Optimal arrangement of connecting elements in linear consecutively connected systems with heterogeneous warm standby groups

Motivated by practical applications such as radio communication and flow transmission systems, this paper models and optimizes linear consecutively connected systems (LCCS) with a set of linearly ordered nodes. Each node may contain multiple connection elements (CE) configured as a warm standby structure, where one CE is online providing a connection between its host node and a certain number of next nodes along the sequence, with the remaining CEs serving as standbys. CEs have heterogeneous types characterized by different time-to-failure distributions and connection ranges. An iterative algorithm is first proposed for determining performance stochastic processes of particular CE standby groups. A universal generating function technique is then used for evaluating instantaneous and expected system connectivity for the considered LCCS. An optimization problem of CE distribution and sequencing is further defined and solved, with the objective of finding CE distribution among LCCS nodes and sequencing of CE activation in standby groups to maximize the expected system connectivity over a specified mission time horizon. Optimization results are useful in guiding optimal decisions on reliable design and operation of LCCSs. Examples are provided to demonstrate application of the proposed methodology and optimization problem.