Optimal Relayed Mobile

Recently, Chiang & Chiang considered a relayed mobile communication system with evenly-spaced mobile relay- stations (spacecraft) moving at the same speed from an origin towards a destination. Such a system can be considered 8s a consecutive-k-out-of-n line. They gave equations for computing the mean number of stations needed for a successful relay and studied the optimal choice of k to minimize the mean number. This paper shows that it is always better to replace a consecutive-k-out-of-n line by a consecutive-1-out-of-n line but with k redundancy. The problem of choosing an optimal k still has no closed-form solution but is much more tractable than the original problem studied by Chiang & Chiang. We provide exact solutions for a wide range of parameters.