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Heavy and light traffic in fluid models with burst arrivals

  • Stochastic Models
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Abstract

We consider the problem of finding a heavy and light traffic limits for the steady-state workload in a fluid model having a continuous burst arrival process. Such a model is useful for describing (among other things) the packetwise transmission of data in telecommunications, where each packet is approximated to be a continuous flow. Whereas in a queueing model, each arrival epoch,t n , corresponds to a customer with a service timeS n , the burst model is different: each arrival epoch,t n , corresponds to a burst of work, that is, a continuous flow of work (fluid, information) to the system at rate 1 during the time interval [t n ,t n +S n ]. In the present paper we show that the burst and queueing models share the same heavy-traffic limit for work, but that their behavior in light traffic is quite different.

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Author information

Authors and Affiliations

  1. Department of Industrial Engineering and Operations Research, Columbia University, Mudd Building, 10027, New York, NY, USA

    Karl Sigman

  2. Tokyo Metropolitan Institute of Technology, 6-6 Asahigaoka, 191, Hino, Tokyo, Japan

    Genji Yamazaki

Authors
  1. Karl Sigman
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  2. Genji Yamazaki
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Additional information

Research supported by the Japan Society for the Promotion of Science, during the author's fellowship in Tokyo.

Research funded by C & C Information Technology Research Laboratories, NEC, and the International Science Foundation.

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Sigman, K., Yamazaki, G. Heavy and light traffic in fluid models with burst arrivals. Ann Inst Stat Math 45, 1–7 (1993). https://doi.org/10.1007/BF00773664

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  • DOI: https://doi.org/10.1007/BF00773664

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