Efficiency of a Two-Channel System with Restructuring and Insurance

Abstract

We consider a system of two conditionally independent alternating renewal processes with restructuring and with a general form of the distribution densities of interval lengths. The system models the operation of two units taking into account operation and repair intervals. The restructuring time is associated with the instant when the two-dimensional process first reaches a state where both components are operational. For a process as a whole, each such time corresponds to the system’s Markov regeneration when it begins working anew, from another initial state. Time intervals between restructurings depend on the so-called fixed guaranteed service times. We use the evolution property of the two-dimensional process between Markov regeneration times, which transforms such an evolution into a breaking second-order semi-Markov process. We derive integral equations for the expectations of system efficiency over the time interval from zero to the time of restructuring.