HEAVY AND LIGHT TRAFFIC IN FLUID MODELS WITH BURST ARRIVALS

KARL SIGMAN^{1} AND GENJI YAMAZAKI^{2}

1Department of Industrial Engineering and Operations Research, Columbia University,

Mudd Building, New York, NY 10027, U.S.A.

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

(Received April 11, 1991; revised March 2, 1992)

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 time S_{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.

Key words and phrases: Fluid model, queue, burst arrivals, heavy traffic, light traffic.