Extending the Steady State Analysis of Hierarchical Semi-Markov Processes with Parallel Regions

Compositional Analysis of Hierarchical UML Statecharts

“…The formalism could be extended with various features. In particular, an HSMP could have multiple final locations per region, each associated with a different successor location distribution, and, as in [11], history steps could be used to account for the last step visited by a region before premature interruption by a parallel region. Though these features would improve the model expressivity while requiring a minor extension of the proposed solution technique, they would burden notation in the overall treatment, and thus they are not included in the present formulation.…”

“…Pursuing the latter approach, a numerical method is presented in [26], [27] to perform availability analysis of a system specified as a dynamic fault tree, exploiting the model structure to compute stochastic bounds on the distribution of the time to failure and evaluate different maintenance policies for the system components. Steady-state analysis of a wider class of stochastic systems specified as statecharts is addressed in [11], [38], reporting preliminary results for a small-sized fault-tolerant system, though requiring that the model does not include a cycle that visits some non-top-level composite state (cycle restriction). The concept in [11], [38] relies on building maximum and minimum over the sojourn time in regions of composite states, and thus it is in some sense a generalization of [72], where a minimum is taken over non-Markovian sojourn time distributions that start simultaneously in the same state.…”

“…Steady-state analysis of a wider class of stochastic systems specified as statecharts is addressed in [11], [38], reporting preliminary results for a small-sized fault-tolerant system, though requiring that the model does not include a cycle that visits some non-top-level composite state (cycle restriction). The concept in [11], [38] relies on building maximum and minimum over the sojourn time in regions of composite states, and thus it is in some sense a generalization of [72], where a minimum is taken over non-Markovian sojourn time distributions that start simultaneously in the same state.…”

“…In this paper, we extend the approach of [11], [38] into a comprehensive methodology for quantitative modeling and analysis of non-Markovian systems specified as an extension of statecharts. 1 In this formalism, parallel regions including steps with GEN duration are synchronized through operators supporting hierarchical composition of the underlying Semi-Markov Processes (SMPs).…”

Model-Based Quantitative Evaluation of Repair Procedures in Gas Distribution Networks

“…In Homm and German (2016), states in parallel regions of a State Chart are associated with GEN sojourn times and synchronized with operators that permit a compositional solution through hierarchical composition of Semi Markov Processes (SMPs). The model expressivity is significantly extended in Biagi et al (2018) allowing system evolution to be dependent on the exited region. The approach proposed in this article translates the Activity Diagram of the procedure and the State Charts of the network and the personnel into a class of stochastic time Petri nets, extending previous results of the literature by representing GEN durations of multiple concurrent activities, DET durations of time zones capturing personnel working hours and load demand profiles, and suspension/resumption of activities that can be performed only during working hours according to the semantics of Preemptive ReSume (Bobbio et al 2000).…”