A novel Markov model for the computation of the Continuity Risk in maritime applications

In this paper we focused on the analysis of the continuity risk for a maritime user and on the derivation of the receiver implementation scheme that fulfills IMO [2] requirements. We started our analysis by considering the model derived in [6], which is accurate for aviation applications, while it is not guaranteed to work in other environments. To take into account the time evolution of the continuity risk, we propose in this paper to introduce Markov models. The derived models can be used to compute the continuity risk when a receiver not implementing exclusion is used, as well as when a receiver implements both snapshot and sequential exclusion. The derived conclusion is that without exclusion, it is not possible to achieve the required performance. It is shown that, considering only satellite faults, over the 3 hours of operation, in principle a snapshot exclusion mechanism is sufficient. When implementing sequential exclusion, at the cost of an increased complexity, the continuity risk is furthermore reduced. We also showed that, under some temporal limitations and with some assumptions on the exclusion mechanism, the results provided by the Markov models and by the model derived in [6] coincide. This final consideration shows that the proposed approach can be seen as a natural extension of the state of the art model from the avionic environment to the maritime environment.