Optimal relayed mobile communication systems

Recently, D.T. Chiang and R.F. Chiang (1986) 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 as 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. In the present work, the authors show 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 it is much more tractable than the original problem studied by Chiang and Chiang. Exact solutions are provided for a wide range of parameters