Network Scheduling and Message-passing

  • Devavrat Shah

Algorithms are operational building-blocks of a network. An important class of network algorithms deal with the scheduling of common resources among various entities such as packets or flows. In a generic setup, such algorithms operate under stringent hardware, time, power or energy constraints. Therefore, algorithms have to be extremely simple, lightweight in data-structure and distributed. Therefore, a network algorithm designer is usually faced with the task of resolving an acute tension between performance and implementability of the algorithm. In this chapter, we survey recent results on novel design and analysis methods for simple, distributed aka message-passing scheduling algorithms. We describe how the asymptotic analysis methods like fluid model and heavy traffic naturally come together with algorithm design methods such as randomization and belief-propagation (message-passing heuristic) in the context of network scheduling.


Schedule Algorithm Output Port Input Port Queue Size Virtual Resource 


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  1. 1.
    Andrews, M. and Kumaran, M. and Ramanan, K. and Stolyar, A. and Vijayakumar, R. and Whiting, P.:Scheduling in a queueing system with asynchronously varying service rates. Probability in the Engineering and Informational Sciences, Vol. 18 (2):191–217, (2004).MATHMathSciNetGoogle Scholar
  2. 2.
    Bambos, N. and Walrand, J.:Scheduling and stability aspects of a general class of parallel processing systems. Advances in Applied Probability, Vol. 25(1):176–202, (1993).MATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Bayati, M. and Shah, D. and Sharma, M.:Max-product for maximum weight matching:convergence, correctness and LP duality. IEEE Information Theory Transactions, Vol. 54 (3):1241–1251, (2008). Preliminary versions appeareared in IEEE ISIT, (2005) and (2006).CrossRefMathSciNetGoogle Scholar
  4. 4.
    Bayati, M. and Prabhakar, B. and Shah, D. and Sharma, M.:Iterative scheduling algorithms. IEEE Infocom, (2007).Google Scholar
  5. 5.
    Betsekas, D.:The auction algorithm:a distributed relaxation method for the assignment problem. Annals of operations research, Vol. 14:105–123., (1988).CrossRefMathSciNetGoogle Scholar
  6. 6.
    Boyd, S. and Ghosh, A. and Prabhakar, B. and Shah, D.:Gossip algorithms:design, analysis and application. In proceedings of IEEE Infocom, (2005).Google Scholar
  7. 7.
    Bramson, M.:State space collapse with application to heavy traffic limits for multiclass queueing networks. Queueing Systems 30 89–148, (1998).MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Dai, J. G. “Jim”:Stability of fluid and stochastic processing networks. MaPhySto Lecture Notes, (1999).
  9. 9.
    Dai, J. and Prabhakar, B.:The throughput of switches with and without speed-up. In proceedings of IEEE Infocom, (2000).Google Scholar
  10. 10.
    Dembo, A. and Zeitouni, O.:Large Deviations Techniques and Applications, 2nd edition, Springer, (1998).Google Scholar
  11. 11.
    Eryilmaz, A. and Srikant, R. and Perkins, J. R.:Stable scheduling policies for fading wireless channels. IEEE/ACM Trans. Networking, Vol. 13(2):411–424, (2005).CrossRefGoogle Scholar
  12. 12.
    Giaccone, P. and Prabhakar, B and Shah, D.:Randomized scheduling algorithms for high-aggregate bandwidth switches. IEEE J. Sel. Areas Commun., 21(4), 546–559, (2003).CrossRefGoogle Scholar
  13. 13.
    Jung, K. and Shah, D.:Low Delay Scheduling in Wireless Network. In Proceedings of IEEE ISIT, (2007).Google Scholar
  14. 14.
    Keslassy, I. and McKeown, N.:Analysis of Scheduling Algorithms That Provide 100% Throughput in Input-Queued Switches. In proceedings of Allerton Conference on Communication, Control and Computing, (2001).Google Scholar
