Maximizing survivability of acyclic transmission networks with multi-state retransmitters and vulnerable nodes

In this paper, an algorithm for optimal allocation of multi-state elements (MEs) in acyclic transmission networks (ATNs) with vulnerable nodes is suggested. The ATNs consist of a number of positions (nodes) in which MEs capable of receiving and sending a signal are allocated. Each network has a root position where the signal source is located, a 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. Each ME that is located in a nonleaf 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. Each ATN node with all the MEs allocated at this node can be destroyed by external impact (common cause failure) with a given probability. The ATN survivability is defined as the probability that a signal from the root node is transmitted to each leaf node. The optimal distribution of MEs with different characteristics among ATN positions provides the greatest possible ATN survivability. It is shown that the node vulnerability index affects the optimal distribution. The suggested algorithm is based on using a universal generating function technique for network survivability evaluation. A genetic algorithm is used as the optimization tool. Illustrative examples are presented.