Design of Minimal Fault Tolerant On-Board Networks: Practical Constructions

The problem we consider originates from the design of efficient on-board networks in satellites (also called Traveling Wave Tube Amplifiers). Signals incoming in the network through ports have to be routed through an on-board network to amplifiers. The network is made of expensive switches with four links and subject to two types of constraints. First, the amplifiers may fail during satellite lifetime and cannot be repaired. Secondly, as the satellite is rotating, all the ports are not well oriented and hence not available. Let us assume that we have p+ λ ports (inputs) and p + k amplifiers (outputs), then a (p, λ, k)−network is said to be valid if, for any choice of p inputs and p outputs, there exist p edge-disjoint paths linking all the chosen inputs to all the chosen outputs. Then, the objective is to design a valid network having the minimum number of switches denoted N(p, λ, k). In the special case where λ = 0, these networks were already studied as selectors. Here we present validity certificates from which derive lower bounds for N(p, λ, k); we also provide constructions of optimal (or quasi optimal) networks for practical values of λ and k (1 ≤ λ ≤ k ≤ 8) and a general way to build networks for any k and any λ.