Semi-Markov Queuing System with Bifurcation of Arrivals for Network Maintenance Problem

In the present paper, a multi-unit redundant system with unreliable, repairable units is considered. Two types of maintenance operations - the replacement of the failed main unit by the redundant one and the repair of the failed unit - are performed. The case of the system with one replacement server with arbitrary replacement time distribution function and repair server with an exponential distribution of repair time is considered. For this system mixed-type semi-Markov queuing model with the bifurcation of arrivals is constructed. It represents a non-classical boundary value problem of mathematical physics with non-local boundary conditions.