, vol. 53, no. 3, pp. 998--1008, 2007.
[14]
M. Neely, "Delay analysis for max weight opportunistic scheduling in wireless systems," IEEE Trans. Autom. Contr., vol. 54, no. 9, pp. 2137--2150, 2009.
[15]
S. Borst, M. Mandjes, and M. van Uitert, "Generalized processor sharing with light-tailed and heavy-tailed input," IEEE/ACM Trans. Netw., vol. 11, no. 5, pp. 821--834, 2003.
[16]
S. Borst, O. Boxma, and M. Van Uitert, "The asymptotic workload behavior of two coupled queues," Queueing Syst., vol. 43, no. 1, pp. 81--102, 2003.
[17]
O. Boxma, Q. Deng, and A. Zwart, "Waiting-time asymptotics for the M/G/2 queue with heterogeneous servers," Queueing Syst., vol. 40, no. 1, pp. 5--31, 2002.
[18]
S. Borst, R. Núñez-Queija, and B. Zwart, "Bandwidth sharing with heterogeneous flow sizes," Annals Telecommun., vol. 59, no. 11, pp. 1300--1314, 2004.
[19]
M. Markakis, E. Modiano, and J. Tsitsiklis, "Scheduling policies for single-hop networks with heavy-tailed traffic," in Proc. 47th Annual Allerton Conf. Communication, Control, Computing, 2009.
[20]
K. Jagannathan, M. Markakis, E. Modiano, and J. Tsitsiklis, "Throughput optimal scheduling in the presence of heavy-tailed traffic," in Proc. 48th Annual Allerton Conf. Communication, Control, Computing, 2010.
[21]
K. Jagannathan, "Asymptotic Performance of Queue Length Based Network Control Policies," Ph.D. dissertation, MIT, Cambridge, MA, USA, 2010.
[22]
L. Huang, S. Moeller, M. Neely, and B. Krishnamachari, "Lifoback-pressure achieves near optimal utility-delay tradeoff," in Proc. WiOpt, 2011.
[23]
O. Boxma and B. Zwart, "Tails in scheduling," Perf. Eval. Rev., vol. 34, no. 4, pp. 13--20, 2007.
[24]
S. Foss, D. Korshunov, and S. Zachary, An Introduction to Heavy-Tailed and Subexponential Distributions. New York, NY, USA: Springer, 2011.
[25]
K. Sigman, "Appendix: A primer on heavy-tailed distributions," Queueing Syst., vol. 33, no. 1, pp. 261--275, 1999.
[26]
S. Resnick, Heavy-Tail Phenomena: Probabilistic and Statistical Modeling. New York, NY, USA: Springer, 2007.
[27]
S. Asmussen, Applied Probability and Queues. New York, NY, USA: Springer, 2003.
[28]
J. Nair, "Scheduling for Heavy-Tailed and Light-Tailed Workloads in Queueing Systems," Ph.D. dissertation, California Institute of Technology, Pasadena, CA, USA, 2012.
[29]
M. G. Markakis, E. Modiano, and J. N. Tsitsiklis, "Max-Weight scheduling in queueing networks with heavy-tailed traffic," IEEE/ACM Trans. Netw., vol. 22, no. 1, pp. 257--270, 2014.
[30]
G. Samorodnitsky, Long Range Dependence, Heavy Tails and Rare Events 2002, Lecture notes {Online}. Available: http://dspace.library.cornell.edu/bitstream/1813/9228/1/TR001350.pdf
[31]
N. N. H. Bingham and R. A. Doney, "Asymptotic properties of super-critical branching processes I: The Galton-Watson process," in Adv. Appl. Probab., 1974, pp. 711--731.
[32]
S. Borst, O. Boxma, R. Núñez-Queija, and B. Zwart, "The impact of the service discipline on delay asymptotics," Perf. Eval., vol. 54, pp. 175--206, 2003.

Cited By

View all
  • (2017)Delay-Based Maximum Power-Weight Scheduling With Heavy-Tailed TrafficIEEE/ACM Transactions on Networking10.1109/TNET.2017.270674325:4(2540-2555)Online publication date: 1-Aug-2017

Recommendations

Comments

Information & Contributors

Information

Published In

cover image IEEE/ACM Transactions on Networking
IEEE/ACM Transactions on Networking  Volume 24, Issue 2
April 2016
646 pages
ISSN:1063-6692
Issue’s Table of Contents

Publisher

IEEE Press

Publication History

Published: 01 April 2016
Published in TON Volume 24, Issue 2

Author Tags

  1. first come first served
  2. heavy-tailed traffic
  3. large deviations
  4. last come first served
  5. light-tailed traffic
  6. maximum weight scheduling
  7. response time tail
  8. stability

Qualifiers

  • Research-article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)2
  • Downloads (Last 6 weeks)0
Reflects downloads up to 06 Oct 2024

Other Metrics

Citations

Cited By

View all
  • (2017)Delay-Based Maximum Power-Weight Scheduling With Heavy-Tailed TrafficIEEE/ACM Transactions on Networking10.1109/TNET.2017.270674325:4(2540-2555)Online publication date: 1-Aug-2017

View Options

Get Access

Login options

Full Access

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media