Decomposable stationary distribution of a multidimensional SRBM

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:125

Article

Dai, J. G.¹  Miyazawa, Masakiyo²  Wu, Jian¹ 

[1] Cornell Univ, Sch Operat Res & Informat Engn, Ithaca, NY 14853 USA

[2] Tokyo Univ Sci, Dept Informat Sci, Noda, Chiba 2788510, Japan

关键词: Semimartingale reflecting Brownian motion;    Queueing network;    Stationary distribution;    Decomposability;    Marginal distribution;    Product form approximation;    Completely-S matrix;   

DOI  :  10.1016/j.spa.2014.11.014

来源: Elsevier

【 摘 要 】

We focus on the stationary distribution of a multidimensional semimartingale reflecting Brownian motion (SRBM) on a nonnegative orthant. Assuming that the stationary distribution exists and is decomposable-equal to the product of two marginal distributions, we prove that these marginal distributions are the stationary distributions of some lower dimensional SRBMs, whose data can be explicitly computed through that of the original SRBM. Thus, under the decomposability condition, the stationary distribution of a high dimensional SRBM can be computed through those of lower dimensional SRBMs. Next, we derive necessary and sufficient conditions for some classes of SRBMs to satisfy the decomposability condition. (C) 2014 Elsevier B.V. All rights reserved.

【 授权许可】

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