Analytical models for reliability estimation of distributed telecommunication networks

To analyze and solve the estimation and optimization problem for distributed systems the explicit analytic expressions for the network reliability have to be found. The distributed network subsystems operate dependently in terms of reliability, the failure and recovery of one subsystem have an influence on the performance of another system. Therefore for distributed networks the assumption of independence of failures of subsystems is not always true. For such systems it is necessary to construct a logical model of reliability, to determine all the possible states and transition subsystems from one state to another (to construct a state graph) and then find an expression for the stationary availability factor. In addition, the distribution function of the time to failure and the recovery time of technical devices of networks, in most cases differ from the exponential law. This paper is devoted to constructing mathematical models of reliability with dependent failures and arbitrary distributed recovery time.