Article ID Journal Published Year Pages File Type
1155752 Stochastic Processes and their Applications 2011 27 Pages PDF
Abstract

Stochastic networks with time varying arrival and service rates and routing structure are studied. Time variations are governed by, in addition to the state of the system, two independent finite state Markov processes XX and YY. The transition times of XX are significantly smaller than typical inter-arrival and processing times whereas the reverse is true for the Markov process YY. By introducing a suitable scaling parameter one can model such a system using a hierarchy of time scales. Diffusion approximations for such multiscale systems are established under a suitable heavy traffic condition. In particular, it is shown that, under certain conditions, properly normalized buffer content processes converge weakly to a reflected diffusion. The drift and diffusion coefficients of this limit model are functions of the state process, the invariant distribution of XX, and a finite state Markov process which is independent of the driving Brownian motion.

Related Topics
Physical Sciences and Engineering Mathematics Mathematics (General)
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