Reliability Evaluation of Acyclic Multi-State Transmission Networks (AMTNs) using the Universal Generating Function Technique

This paper is devoted to reliability evaluation of acyclic multi-state transmission networks (AMTNs) using the universal generating function (UGF) technique. In this paper, AMTNs consist of a number of positions in which multi-state elements (MEs) capable of receiving and/or sending a signal are allocated. The MEs located at each non-leaf positions. The two MEs located at first position. The number of MEs is not equal to the number of non-leaf positions. The AMTNs reliability is defined as the comparison of two networks. All the MEs in the network are assumed to be statistically independent.

The number of leaf positions that can only receive a signal and a number of intermediate positions containing MEs capable of transmitting the received signal to some other nodes. The signal transmission is possible only along links between the nodes. The AMTNs reliability is defined as the probability that a signal from the root node is transmitted to each leaf node. The networks are arranged in such a way that no signal leaving a node can return to this node through any sequence of nodes otherwise we can say that no cycle exist.