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

Abstract

We propose an approach for assessing the impact of multi-phased repair procedures on gas distribution networks, capturing load profiles that can depend on time for different classes of users, suspension of activities during non-working hours, and random execution times depending on topological, physical, and geographical characteristics of the network. The problem is characterized through a semi-formal specification based on artifacts of the Systems Modeling Language (SysML), which is then translated into a formal model based on stochastic time Petri nets. The solution method interleaves fluid-dynamic analysis of the gas behavior and stochastic analysis of the time spent in the repair process, decoupling complexities and making stochastic analysis almost insensitive to the network size and topology. Hence, our approach turns out to be applicable to real scale cases, notably computing the optimal time of day to start the repair procedure. Moreover, by encompassing general (non-Markovian) distributions, the approach enables effective fitting of durations.

The ORIS Tool: Quantitative Evaluation of Non-Markovian Systems

“…We illustrate how ORIS can be exploited in quantitative evaluation of non-Markovian models by reviewing some selected cases of application [55], [24], [14], [25], [13], [20], [11], in various domains and with different usage patterns.…”

“…To facilitate the procedure modeling, the approach of [14] extends STPNs implemented in the SIRIO library with two transition features (not included in the present distribution): i) fickle functions, which shift the time to fire of persistent transitions by a deterministic value upon a transition firing, representing suspension and resumption of activities at deterministic time points according to work shifts of personnel; and, ii) marking-dependent CDFs, which sample the time to fire at newly-enabling from a different CDF depending on the marking, modeling pressure restoration with duration that depends on the number of completed regulation steps. GEN distributions of repair times are assumed to be derived from data that could be actually captured by the increasingly Figure 6: STPN model of the ERTMS/ETCS-L3 railway signalling case study analyzed in [13].…”

“…GEN distributions of repair times are assumed to be derived from data that could be actually captured by the increasingly Figure 6: STPN model of the ERTMS/ETCS-L3 railway signalling case study analyzed in [13]. To evaluate the network performability, the procedure model of [14] is solved through forward transient analysis (since the number of reached regenerations is low), with (limited) complexity mainly due to the number of concurrent GEN and DET transitions and on the length (i.e., number of discrete events) of behaviors where their enabling intervals overlap. On the one hand, the CDF of the completion time of the n-th phase of the procedure, with n ∈ {1, .…”

“…ORIS has been developed for several years and put to the test of practice in various application domains, addressing different modeling and evaluation challenges [55], [24], [14], [25], [13], [20], [11]. Overall, ORIS is now a well-engineered software tool, fully implemented in Java, designed so as to accommodate agile implementation of new features for Petri net models and new solution techniques for their underlying stochastic processes.…”

“…Specifically, in Sections 2 and 3, we illustrate how to construct STPN models and perform quantitative analysis of their underlying stochastic processes, respectively, using a running example from the literature on software rejuvenation to describe the typical modeling and evaluation workflow in ORIS (including derivation of distributions of GEN durations), the class of properties that can be analyzed, and the limits of the analysis methods. In Section 4, we review selected case studies where ORIS has been applied to the quantitative evaluation of models of real-time software [24], [55], railway signalling systems [13], repair procedures for gas and water distribution networks [14], [25], and activity recognition [20], [11]. Finally, conclusions are drawn in Section 5.…”