Relayed Communication via Consecutive-k-out-of-n: F System

A special communication system with moving relay stations is introduced in this paper. The relay stations are all moving at the same speed from an origin toward a destination. If k consecutive stations fail before the first station reaches the destination, all stations ahead of the k failed stations as well as the k failed stations are lost. The objective is to have one station reach the destination without k or more consecutive failed stations between the destination and the origin. When the station reliability is known, a formula to compute the mean number of stations needed for the communication system is derived. An example demonstrates how the formula might be used to determine the optimal system configuration given a station's reliability and to judge the tradeoff between station reliability and the available budget for the communication system.