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  • Cited by 6
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Tunc, Caglar and Akar, Nail 2016. Fixed-point analysis of a network of routers with persistent TCP/UDP flows and class-based weighted fair queuing. Telecommunication Systems,

    Fiems, Dieter Prabhu, Balakrishna and De Turck, Koen 2013. Analytic approximations of queues with lightly- and heavily-correlated autoregressive service times. Annals of Operations Research, Vol. 202, Issue. 1, p. 103.

    2012. End to End Adaptive Congestion Control in TCP/IP Networks.

    Bhatnagar, Shalabh and Patro, Rajesh 2009. A proof of convergence of the B-RED and P-RED algorithms for random early detection. IEEE Communications Letters, Vol. 13, Issue. 10, p. 809.

    Wang, Yung-Chung Tseng, Chwan-Lu Chu, Ren-Guey and Tsai, Fu-Hsiang 2009. Per-stream loss behavior of ∑MAP/M/1/K queuing system with a random early detection mechanism. Information Sciences, Vol. 179, Issue. 22, p. 3893.

    Do Young Eun, and Xinbing Wang, 2008. Achieving 100% Throughput in TCP/AQM Under Aggressive Packet Marking With Small Buffer. IEEE/ACM Transactions on Networking, Vol. 16, Issue. 4, p. 945.

  • Probability in the Engineering and Informational Sciences, Volume 16, Issue 3
  • July 2002, pp. 367-388


  • V. Sharma (a1), J. Virtamo (a2) and P. Lassila (a3)
  • DOI:
  • Published online: 01 July 2002

In this article we consider a finite queue with its arrivals controlled by the random early detection algorithm. This is one of the most prominent congestion avoidance schemes in the Internet routers. The aggregate arrival stream from the population of transmission control protocol sources is locally considered stationary renewal or Markov modulated Poisson process with general packet length distribution. We study the exact dynamics of this queue and provide the stability and the rates of convergence to the stationary distribution and obtain the packet loss probability and the waiting time distribution. Then we extend these results to a two traffic class case with each arrival stream renewal. However, computing the performance indices for this system becomes computationally prohibitive. Thus, in the latter half of the article, we approximate the dynamics of the average queue length process asymptotically via an ordinary differential equation. We estimate the error term via a diffusion approximation. We use these results to obtain approximate transient and stationary performance of the system. Finally, we provide some computational examples to show the accuracy of these approximations.

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Probability in the Engineering and Informational Sciences
  • ISSN: 0269-9648
  • EISSN: 1469-8951
  • URL: /core/journals/probability-in-the-engineering-and-informational-sciences
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