Hindawi Journal of Electrical and Computer Engineering Volume 2020, Article ID 6265379, 12 pages https://doi.org/10.1155/2020/6265379 Research Article Distributed Monitoring Based on P-Time Petri Nets and Chronicle Recognition of the Tunisian Railway Network Anis M’halla ,1 Dimitri Lefebvre ,2 and Mouhaned Gaied3 1Research Laboratory LARA in Automatic Control, National Engineering School of Tunis (ENIT), University of Tunis el Manar, Tunis, Tunisia 2GREAH, Universite´ Le Havre Normandie, 75 Rue Bellot, Le Havre 76600, France 3Research Unit LAS2E, .e National Engineering School of Monastir (ENIM), Avenue Ibn El Jazzar 5019 Monastir, Tunisia Correspondence should be addressed to Anis M’halla; [email protected] Received 13 July 2019; Revised 27 July 2020; Accepted 10 August 2020; Published 25 August 2020 Academic Editor: Vinod Sharma Copyright © 2020 Anis M’halla et al. (is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (is paper falls under the problems of the monitoring of a Discrete Event System (DES) with time constraints. Among the various techniques used for online and distributed monitoring, we are interested in the chronicle recognition. Chronicles are temporal patterns that represent the system’s possible evolutions. (e proposed models are based on P-time Petri nets that are suitable to represent with accuracy and modularity the Tunisian railway network. (ese models are scalable and may be used to represent a large variety of railway networks. (en, monitoring is based on the generation of chronicles that are suitable to detect and isolate traffic incidents in a distributed setting. Consequently, the proposed approach is tractable for large networks. Finally, to demonstrate the effectiveness and accuracy of the approach, an application to the case study of the Tunisian railway network is outlined. 1. Introduction and chronicles for the analysis of traffic disruptions. (e overall goal is to maintain the stability and efficiency of the Transport systems need to be monitored online to avoid studied railway network. critical situations and temporal disturbances. (ese dis- Over the past decade, the chronicle formalism has been turbances concern either the railway infrastructure or the developed and used by numerous authors, particularly for traffic management and may lead to service disruptions due faults diagnosis [1–4]. It was also used by the Telecom to weather, obstacles on the tracks, malice, social move- operators for fault diagnosis in telecommunication net- ments, and so on. In the systems under consideration, the works [5] or for the diagnosis of web service failures [6, 7]. processing times are interval-valued with parameters that Lately, to deal with the time aspects inherent to the depend on the operation to be performed. Any deviations chronicles, the authors in [8] propose an automated from the specified interval will characterize a traffic dis- translation of chronicles into a set of Labeled Time Petri turbance. Consequently, the monitoring of the time intervals Nets with Priorities (LTPNPr). (e aim of this study was to will be used as the main principle to detect and isolate the improve the characterization of diagnosability for a dis- disturbances that affect the system. In this context, we crete event system by taking into account the notion of propose the chronicles as a formalism for interpreting events finite durations between the occurrence of two events. (e to monitor temporal disruptions. A chronicle is composed of diagnosability study was done by comparing the chronicles a set of events and a set of temporal constraints linking the associated with the normal behavior to the chronicle as- pairs of events. (e proposed approach is applied to the sociated with faulty behaviors. (e diagnosability analysis railway transport network in Tunisia. (e main contribution is based on LTPNPr in which priority relationships on of this paper is to use the combination of Petri net formalism transitions are used to complete the firing conditions. (is 2 Journal of Electrical and Computer Engineering approach is different from our contribution that uses paper. Some perspectives for further works are also P-time Petri nets for modelling issues and that excludes the proposed. notion of priority for transition firings. In [9], the authors proposed a diagnosis approach based on chronicles and 2. Modelling of the Tunisia Sahel Railway Network modular temporal analysis. In fact, a failure was allocated to each set of chronicles, and each chronicle recognized the 2.1. Presentation of the Studied Transport Network. (e fault signature which was obtained from the state diag- railway network of the Sahel Tunisia, Figure 1, ensures the nosed with the finite state automata associated to each transportation of passengers between the main cities of the process module. Sahel from Sousse to Mahdia. It starts