On Application of Stochastic Processes of the Stock Theory to Modeling Computerized Information Networks

We investigate a system of stochastic integral equations describing the operation of an $N$-node open network for information storage and transmission, with information flows coming from the outside. It is assumed that these flows are described by $N$ independent Levy processes with nondecreasing trajectories and drift equal to zero. A linear stochastic network of arbitrary structure, as well as models of some rather simple nonlinear networks are analyzed in detail. For these networks, we found explicit solutions to the corresponding stochastic integral equations and joint distributions of the amounts of information stored at each node. Asymptotics of some distributions is studied.