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This 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. The proposed models are based on

Transport systems need to be monitored online to avoid critical situations and temporal disturbances. These disturbances concern either the railway infrastructure or the traffic management and may lead to service disruptions due to weather, obstacles on the tracks, malice, social movements, and so on. In the systems under consideration, the processing times are interval-valued with parameters that depend on the operation to be performed. Any deviations from the specified interval will characterize a traffic disturbance. Consequently, the monitoring of the time intervals will be used as the main principle to detect and isolate the disturbances that affect the system. In this context, we propose the chronicles as a formalism for interpreting events to monitor temporal disruptions. A chronicle is composed of a set of events and a set of temporal constraints linking the pairs of events. The proposed approach is applied to the railway transport network in Tunisia. The main contribution of this paper is to use the combination of Petri net formalism and chronicles for the analysis of traffic disruptions. The overall goal is to maintain the stability and efficiency of the studied railway network.

Over the past decade, the chronicle formalism has been developed and used by numerous authors, particularly for faults diagnosis [

To describe clearly all desired behaviors of an automated production system, an incremental learning approach, based on Causal Temporal Signatures (CTS) was proposed in [

The association of the Petri net formalism and chronicles for the monitoring and diagnosis is widely proposed in the literature [

In transportation systems, a large number of observations 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 analyze such data in order to recognize normal and faulty behaviors. The main advantage of this tool is the ability to describe and represent the possible evolutions of the transport systems and to recognize these behaviors in a flow of events.

The contributions presented in this paper are devoted to distributed monitoring of rail transport networks and deal with the detection of traffic disturbance symptoms in these systems.

The paper is organized as follows. Section two presents the railway transport system in Tunisia and gives some basic notions about

The railway network of the Sahel Tunisia, Figure

Sahel railway network.

With an average of 40 minutes of frequency, the metro of Sahel ensures daily 44 journeys scheduled between 5 : 00 am until 10 : 00 pm and ensures the transport of more than 9 million passengers per year with an average of 27,000 passengers daily. Figure

Travel times between stations belonging to the Sahel railway transport network.

Several modelling approaches have been proposed for transport networks. Models may be graphical or analytical or both as the same time as Petri nets. In this work,

The formal definition of a P-TPN is given by a pair <

IS_{i} defines the static interval of sojourn time of a mark in the place ^{+} is the set of positive rational numbers). A token in the place _{i} and at most _{i}. After the duration _{i}, there is a death of mark in

The Sahel railway network consists of 3 main stations (Sousse, Monastir, and Mahdia) and 28 other stations, Figure

P-TPN model for the Sahel railway network.

The sojourn duration _{i} in each place _{ie}) which should be computed in order to satisfy the planned schedule (Table

Sectors of the railway network between Sousse and Monastir.

