Connectivity evaluation and optimal service centers allocation in repairable linear consecutively connected systems

Many real-world systems in applications such as radio communication, wireless communication, and pipeline transportation can be modeled as linear consecutively connected systems (LCCS) with nodes forming a linear sequence. An LCCS provides a connection between the first and last nodes of the sequence using connecting elements (CEs) located at its nodes. This paper models an LCCS with repairable CEs characterized by different up and down time distributions, and different connection ranges. The distribution parameters of CE down times depend on the location of available service centers (SCs). Thus, the optimal allocation of SCs becomes a relevant and significant optimization problem to formulate and solve for guiding optimal decisions on LCCS maintenance. The objective is to find an SC allocation among predetermined positions that maximizes the expected LCCS connectivity over a specified mission time horizon. To evaluate the objective function of the proposed optimization problem, instantaneous availabilities of repairable CEs with arbitrary up and down time distributions are first determined through a numerical iterative algorithm. Instantaneous and expected LCCS connectivity are then evaluated using a universal generating function method. As demonstrated through examples, the proposed optimization leads to significant improvements in LCCS connectivity and effective allocation and management of maintenance resources.