  15. 15.
    McKeown, N.:The iSLIP scheduling algorithm for input-queued switches. IEEE/ACM Transactions on Networking, 7(2), 188–201, (1999).CrossRefGoogle Scholar
  16. 16.
    McKeown, N. and Anantharam, V. and Walrand, J.:Achieving 100% throughput in an input-queued switch. In Proceedings of IEEE Infocom, 296–302 (1996).Google Scholar
  17. 17.
    Meyn, S. P. and Tweedie, R. L.:Markov Chains and Stochastic Stability. Springer-Verlag, London, (1993). MATHGoogle Scholar
  18. 18.
    Modiano, E. and Shah, D. Zussman, G.:Maximizing Throughput in Wireless Network via Gossiping. In Proceedings of ACM SIGMETRIC/Performance, (2006).Google Scholar
  19. 19.
    Mosk-Aoyama, D. and Shah, D. Computing separable functions via gossip. In Proceedings of ACM PODC, (2006). Longer version to appear in IEEE Transaction on Information Theory, (2008).Google Scholar
  20. 20.
    Tassiulas, L. and Ephremides, A.:Dynamic server allocation to parallel queues with randomly varying connectivity. IEEE Transactions on Information Theory, Vol. 39(2), 466–478, (1993).MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    Sanghavi, S. and Shah, D. and Willsky, A.:Message-passing for Maximum Weight Independent Set. Submitted. In Proceedings of NIPS, (2007).Google Scholar
  22. 22.
    Shah, D.:Stable algorithms for Input Queued Switches. In Proceedings of Allerton Conference on Communication, Control and Computing, (2001).Google Scholar
  23. 23.
    Shah, D. and Kopikare, M.:Delay bounds for the approximate Maximum Weight matching algorithm for input queued switches. In Proceedings of IEEE Infocom, (2002).Google Scholar
  24. 24.
    Shah, D. and Tse, D. and Tsitsiklis, J. N.:On hardness of low delay scheduling. Pre-print, (2008).Google Scholar
  25. 25.
    Shah, D. and Wischik, D. J.: Optimal scheduling algorithms for input-queued switches. In Proceedings of IEEE Infocom, (2006).Google Scholar
  26. 26.
    Shah, D. and Wischik, D. J.: Heavy traffic analysis of optimal scheduling algorithms for switches networks. Submitted. Preliminary version appeared in proceedings of IEEE Infocom, (2006).
  27. 27.
    Shakkottai, S. and Srikant, R. and Stolyar, A. L.:Pathwise Optimality of the Exponential Scheduling Rule for Wireless Channels. Advances in Applied Probability, Vol. 36(4), 1021–1045, (2004).MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Stolyar, A. L.:On the stability of multiclass queueing networks:A relaxed sufficient condition via limiting fluid processes. Markov Processes and Related Fields, 491–512, (1995). mprf.pdf
  29. 29.
    Stolyar, A. L.:Maxweight scheduling in a generalized switch:State space collapse and work-load minimization in heavy traffic. Annals of Applied Probability, Vol. 14(1), 1–53, (2004).MATHCrossRefMathSciNetGoogle Scholar
  30. 30.
    Tassiulas, L.:Linear complexity algorithms for maximum throughput in radio networks and input queued switches. In Proceedings of IEEE INFOCOM'98, (1998).Google Scholar
  31. 31.
    Tassiulas, L. and Ephremides, A.:Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks. IEEE Transactions on Automatic Control, 37, 1936-1948 (1992).MATHCrossRefMathSciNetGoogle Scholar
  32. 32.
    Tsitsiklis, J. N.:Problems in decentralized decision making and computation. Ph.D. Thesis, Department of EECS, MIT, (1984).Google Scholar
  33. 33.
    Williams, R.:iffusion approximations for open multiclass queueing networks:sufficient conditions involving state space collapse. Queueing Systems 30 27–88, (1998).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Devavrat Shah
    • 1
  1. 1.Department of EECSMassachusetts Institute of TechnologyCambridge

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