@article{FAN2011, 
author = {Hua FAN and Xiuming SHAN and Jian YUAN and Yong REN},
title = {Covariances of Linear Stochastic Differential Equations for Analyzing Computer Networks},
year = {2011},
journal = {Tsinghua Science and Technology},
volume = {16},
number = {3},
pages = {264-271},
keywords = {covariance matrix, stochastic differential equation (SDE), compound Poisson white noise, transmission control protocol (TCP) flow},
url = {https://www.sciopen.com/article/10.1016/S1007-0214(11)70038-4},
doi = {10.1016/S1007-0214(11)70038-4},
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.}
}