Author/Authors :
FAN, Hua Tsinghua University - Department of Electronic Engineering, China , FAN, Hua Beijing Film Academy - Department of Cinematography, China , SHAN, Xiuming Tsinghua University - Department of Electronic Engineering, China , YUAN, Jian Tsinghua University - Department of Electronic Engineering, China , REN, Yong Tsinghua University - Department of Electronic Engineering, China
Abstract :
Analyses of dynamic systems with random oscillations need to calculate the system covariance matrix, but this is not easy even in the linear case if the random term is not a Gaussian white noise. A universal method is developed here to handle both Gaussian and compound Poisson white noise. The quadratic variations are analyzed to transform the problem into a Lyapunov matrix differential equation. Explicit formulas are then derived by vectorization. These formulas are applied to a simple model of flows and queuing in a computer network. A stability analysis of the mean value illustrates the effects of oscillations in a real system. The relationships between the oscillations and the parameters are clearly presented to improve designs of real systems.
Keywords :
covariance matrix , stochastic differential equation (SDE) , compound Poisson white noise , transmission control protocol (TCP) flow
