Abstract
Various aspects of privacy and safety in many application domains can be assessed based on proper analysis of successive measurements that are collected about a given system. This work is devoted to such issues in the context of timed stochastic discrete event systems (DES) that are modeled with partially observed timed stochastic Petri net models. The first contribution is to introduce a k-step trajectory-observer, which is a construction that captures all possible k-suffixes of the trajectories that are consistent with a given sequence of measurements that has been recorded. When the system behaves according to Markovian dynamics (i.e., all event occurrences are distributed in time with exponential probability density functions), a parallel-like composition of the timed system with the resulting observer is proposed that leads to a Markovian process. The second contribution is to take advantage of the Markovian analysis to compute certain important characteristic times during which the underlying system should satisfy a given property (based on the suffixes of length k of a given trajectory). To illustrate the approach, we consider two particular properties, namely k-suffix language opacity and k-diagnosability, which can be studied in a stochastic timed context using the Markovian trajectory observer.
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Notes
A transient state in CTMM is a state with a mean probability that equals 0. In practice, this means that, after a certain time, such a state becomes unreachable. On the contrary, the steady state of a CTMM is composed by the states that have a mean probability strictly larger than 0. In practice, this means that, there exist arbitrarily long runs where such states remain reachable forever.
C is a strongly connected (or equivalently irreducible) component of a directed graph G if for any pair of nodes (S,S′) ∈ C, there exists a path from S to S′. In addition, C is a (closed) absorbing strongly connected component if C is a strongly connected component of G and for any node S ∈ C and for any node S′ ∈ G, S′ ∈ C if a path exists from S to S′.
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Lefebvre, D., Hadjicostis, C.N. Privacy and safety analysis of timed stochastic discrete event systems using Markovian trajectory-observers. Discrete Event Dyn Syst 30, 413–440 (2020). https://doi.org/10.1007/s10626-019-00307-8
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DOI: https://doi.org/10.1007/s10626-019-00307-8