Section 1: Sousse Med 5 sector |

Section 2: Sousse Sud sector |

Section 3: Sousse Z.Ind sector |

Section 4: Sahline sector |

Section 5: Sahline Sabkha sector |

Section 6: Hôtels sector |

Section 7: Les Hôtels sector |

Section 8: L’Aeroport sector |

Section 9: La faculté sector |

Section 10: Monastir sector |

The values of the static intervals IS

IS_{i} | _{i} | |
---|---|---|

1 | IS_{1} = [60, inf] | 99 |

2 | IS_{2} = [230, 250] | 236 |

3 | IS_{3} = [60, 120] | 80 |

4 | IS_{4} = [172, 188] | 177 |

5 | IS_{5} = [60, 120] | 80 |

6 | IS_{6} = [174, 186] | 178 |

7 | IS_{7} = [60, 120] | 80 |

8 | IS_{8} = [173, 187] | 177 |

9 | IS_{9} = [60, 120] | 80 |

10 | IS_{10} = [168, 192] | 176 |

12 | IS_{12} = [60, 120] | 80 |

13 | IS_{13} = [170, 190] | 176 |

15 | IS_{15} = [60, 120] | 80 |

16 | IS_{16} = [227, 253] | 235 |

17 | IS_{17} = [60, 120] | 80 |

18 | IS_{18} = [111, 129] | 117 |

19 | IS_{19} = [60, 120] | 80 |

20 | IS_{20} = [168, 192] | 176 |

21 | IS_{21} = [60, 120] | 80 |

22 | IS_{22} = [112, 128] | 117 |

23 | IS_{23} = [60, 120] | 80 |

24 | IS_{24} = [110, 130] | 116 |

25 | IS_{25} = [60, 120] | 80 |

26 | IS_{26} = [113, 127] | 117 |

27 | IS_{27} = [60, 120] | 80 |

28 | IS_{28} = [107, 133] | 115 |

29 | IS_{29} = [60, 120] | 80 |

30 | IS_{30} = [109, 131] | 116 |

31 | IS_{31} = [60, 120] | 80 |

32 | IS_{32} = [110, 130] | 116 |

33 | IS_{33} = [60, 120] | 80 |

34 | IS_{34} = [172, 188] | 177 |

35 | IS_{35} = [60, 120] | 80 |

36 | IS_{36} = [165, 195] | 175 |

37 | IS_{37} = [60, 120] | 80 |

38 | IS_{38} = [106, 134] | 115 |

39 | IS_{39} = [60, 120] | 80 |

40 | IS_{40} = [110, 130] | 116 |

41 | IS_{41} = [60, 120] | 80 |

42 | IS_{42} = [110, 130] | 116 |

43 | IS_{43} = [60, 120] | 80 |

44 | IS_{44} = [832, 848] | 837 |

45 | IS_{45} = [60, inf] | 78 |

46 | IS_{46} = [233, 247] | 237 |

47 | IS_{47} = [60, 120] | 80 |

48 | IS_{48} = [351, 369] | 357 |

49 | IS_{49} = [60, 120] | 80 |

50 | IS_{50} = [108, 132] | 116 |

51 | IS_{51} = [60, 120] | 80 |

52 | IS_{52} = [166, 194] | 175 |

53 | IS_{53} = [60, 120] | 80 |

54 | IS_{54} = [230, 250] | 236 |

55 | IS_{55} = [60, 120] | 80 |

56 | IS_{56} = [173, 187] | 177 |

57 | IS_{57} = [60, 120] | 80 |

58 | IS_{58} = [171, 189] | 177 |

59 | IS_{59} = [60, 120] | 80 |

60 | IS_{60} = [170, 190] | 176 |

61 | IS_{61} = [60, 120] | 80 |

62 | IS_{62} = [113, 127] | 117 |

63 | IS_{63} = [60, inf] | 71 |

64 | IS_{64} = [110, 130] | 116 |

65 | IS_{65} = [60, 120] | 80 |

66 | IS_{66} = [168, 192] | 176 |

67 | IS_{67} = [60, 120] | 80 |

68 | IS_{68} = [166, 194] | 175 |

69 | IS_{69} = [60, 120] | 80 |

70 | IS_{70} = [167, 193] | 175 |

71 | IS_{71} = [60, 120] | 80 |

72 | IS_{72} = [233, 247] | 237 |

73 | IS_{73} = [60, 120] | 80 |

74 | IS_{74} = [176, 184] | 178 |

75 | IS_{75} = [60, 120] | 80 |

76 | IS_{76} = [110, 130] | 116 |

77 | IS_{77} = [60, 120] | 80 |

78 | IS_{78} = [349, 371] | 356 |

79 | IS_{79} = [60, 120] | 80 |

80 | IS_{80} = [228, 252] | 236 |

81 | IS_{81} = [832, 848] | 837 |

82 | IS_{82} = [60, 120] | 80 |

83 | IS_{83} = [111, 129] | 117 |

84 | IS_{84} = [60, 120] | 80 |

85 | IS_{85} = [110, 130] | 116 |

86 | IS_{86} = [60, 120] | 80 |

87 | IS_{87} = [107, 133] | 115 |

88 | IS_{88} = [60, 120] | 80 |

89 | IS_{89} = [173, 187] | 177 |

90 | IS_{90} = [60, 120] | 80 |

91 | IS_{91} = [170, 190] | 176 |

92 | IS_{92} = [60, 120] | 80 |

93 | IS_{93} = [105, 135] | 115 |

94 | IS_{94} = [60, 120] | 80 |

95 | IS_{95} = [115, 125] | 118 |

96 | IS_{96} = [60, 120] | 80 |

97 | IS_{97} = [109, 131] | 116 |

98 | IS_{98} = [60, 120] | 80 |

99 | IS_{99} = [108, 132] | 116 |

100 | IS_{100} = [60, 120] | 80 |

101 | IS_{101} = [108, 132] | 116 |

102 | IS_{102} = [60, 120] | 80 |

103 | IS_{103} = [105, 135] | 115 |

104 | IS_{104} = [60, 120] | 80 |

105 | IS_{105} = [174, 186] | 178 |

106 | IS_{106} = [60, 120] | 80 |

107 | IS_{107} = [108, 132] | 116 |

108 | IS_{108} = [60, 120] | 80 |

109 | IS_{109} = [230, 250] | 236 |

110 | IS_{110} = [171, 189] | 177 |

111 | IS_{111} = [167, 193] | 175 |

112 | IS_{112} = [175, 185] | 178 |

113 | IS_{113} = [60, 120] | 80 |

114 | IS_{114} = [172, 188] | 177 |

115 | IS_{115} = [60, 120] | 80 |

116 | IS_{116} = [170, 190] | 176 |

117 | IS_{117} = [60, 120] | 80 |

118 | IS_{118} = [233, 247] | 237 |

The main parameters of the models are defined as follows:

A time interval [_{i}, _{i}] expressed with time unit TU is associated to each segment between two successive stations. Its lower bound _{i} indicates the minimum time required for the travel and the upper bound _{i} fixes the maximum time not to be exceeded in order to avoid any temporal disturbance on railway traffic.

