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Optimal Periodicity of Scheduled Reinstallings of Operating System in Computer Network

Student: Aleksandr Bulekov

Supervisor: Yulia Grishunina

Faculty: HSE Tikhonov Moscow Institute of Electronics and Mathematics (MIEM HSE)

Educational Programme: Applied Mathematics (Bachelor)

Year of Graduation: 2018

The paper consists of 45 pages, contains 6 figures, 1 table, 4 appendices and 7 references. In this work, the computer network functioning in a viral environment is investigated. The aim of the work is to determine the optimal strategy for anti-virus protection. The search for the strategy consists in finding the optimal cumulative distribution function (CDF) of intervals between scheduled reinstallings of the operating system. In the course of the work, a mathematical model of the computer network was constructed, represented as a regenerative stochastic process. A system of integral equations of income gained by network operation is described. A maximization problem of average unit income gained by network operation on a set of CDFs is formulated. The set of CDFs of intervals between reinstallings is reduced to the set of degenerate distributions. An algorithm for solving maximization problem was determined and a program for numerical determination of optimal periodicity of scheduled reinstallings for given parameters was designed.

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