Reliability evaluation for acyclic transmission networks of multi-state elements with delays

Abstract

Acyclic transmission networks (ATN) consist of a number of positions in which s-independent multi-state elements (ME) capable of receiving and/or sending a signal are allocated. Each network has: a root position where the signal source is located, a number of terminal positions that can only receive a signal, and a number of intermediate positions containing ME that retransmit the received signal to some other positions. The signal propagation is allowed only in direction of the terminal nodes, which avoids cycles in the network. Each ME that is located in a nonterminal node can have different states determined by a set of nodes receiving the signal directly from this ME. The probability of each state is assumed to be known for each ME. The signal retransmission process is associated with delays. The system fails if the signal generated at the first position (source) cannot reach the terminal nodes within a specified time. An algorithm for ATN reliability evaluation is suggested; it is based on an extended universal generating function method that uses a state enumeration approach. A procedure for recurrent derivation of probabilistic distribution of a vector representing delays in ATN is described. A technique for computational complexity reduction is developed.