Optimal component allocation in a multi-state system with hierarchical performance sharing groups

Performance sharing is a common technique to save energy and increase system reliability. This paper considers a multi-state system with hierarchical performance sharing groups. The system has several subsystems connected with a primary common bus, and each subsystem has some groups of components connected with a secondary common bus. Each component group has a demand to satisfy. The groups within the same subsystem can share performance through the secondary common bus, whereas the different subsystems can share capacity with each other through the primary common bus. Both primary and secondary common buses have a maximum transmission capacity. The system fails if the demand for any group cannot be satisfied. The system reliability is evaluated with a universal generating function technique, and the optimal allocation of components which maximises the system reliability is studied.