A train can park in a principal station for at least one minute. The static intervals associated with the three main stations are

The sojourn time of a metro in any other station is estimated from one to two minutes: IS_{i} = [60, 120]; Figure

At the beginning of each day, it is assumed that 4 trains start from the Mahdia station, and 2 others are stationed at the Sousse station; Figure

The static intervals IS_{i} and the effective sojourn time _{ie} associated with the stations and with the segments between two successive stations are detailed in Table

Chronicles provide formalism for monitoring transport systems. A chronicle is composed of a set of events, a set of temporal constraints linking the pairs of events, and the diagnosis test that describes the recognized situation [

Preliminary definitions, useful for the rest of this paper, are given in order to explain the distributed detection principles.

An event is a stimulus to which the system can react by a state change [

The occurrence date is the time corresponding to an event issued from the process. Let _{i} its occurrence date _{i}); then,

A constraint is a relationship expressed by the duration between event occurrences. Two types of constraints can be distinguished; Figure

Local constraints link timed events in the same monitoring site

Global constraints link timed events in different monitoring sites

In our study, the monitoring system (site) _{i} manages a physical zone (i.e., a set of sensors and resources) in the system considered as a Discrete Event System. A monitoring site is composed of six functions: failure detection, diagnosis, prognosis, follow, resumption, and emergency. Our study is limited to the detection function, whose role consists in recognizing a deviation from the normal (expected) functioning, locally or in a distributed manner by communication and cooperation between different monitoring sites.

In many cases, the local information generated by each monitoring site is insufficient, and communications between sites become essential to compensate this deficiency. When these systems are connected, we have a distributed monitoring system. The ease of implementation, test, and maintenance and the reduction of the software complexity in distributed systems are furthered by a high degree of modularity and a low degree of coupling between modules [

In a distributed monitoring architecture, the communication aspects are significant and specific problems must be taken into account, such as the clocks synchronization, the reconstitution of the exchanged messages order, and the communication delays. In this context, the main contribution of this paper is the evaluation of the influence of the communication delays between modules, on the temporal constraints verification. In particular, the proposed solution, inspired from the work of Boufaied, evaluates the impact of the uncertainties that concern communications delays, on the global constraints in railway transport networks.

Global and local constraints.

The time constraints verification is based on some assumptions:

The communication delays Ω belong to the interval [Ω_{min}, Ω_{max}]

Each monitoring site has its own clock, and all clocks have the same time base. Therefore, an event is dated only in the time frame associated to the receiving site. The occurrence function represents its temporal coordinate in the associated time frame.

The proposed technique is suitable for any system in which the operational constraints and the communication time uncertainties are of the same order, such as railway transport systems.

The problem to be solved can be summarized as follows:

Let _{X,Y} be a global constraint linking an event _{X} to _{Y}; Figure _{X,Y} will be defined by

Operating delays between monitoring sites.

Since events _{X} and _{Y} are received and dated by two different sites, it is not possible to directly evaluate the duration _{X}) − _{Y}). Therefore, it is necessary that the site _{Y} informs the site _{X} when it received the event _{Y} (if we consider that only the site _{k}; Figure

The global constraint C_{X,Y}

The occurrences times of events _{x} and _{k} on the site

The communication delay Ω between the two sites _{X}) − _{Y}) = _{X}) − _{k}) + Ω)

The question is that is it possible to know if the constraint C_{Y,X} is satisfied (i.e., if the occurrence time _{Y}) satisfies the C_{Y,X} constraint)? It is possible to reformulate the initial global constraint into a new constraint which is a local constraint, for which it is possible to evaluate the involved durations.

