Probability distributions of link durations with n disruptive channels: application to ground-space optical communications

We consider n independent disruptive channels with random availability periods and make use of channel diversity to maintain a link as often as possible. This situation arises when an optical link is to be maintained between a spacecraft and n ground stations affected by cloud coverage. Statistical independence between the stations and equal (un)availability duration distributions are assumed. Based on a given single-station (un)availability duration distribution, we derive analytically the network (un)availability duration distributions. Also derived is the distribution of the station operation duration within a network. Derived expressions allow evaluating the increase of the continuous operation duration of a station and the decrease of the network unavailability durations.