Queueing Systems

, Volume 50, Issue 4, pp 401–457 | Cite as

Maximizing Queueing Network Utility Subject to Stability: Greedy Primal-Dual Algorithm

Article

Abstract

We study a model of controlled queueing network, which operates and makes control decisions in discrete time. An underlying random network mode determines the set of available controls in each time slot. Each control decision “produces” a certain vector of “commodities”; it also has associated “traditional” queueing control effect, i.e., it determines traffic (customer) arrival rates, service rates at the nodes, and random routing of processed customers among the nodes. The problem is to find a dynamic control strategy which maximizes a concave utility function H(X), where X is the average value of commodity vector, subject to the constraint that network queues remain stable.

We introduce a dynamic control algorithm, which we call Greedy Primal-Dual (GPD) algorithm, and prove its asymptotic optimality. We show that our network model and GPD algorithm accommodate a wide range of applications. As one example, we consider the problem of congestion control of networks where both traffic sources and network processing nodes may be randomly time-varying and interdependent. We also discuss a variety of resource allocation problems in wireless networks, which in particular involve average power consumption constraints and/or optimization, as well as traffic rate constraints.

Keywords

queueing networks convex optimization primal-dual algorithm stability congestion control resource allocation scheduling wireless power and rate constraints 

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References

  1. [1]
    M. Andrews, K. Kumaran, K. Ramanan, A.L. Stolyar, R. Vijayakumar and P. Whiting, Providing quality of service over a shared wireless link, IEEE Communications Magazine 39(2) (2001) 150–154.Google Scholar
  2. [2]
    M. Andrews, L. Qian and A.L. Stolyar, Optimal utility based multi-user throughput allocation subject to throughput constraints, in: Proceeding of INFOCOM’2005, Miami, March 13–17, 2005.Google Scholar
  3. [3]
    R. Agrawal and V. Subramanian, Optimality of certain channel aware scheduling policies, in: Proc. of the 40th Annual Allerton Conference on Communication, Control, and Computing, (Monticello, Illinois, USA, October 2002).Google Scholar
  4. [4]
    J.G. Dai and W. Lin, Maximum pressure policies in stochastic processing networks, Operations Research 53(2) (2005) 197–218.CrossRefGoogle Scholar
  5. [5]
    S.N. Ethier and T.G. Kurtz, Markov Processes: Characterization and Convergence, (John Wiley and Sons, New York, 1986).Google Scholar
  6. [6]
    A. Eryilmaz and R. Srikant, Fair resource allocation in wireless networks using Queue-length-based scheduling and congestion control, in: Proceedings of INFOCOM’2005, Miami, March 13–17, 2005.Google Scholar
  7. [7]
    J.M. Harrison. Brownian Motion and Stochastic Flow Systems, (Wiley, 1985).Google Scholar
  8. [8]
    A. Jalali, R. Padovani and R. Pankaj, Data Throughput of CDMA-HDR, a high efficiency—high data rate personal communication wireless system, in: Proc. of the IEEE Semiannual Vehicular Technology Conference, VTC2000-Spring (Tokyo, Japan, May 2000).Google Scholar
  9. [9]
    L.V. Kantorovich and G.P. Akilov, Functional Analysis, 2nd ed. (Pergamon Press, New York, 1982).Google Scholar
  10. [10]
    F.P. Kelly, A.K. Maullo and D.K.H. Tan, Rate control in communication networks: Shadow prices, proportional fairness and stability, Journal of the Operational Research Society 49 (1998) 237–252.CrossRefGoogle Scholar
  11. [11]
    F.P. Kelly, Fairness and stability of end-to-end congestion control, European Journal of Control 9 (2003) 159–176.Google Scholar
  12. [12]
    T. Klein and H. Viswanathan, Centralized power control for multi-hop wireless networks, (2003), submitted.Google Scholar
  13. [13]
    S. Karlin, Mathematical Methods in Games, Programming, and Economics (Dover, New York, 1992).Google Scholar
  14. [14]
    S. Liu, T. Basar and R. Srikant, Controlling the Internet: A survey and some new results (2003), preprint.Google Scholar
  15. [15]
    X. Liu, E.K.P. Chong and N.B. Shroff, A framework for opportunistic scheduling in wireless networks, Computer Networks 41 (2003) 451–474.CrossRefGoogle Scholar
  16. [16]
    S. Low, A duality model of TCP and queue management algorithms, IEEE/ACM Transactions on Networkin 11(4) (2003) 525–536.Google Scholar
  17. [17]
    R.T. Rockafellar, Convex Analysis, Princeton Univ. Press, 1970.Google Scholar
  18. [18]
    R. Srikant, The Mathematics of Internet Congestion Control (Birkhauser, 2004).Google Scholar
  19. [19]
    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) (1995) 491–512.Google Scholar
  20. [20]
    A.L. Stolyar, MaxWeight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic, Annals of Applied Probability 14(1) (2004) 1–53.CrossRefGoogle Scholar
  21. [21]
    A.L. Stolyar, On the asymptotic optimality of the gradient scheduling algorithm for multi-user throughput allocation, Operations Research 53(1) (2005) 12–25.CrossRefGoogle Scholar
  22. [22]
    L. Tassiulas and A. Ephremides, Stability properties of constrained queueing systems and scheduling policies for maximum throughput in multihop radio networks, IEEE Transactions on Automatic Control 37 (1992) 1936–1948.CrossRefGoogle Scholar
  23. [23]
    L. Tassiulas and P.P. Bhattacharya, Allocation of interdependent resources for maximal throughput, Commun. Statist.—Stochastic Models 16 (2000) 27–48.Google Scholar
  24. [24]
    D. Tse and S. Hanly, Multi-access fading channels: Part I: Polymatroid structure, optimal resource allocation and throughput capacities, IEEE Transactions on Information Theory 44(7) (1998) 2796–2815.CrossRefGoogle Scholar
  25. [25]
    P. Viswanath, D. Tse and R. Laroia, Opportunistic beamforming using dumb antennas, IEEE Transactions on Information Theory 48(6) (2002) 1277–1294.Google Scholar
  26. [26]
    J.T. Wen and M. Arcak, A unifying passivity framework for network flow control, IEEE Transactions on Automatic Control 49(2) (2004) 162–174.CrossRefGoogle Scholar
  27. [27]
    E.M. Yeh and A.S. Cohen, Throughput and delay optimal resource allocation in multiaccess fading channels, in: Proceedings of ISIT, (Yokohama, Japan, June–July 2003).Google Scholar

Copyright information

© Springer Science + Business Media, Inc. 2005

Authors and Affiliations

  1. 1.Bell Labs, Lucent TechnologiesUSA

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