An alternating renewal process to model constellation availability

Abstract Constellation availability is an important assessment criteria of a constellation usually modeled with the assumption of the Markov property. We show this assumption does not hold for the time to long-term outage distribution of GPS satellites. In this paper, we propose an alternate method to calculate slot availability by modelling the outage process as an alternating renewal process. This proposed method avoids the assumption of the Markov property. The method is then validated against the slot availability data from the GPS 24 constellation, where both long-term and short-term outages are shown to approximate independent alternate renewal processes. In addition, the similarities of various constellation state probabilities with the binomial distribution based on average slot availability are shown. Using the model, future constellation availability performance can be estimated directly from historical data and also provide accurate estimates of the expected number of satellite replacements.

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