As Ω_{min} ≤ Ω ≤ Ω_{max}, we obtain

The verification of the interval constraint consists, by means of the measurable duration Φ, of looking for the durations _{X}) − _{Y}) that verify both:

A graphical representation of these two constraints is shown in Figure _{Y}) − _{k}), _{Y}) − _{A})), the inequalities (1) and (2) define two bands. The searched durations belong to the intersection of these two bands which defines a polygon noted PO. The position of PO depends not only on the duration _{Y}) − _{X}) but also on the terminal positions of the duration Ω with respect to _{Y,X} and _{Y,X}. For any duration Ω, PO is defined by 4 points: _{1} = _{Y,X} − Ω_{max}; _{Y,X} − Ω_{min}; _{Y,X} − Ω_{min}; and _{Y,X} − Ω_{max.}

Representation of the admissible domain [

In many usual diagnosis approaches, the notions of uncertainty, inaccuracy, and incompleteness of information are modeled through bounded intervals. Whether the observation belongs to the expected interval leads to a binary reasoning about the detected inconsistencies. This type of binary reasoning may be insufficient for monitoring and diagnosis, especially for the evaluation of marginal deviations that can occur during transient phases. To enrich the reasoning, fuzzy sets and the theory of possibilities were integrated and lead to the definition of new fuzzy models. In order to quantify the set of possible durations Φ, a graphical representation, inspired from [

Possibility function for an interval constraint with _{1} ≥ 0, _{2} ≥ 0, _{3} ≥ 0 and _{4} ≥ 0.

Centralized monitoring consists of associating a single diagnoser to the whole process model. The latter collects the various process information before making a final decision on the process operating state. Although powerful in terms of diagnosis, the centralized structure is difficult to use for large and distributed systems such as transport systems since the building of a global model generates, in most cases, combinatorial explosion problems.

In distributed monitoring structures, the process is decomposed into several local models. To each model is associated a local diagnoser. Each diagnoser makes his decision based on local observation. In the case of global specifications, a protocol allows the communication between the different diagnosers in order to make a final decision. The distributed monitoring, based on chronicles, verifies that each observed event is consistent with the chronicles specified by the time constraints. If the chronicles represent an abnormal behavior model, chronicles recognition is used for monitoring purposes.

In the studied railway networks, every set of sensors providing useful information has its own monitoring sites. Then, these sites are connected in distributed architecture. According to Figure _{i}. Each diagnoser monitors locally a subsystem and communicates with other diagnosers in order to get necessary information in order to take decisions relative to the distributed diagnosis; Figure

Distributed monitoring architecture based on chronicles.

In order to help the supervisor in charge of managing the studied railway networks (i.e., detecting traffic perturbations, alert traveler claims, and maintain stability and security of the networks), a monitoring task is needed. The overall aim of the proposed monitoring approach is to control that the railway traffic proceeded well to avoid undesirable situations. The distributed monitoring of the Sahel railway networks based on the chronicle method involves the following steps.

The first task is to subdivide the railway network system into sectors (subsystems).

The railway network between Sousse and Monastir has been split into 10 sectors, as shown in Figure

Travel time from Sousse to Monastir stations.

This step consists of identifying the sensors needed to perform the system monitoring. In the proposed approach, each site _{i}, Figure _{i}”.

To each event is associated a diagnoser _{i}, Figure

_{S1}: Beginning journey from the Sousse Bab Jdid station (Sensor S1).

_{S2}: Metro arrival at Sousse Med.5 (Sensor S2).

_{S3}: Departure from the subway station Sousse Med.5 (Sensor S3).

_{S4}: Metro arrival at Sousse Sud Station (Sensor S4).

_{S5}: Departure from the subway station Sousse Sud (Sensor S5).

_{S6}: Metro arrival at Sousse Z.Ind Station (Sensor S6).

_{S7}: Departure from the subway station Sousse Z.Ind (Sensor S7).

_{S8}: Metro arrival at Sahline Ville station (Sensor S8).

_{S9}: Departure from the subway station Sahline Ville (Sensor S9).

_{S10}: Metro arrival at Sahline Sabkha station (Sensor S10).

_{S11}: Departure from the subway station Sahline Sabkha (Sensor S11).

_{S12}: Metro arrival at the Les Hôtels station (Sensor S12).

_{S13}: Departure from the subway station Les Hôtels (Sensor S13).