at the Sousse Bab Jdid To describe clearly all desired behaviors of an automated station, crosses the industrial zone of Sousse, and bypasses production system, an incremental learning approach, based the Sahline city until the Monastir station by the serving the on Causal Temporal Signatures (CTS) was proposed in [10]. airport, the tourist zone, and the University of Monastir; (e CTS was defined as “a subset of partially-ordered ob- Figure 1. South of Monastir, the line continues to the Ksar servable events that characterizes the system’s faulty be- Hellal city going through the industrial zone, and the main havior”. (e formalism of CTS, based on chronicles, was agglomerations located on this axis are Khniss, Ksibet used to diagnose faults in Discrete Event Systems (DES). (e Elmedouini, Bouhjar, and Sayada. Leaving Moknine, it main benefits of this formalism were the readability and the serves the industrial zone of Teboulba and continues to expressiveness. In [11], the authors proposed a chronicle Mahdia. (e particularity of this railway network is the model allowing integrating prohibition constraints repre- single line connecting the Bekalta station to Mahdia tourist senting the absence of events in the model. Based on this zone station. (erefore, the segments are unidirectional in formalism, criteria were proposed to characterize the this area, while it has double tracks in the rest of the network. chronicles and to compare them in order to evaluate the With an average of 40 minutes of frequency, the metro of relevance of the chronicle database used for the diagnosis. Sahel ensures daily 44 journeys scheduled between 5 : 00 am (e chronicles were modeled by temporal Petri nets, and the until 10 : 00 pm and ensures the transport of more than 9 exclusivity test was solved by a model checking approach. million passengers per year with an average of 27,000 (e association of the Petri net formalism and chronicles passengers daily. Figure 2 shows the travel times between the for the monitoring and diagnosis is widely proposed in the various stations deserved by the metro of the Sahel. literature [12–15]. In these works, the notions of causality, conflict, competition, unfolding, time branching formulated in Petri net setting lead to the modelling, identification, and 2.2. Model of the Studied Railway Network discrimination of fault patterns. (ese approaches can be 2.2.1. P-Time Petri Net. Several modelling approaches have extended to more complex monitoring problems where the been proposed for transport networks. Models may be places not only represent faults but also process states. (is graphical or analytical or both as the same time as Petri nets. context was also exploited in our approach: no specific In this work, P-time Petri Nets (P-TPNs) are used for assumption is made about what the chronicle represents, modelling the transport network. In such models, travel and it can be associated with normal or faulty behaviors. durations are included within a minimum value and a In transportation systems, a large number of observations maximum one. are regularly collected and should be processed. Such a large amount of data cannot be treated online efficiently by a human operator. On the contrary, chronicles are suitable to Definition 1 (see Reference [16]). (e formal definition of a analyze such data in order to recognize normal and faulty P-TPN is given by a pair <R, IS>, where R is a marked Petri behaviors. (e main advantage of this tool is the ability to net: describe and represent the possible evolutions of the transport IS: P ⟶ Q+ ×Q+ ∪ f+∞ g �; systems and to recognize these behaviors in a flow of events. (1) p ��a ; b � a b : (e contributions presented in this paper are devoted to i ⟶ ISi i i with 0 ≤ i ≤ i distributed monitoring of rail transport networks and deal ISi defines the static interval of sojourn time of a mark in with the detection of traffic disturbance symptoms in these the place p belonging to the set of places P (Q+ is the set of systems. P-time Petri nets are used for modelling aspects. i positive rational numbers). A token in the place pi fires an Among the various techniques used for the distributed output transition when it has stayed in p a duration at least monitoring, we are interested in the chronicles recognition. i ai and at most bi. After the duration bi, there is a death of (e paper is organized as follows. Section two presents mark in p . the railway transport system in Tunisia and gives some basic i notions about P-time Petri nets. (e third section presents the chronicle formalism and illustrates how chronicles are 2.2.2. Modelling. (e Sahel railway network consists of 3 applied to the distributed monitoring. In Section four, the main stations (Sousse, Monastir, and Mahdia) and 28 other approach is applied to the Tunisian railway transport net- stations, Figure 3.