Availability analysis for software system with intrusion tolerance

This paper is devoted to analyzing the instantaneous availability of a typical software system with intrusion tolerance. By formulating the system with a couple of ordinary differential and partial differential equations, this paper describes the system as a time-delay partial differential equation. Based on the time-delay model, both steady-state availability and instantaneous availability are investigated. The optimal policy for preventive patch management to maximize the steady-state availability of the software system is obtained, and its related availability criterions are also presented. Employing the finite difference scheme and Trotter-Kato theorem, we converted the time-delay partial equation into a time-delay ordinary equation. As a result, the instantaneous availability of the system is derived. Some numerical results are given to show the effectiveness of the method presented in the paper.