Closed and Mixed Type Queuing Systems as Mathematical Models of Reliability and Survivability

Abstract

The given paper deals with the redundancy and maintenance problem for a wide class of any territorially distributed standby systems consisting of unreliable repairable components. Mathematical models for interaction of degradation and its compensation processes in the said systems are proposed and their possible applications are partially analysed. These models represent closed and mixed type queuing systems for two parallel maintenance operations -- replacements and repairs. The problems for optimization of said system by economic criterion and the possible ways of its solution are discussed. Finally a closed one-line Semi-Markov priority queuing model is constructed and partly investigated.