A multi-dimensional SRBM: geometric views of its product form stationary distribution

被引：2

作者：

Dai, J. G. ^{[1
]}

Miyazawa, Masakiyo ^{[2
]}

Wu, Jian ^{[1
]}

机构：

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

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

来源：

QUEUEING SYSTEMS | 2014年 / 78卷 / 04期

基金：

美国国家科学基金会;

关键词：

Semimartingale reflecting Brownian motion; Variational problem; Skew symmetry condition; Queueing networks; Diffusion approximations; LARGE DEVIATIONS; BROWNIAN-MOTION;

D O I：

10.1007/s11134-014-9411-0

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

We present a geometric interpretation of a product form stationary distribution for a -dimensional semimartingale reflecting Brownian motion (SRBM) that lives in the nonnegative orthant. The -dimensional SRBM data can be equivalently specified by geometric objects: an ellipse and rays. Using these geometric objects, we establish necessary and sufficient conditions for characterizing product form stationary distribution. The key idea in the characterization is that we decompose the -dimensional problem to two-dimensional SRBMs, each of which is determined by an ellipse and two rays. This characterization contrasts with the algebraic condition of Harrison and Williams (Ann Probab 15:115-137, 1987b). A -station tandem queue example is presented to illustrate how the product form can be obtained using our characterization. Drawing the two-dimensional results in Avram et al. (Queueing Syst 37:259-289, 2001), Dai and Miyazawa (Queueing Syst 74:181-217, 2013), we discuss potential optimal paths for a variational problem associated with the three-station tandem queue.

引用

页码：313 / 335

页数：23

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