Optimal Antivirus Protection Strategy in Computer Networks

P. 75–82.

Grishunina Y., Manita L.

We construct a mathematical model of anti-virus protection of local area networks. The model belongs to the class of regenerative processes. To protect the network from the external attacks of viruses and the spread of viruses within the network we apply two methods: updating antivirus signatures and reinstallings of operating systems (OS). Operating systems are reinstalled in the case of failure of any of the computers (non-scheduled emergent reinstalling) or at scheduled time moments. We consider a maximization problem of an average unit income. The cumulative distribution function (CDF) of the scheduled intervals between complete OS reinstallings is considered as a control. We prove that the optimal CDF has to be degenerate, i.e., it is localized at a point tau. 

Keywords: Laplace transform, преобразование Лапласа, Regenerative process, Average unit profit, Viruses propagation, Регенерирующий процесс, средний удельный доход, стохастическая модель распространения вирусов

In book

Analytical and Computational Methods in Probability Theory

Vol. 10684: Analytical and Computational Methods in Probability Theory. , Berlin: Springer, 2017.