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

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.