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Heavy and light traffic in fluid models with burst arrivals
Authors:Karl Sigman and Genji Yamazaki
Institution:(1) Department of Industrial Engineering and Operations Research, Columbia University, Mudd Building, 10027 New York, NY, USA;(2) Tokyo Metropolitan Institute of Technology, 6-6 Asahigaoka, 191 Hino, Tokyo, Japan
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.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.
Keywords:Fluid model  queue  burst arrivals  heavy traffic  light traffic
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