Multiscale diffusion approximations for stochastic networks in heavy traffic

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Budhiraja, Amarjit¹  Liu, Xin¹ 

[1] Univ N Carolina, Dept Stat & Operat Res, Chapel Hill, NC 27599 USA

关键词: Diffusion approximations;    Queueing networks in a random environment;    Heavy traffic;    Multiscale analysis;    Reflected Markov modulated diffusions;    Constrained martingale problems;   

DOI  :  10.1016/j.spa.2010.10.009

来源: Elsevier

【 摘 要 】

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 X and Y. The transition times of X are significantly smaller than typical inter-arrival and processing times whereas the reverse is true for the Markov process Y. 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 X, and a finite state Markov process which is independent of the driving Brownian motion. (C) 2010 Elsevier B.V. All rights reserved.

【 授权许可】

Free