Optimal Allocation of Connecting Elements in Phase Mission Linear Consecutively-Connected Systems

Many continuous transportation systems and communication networks can be modeled as a linear consecutively connected system (LCCS) consisting of n+1 linearly ordered nodes. Some of these nodes contain connection elements (CEs) with different characteristics. Each CE i in its working state provides a connection between the node to which it belongs and L(i) next nodes, the set of nodes that follow the given node. If the system contains any node not connected with any previous node, then it fails. We consider multi-phase LCCS that should perform a sequence of transmission tasks. In each phase, it should provide continuous connection along a specific path of nodes. Different paths can contain the same nodes, which creates statistical dependence across the phases. Different nodes are characterized by specific conditions expressed by different failure acceleration factors affecting the CEs located at these nodes. Thus, an accurate reliability analysis of a multi-phase LCCS must consider the statistical dependencies of CE states across phases, and dynamics in path structures as well as in the failure acceleration factors. In this paper, we propose a method for optimal allocation of CEs in multi-phase LCCS. The method is based on a recursive algorithm for exact system reliability evaluation, and the genetic algorithm for the optimal allocation of CEs to nodes of LCCS. The proposed approach is illustrated using a practical example of wireless sensor networks.