A New Approach for Partitioning the Received SNR Space for Tractable Performance Analysis in Wireless Packet Networks

  • Mohamed Hassan
  • Marwan Krunz
  • William Ryan


Successful provisioning of multimedia services over wireless networks hinges on the ability to guarantee certain levels of quality of service (QoS). Prior assessment of the QoS performance requires employing realistic channel models that not only reflect the physical characteristics of the channel, but that also facilitate analytical investigation of its performance. Finite-state Markov chain (FSMC) models have often been used to characterize the wireless channel, whereby the range of the signal-to-noise ratio (SNR) is partitioned according to some criteria into a set of intervals (states). Different partitioning criteria have been used in the literature, but none of them was targeted to facilitating the performance analysis of the packet delay and loss performance over the wireless link. In this paper, we propose a new method for partitioning the received SNR space that results in a FSMC model with tractable queueing performance. We make use of the level-crossing analysis, the distribution of the received SNR, and the producer-consumer queueing model of Mitra [14] to arrive at the proposed FSMC model. An algorithm is provided for computing the various parameters of the model, including the number of states, the partitioning thresholds, and the “nominal” bit error rates. The usefulness of the obtained model is then highlighted by deriving a closed-form expression for the effective bandwidth (EB) subject to a packet loss constraint. Numerical examples are presented to study the interactions between various key parameters and the adequacy of the proposed model.


Packet Loss Effective Bandwidth BPSK Modulation Wireless Packet Network Service Ratio 


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  1. [1]
    M. Zorzi, R. R. Rao, and L. B. Milstein, “Error statistics in data transmission over fading channels,” IEEE Trans. Commun., vol. 46, pp. 1468–1477, 1998.CrossRefGoogle Scholar
  2. [2]
    H. Bischl and E. Lutz, “Packet error rate in the non-interleaved Rayleigh channel,” IEEE Trans. Commun., vol. 43, pp. 1375–1382, 1995.CrossRefGoogle Scholar
  3. [3]
    H. Steffan, “Adaptive generative radio channel models,” In Proceedings of the 5th IEEE International Symposium on Personal, Indoor and Mobile Radio Communications., vol. 1, pp. 268–273, 1994.Google Scholar
  4. [4]
    S. Lin and D. J. Costello, Error Coding: Fundamentals and Applications, Englewood Cliffs, NJ: Printce Hall, 1984.Google Scholar
  5. [5]
    W. C. Jakes, Microwave Mobile Communications, New York, NY: John Wiley and Sons, INC., 1977.Google Scholar
  6. [6]
    B. Vucetic, “An adaptive coding scheme for time-varying channels,” IEEE Trans. Commun., vol. 39, pp. 653–663, May 1991.CrossRefGoogle Scholar
  7. [7]
    M. Rice and S. B. Wicker, “Adaptive error control for slowly-varying channels,” IEEE Trans.Commun., vol. 42, pp. 917–925, 1994.CrossRefGoogle Scholar
  8. [8]
    H.S. Wang and N. Moayeri, “Finite-state Markov Channel-a useful model for radio communication channels,” IEEE Trans. Vech. technol.,vol. 44, pp. 163171, 1995.Google Scholar
  9. [9]
    Q. Zhang and Salem A. Kassam, “Finite-state Markov model for Rayleigh fading channels,” IEEE Trans. Commun., vol. 47, Nov. 1999.Google Scholar
  10. [10]
    Y. L. Guan and L. F. Turner, “Generalized FSMC model for radio channels with corrlated fading,” IEEE Proc. Commun., vol. 146, April. 1999.Google Scholar
  11. [11]
    J. Kim, and M. Krunz, “Bandwidth allocation in wireless networks with guaranteed packet-loss performance,” IEEE/ACM Transactions on Networking, vol. 8, pp. 337–349, 2000.CrossRefGoogle Scholar
  12. [12]
    M. Hassan, M. Krunz, and I. Matta “Markov-based Channel Characterization for Tractable Performance Analysis in Wireless Packet Networks,” Submitted to IEEE Transactions on Wireless Communications.Google Scholar
  13. [13]
    D. Anick, D. Mitra, and M. M. Sondhi,“Stochastic theory of a data—handling system with multiple sources,”Bell Syst. Tech. J., vol. 61, pp. 1871–1894, Feb. 1982.MathSciNetGoogle Scholar
  14. [14]
    D. Mitra, “Stochastic theory of a fluid model of producers and consumers coupled by a buffer,” Adv. Appl. Prob., vol. 20, pp. 646–676, 1988.MATHCrossRefGoogle Scholar
  15. [15]
    A. I. Elwalid and D. Mitra, “Effective bandwidth of general Markovian traffic sources and admission control of high speed networks, ”IEEE/ACM Trans. Networking, vol. 1, pp. 329–343, 1993.CrossRefGoogle Scholar
  16. [16]
    A. I. Elwalid, and D.Mitra, “Statistical multiplexing with loss priorities in rate-based congestion control of high-speed networks,” IEEE Trans. Commun., vol. 42, pp. 2989–3002, 1994.CrossRefGoogle Scholar
  17. [17]
    C.-S. Chang, Performance Guarantees in Communication Netwoks, London Berlin Heidelberg: Springer-Verlag, 2000.CrossRefGoogle Scholar
  18. [18]
    P G. Hoel, S. Port, and C. Stone, Introduction to Stochastic Processes, Prospect Heights, IL: Waveland Press, Inc., 1972.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Mohamed Hassan
    • 1
  • Marwan Krunz
    • 1
  • William Ryan
    • 1
  1. 1.Department of Electrical & Computer EngineeringUniversity of ArizonaTucsonUSA

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