Second-order stochastic fluid models with fluid-dependent flow rates

Authors:
Dongyan Chen;Yiguang Hong;Kishor S. Trivedi
Affiliations:
Department of Electrical and Computer Engineering, Center for Advanced Computing and Communications(CACC), Duke University, Durham, NC;Department of Electrical and Computer Engineering, Center for Advanced Computing and Communications(CACC), Duke University, Durham, NC and Institute of Systems Science, Chinese Academy of Sciences ...;Department of Electrical and Computer Engineering, Center for Advanced Computing and Communications(CACC), Duke University, Durham, NC
Venue:
Performance Evaluation
Year:
2002

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Abstract

In this paper, the analysis of second-order stochastic fluid models, where the fluid rate is dependent on the fluid level, is addressed. The boundary conditions are presented for the fluid models under consideration, which have extended previous work with only reflecting barrier assumptions. To obtain the transient solution of the fluid dynamics, a finite difference solution method is presented, which confirms to the boundary conditions and satisfies the normalization condition at the same time. With our approach, the modeling power of second-order fluid models is directly extended to include the case with fluid-dependent rates. As an application example, a statistical multiplexing problem is analyzed with our proposed method.