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MaxWeight Scheduling: Asymptotic Behavior of Unscaled Queue-Differentials in Heavy Traffic

Published: 15 June 2015 Publication History

Abstract

The model is a "generalized switch", serving multiple traffic flows in discrete time. The switch uses MaxWeight algorithm to make a service decision (scheduling choice) at each time step, which determines the probability distribution of the amount of service that will be provided. We are primarily motivated by the following question: in the heavy traffic regime, when the switch load approaches critical level, will the service processes provided to each flow remain "smooth" (i.e., without large gaps in service)? Addressing this question reduces to the analysis of the asymptotic behavior of the unscaled queue-differential process in heavy traffic. We prove that the stationary regime of this process converges to that of a positive recurrent Markov chain, whose structure we explicitly describe. This in turn implies asymptotic "smoothness" of the service processes.

References

[1]
M. Andrews, K. Kumaran, K. Ramanan, A. L. Stolyar, R. Vijayakumar, P. Whiting. Providing Quality of Service over a Shared Wireless Link. IEEE Communications Magazine, 2001, Vol.39, No. 2, pp. 150--154.
[2]
M. Andrews, K. Jung, A. L. Stolyar. Stabilityof the Max-Weight Routing and Scheduling Protocol in Dynamic Networks and at Critical Loads. STOC'07, San Diego, CA, June 11-13, 2007.
[3]
A. Eryilmaz and R. Srikant. Asymptotically Tight Steady-State Queue Length Bounds Implied by Drift Conditions. Queueing Systems, 2012, Vol. 72, No.3--4, pp .311--359.
[4]
B. Hajek. Hitting-Time and Occupation-Time Bounds Implied by Drift Analysis with Applications. Advances in Applied Probability, 1982, Vol. 14, No. 3, pp. 502--525.
[5]
I-H. Hou, V. Borkar and P.R. Kumar. A Theory of QoS for Wireless. INFOCOM 2009.
[6]
R. Li, A. Eryilmaz, B. Li. Throughput-Optimal Wireless Scheduling with Regulated Inter-Service Times. INFOCOM 2013.
[7]
B. Li, R. Li, A. Eryilmaz. Heavy-Traffic-Optimal Scheduling with Regular Service Guarantees in Wireless Networks. MobiHoc 2013.
[8]
S. P. Meyn and R.L. Tweedie. Stability of Markovian Processes I: Criteria for Discrete-Time chains. Advances in Applied Probability, 1992, Vol. 24, No. 3,pp. 542--574.
[9]
A.L. Stolyar.Max Weight Scheduling in a Generalized Switch: State Space Collapse and Workload Minimization in Heavy Traffic. Annals of Applied Probability, 2004, Vol. 14, No. 1, pp. 1--53.
[10]
L. Tassiulas, E. Ephremides. Stability properties of constrained queueingsystems and scheduling policies for maximum throughput in multihop radio networks. IEEE Trans. Automat. Control, 1992, Vol. 37, No. 1, pp. 1936-1948.
[11]
J. Ni, B. Tan and R. Srikant. Q-CSMA: Queue-Length Based CSMA/CA Algorithms for Achieving Maximum Throughput and Low Delay in Wireless Networks. INFOCOM 2010.
[12]
R. Singh and A. Stolyar. MaxWeight Scheduling: Asymptotic Behavior of Unscaled Queue-Differentials in Heavy Traffic. http://arxiv.org/abs/1502.03793

Cited By

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  • (2022)Logarithmic heavy traffic error bounds in generalized switch and load balancing systemsJournal of Applied Probability10.1017/jpr.2021.8259:3(652-669)Online publication date: 21-Jun-2022
  • (2018)A Risk-Sensitive Approach for Packet Inter-Delivery Time Optimization in Networked Cyber-Physical SystemsIEEE/ACM Transactions on Networking10.1109/TNET.2018.285688326:4(1976-1989)Online publication date: 1-Aug-2018
  • (2018)Optimal heavy-traffic queue length scaling in an incompletely saturated switchQueueing Systems: Theory and Applications10.1007/s11134-017-9562-x88:3-4(279-309)Online publication date: 1-Apr-2018
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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
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.

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Publication History

Published: 15 June 2015

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Author Tags

  1. dynamic scheduling
  2. heavy traffic asymptotic regime
  3. markov chain
  4. maxweight algorithm
  5. queue length differentials
  6. smooth service process

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SIGMETRICS '15 Paper Acceptance Rate 32 of 239 submissions, 13%;
Overall Acceptance Rate 459 of 2,691 submissions, 17%

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Cited By

View all
  • (2022)Logarithmic heavy traffic error bounds in generalized switch and load balancing systemsJournal of Applied Probability10.1017/jpr.2021.8259:3(652-669)Online publication date: 21-Jun-2022
  • (2018)A Risk-Sensitive Approach for Packet Inter-Delivery Time Optimization in Networked Cyber-Physical SystemsIEEE/ACM Transactions on Networking10.1109/TNET.2018.285688326:4(1976-1989)Online publication date: 1-Aug-2018
  • (2018)Optimal heavy-traffic queue length scaling in an incompletely saturated switchQueueing Systems: Theory and Applications10.1007/s11134-017-9562-x88:3-4(279-309)Online publication date: 1-Apr-2018
  • (2017)Risk-sensitive optimal control of queues2017 IEEE 56th Annual Conference on Decision and Control (CDC)10.1109/CDC.2017.8264182(3563-3568)Online publication date: Dec-2017
  • (2016)Optimal Heavy-Traffic Queue Length Scaling in an Incompletely Saturated SwitchACM SIGMETRICS Performance Evaluation Review10.1145/2964791.290146644:1(13-24)Online publication date: 14-Jun-2016
  • (2016)MaxWeight scheduling: “Smoothness” of the service processIEEE INFOCOM 2016 - The 35th Annual IEEE International Conference on Computer Communications10.1109/INFOCOM.2016.7524518(1-9)Online publication date: Apr-2016
  • (2015)A High Reliability Asymptotic Approach for Packet Inter-Delivery Time Optimization in Cyber-Physical SystemsProceedings of the 16th ACM International Symposium on Mobile Ad Hoc Networking and Computing10.1145/2746285.2746305(197-206)Online publication date: 22-Jun-2015
  • (2015)Optimizing quality of experience of dynamic video streaming over fading wireless networks2015 54th IEEE Conference on Decision and Control (CDC)10.1109/CDC.2015.7403354(7195-7200)Online publication date: Dec-2015
  • (2015)Decentralized throughput maximizing policies for deadline-constrained wireless networks2015 54th IEEE Conference on Decision and Control (CDC)10.1109/CDC.2015.7402803(3759-3766)Online publication date: Dec-2015
  • (2017)Risk-sensitive optimal control of queues2017 IEEE 56th Annual Conference on Decision and Control (CDC)10.1109/CDC.2017.8264182(3563-3568)Online publication date: Dec-2017

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