_{S14}: Metro arrival at the L’Aeroport station (Sensor S14).

_{S15}: Departure from the subway station L’Aeroport (Sensor S15).

_{S16}: Metro arrival at the La faculté station (Sensor S16).

_{S17}: Departure from the subway station La faculté (Sensor S17).

_{S18}: Metro arrival at the Monastir station (Sensor S18).

A scenario is defined for each possible deviation in each section bringing the system to an erroneous situation. Deviations can occur due to unavailability of transportation systems, temporal disruptions, or traffic management and disturbances.

Let us detail the monitoring between the two events, _{S18} (metro arrival at the Monastir station) and _{S1} (departure from Sousse Bab Jdid); Figure _{S18} and _{S1}. This timing constraint is a global one; therefore, the verification of this constraint can be performed through the measure of the travelling time between the station and parking time of a metro in stations. As long as these durations are included in the mentioned intervals, no disturbance is detected. Otherwise, a traffic disturbance is detected. As previously mentioned, the global constraint to compute is an interval constraint type defined as _{S18,S1}: _{S18,S1} ≤ _{S18}) − _{S1}) ≤ _{S18,S1}, with

According to the time intervals (Figure _{S18,S1}) of the travel between the Sousse and Monastir stations is 2315 s, whereas the maximum time (_{S18,S1}) is 3085 s.

In the studied railway network, the detection function monitors the system evolution through the verification of time constraints. Let us suppose that

From an experimental point of view, at the end of each journey, the current real-time values are collected and stored in an SNCFT database. The only data, from which the identification is computed is, therefore, a sequence of vectors indicating the planned schedule and the actual train departure times at each station. In order to illustrate our approach, a small part of the real data has been extracted from Table

Planned and measured times: Sousse to Mahdia direction.

Station | Planned time | Real time |
---|---|---|

Sousse Bab Jdid | 05 : 40 : 00 | 05 : 41 : 22 |

Sousse Mohamed V | 05 : 42 : 00 | 05 : 43 : 43 |

Sousse Sud | 05 : 45 : 00 | 05 : 48 : 28 |

Sousse zone industrielle | 05 : 48 : 00 | 05 : 52 : 34 |

Sahline Ville | 05 : 51 : 00 | 05 : 55 : 33 |

Sahline Sabkha | 05 : 54 : 00 | 05 : 57 : 33 |

Les Hôtels | 05 : 58 : 00 | 06 : 01 : 01 |

Aeroport | 06 : 00 : 00 | 06 : 02 : 01 |

La faculté | 06 : 06 : 00 | 06 : 08 : 00 |

Monastir | 06 : 10 : 00 | 06 : 21 : 25 |

La faculté 2 | 06 : 24 : 00 | 06 : 24 : 24 |

Monastir zone industrielle | 06 : 26 : 00 | 06 : 28 : 24 |

Frina | 06 : 28 : 00 | 06 : 30 : 05 |

Khnis Bembla | 06 : 30 : 00 | 06 : 33 : 24 |

Ksibet Bennane | 06 : 34 : 00 | 06 : 37 : 23 |

Bouhadjar | 06 : 37 : 00 | 06 : 40 : 23 |

Lamta | 06 : 39 : 00 | 06 : 43 : 22 |

Sayada | 06 : 41 : 00 | 06 : 44 : 43 |

Ksar Hellal Z.I. | 06 : 43 : 00 | 06 : 47 : 03 |

Ksar Hellal | 06 : 45 : 00 | 06 : 48 : 03 |

Moknine Gribaa | 06 : 47 : 00 | 06 : 50 : 02 |

Moknine | 06 : 50 : 00 | 06 : 52 : 03 |

Téboulba Z.I. | 06 : 53 : 00 | 06 : 56 : 20 |

Téboulba | 06 : 56 : 00 | 06 : 59 : 21 |

Bekalta | 07 : 00 : 00 | 07 : 06 : 02 |

Baghdadi | 07 : 10 : 00 | 07 : 13 : 04 |

Mahdia Z.T. | 07 : 15 : 00 | 07 : 18 : 03 |

Sidi Massaoud | 07 : 18 : 00 | 07 : 20 : 34 |

Borj Arif | 07 : 21 : 00 | 07 : 22 : 33 |

Ezzahra | 07 : 24 : 00 | 07 : 26 : 54 |

Mahdia | 07 : 30 : 00 | 07 : 28 : 54 |

Let us suppose a late departure of the metro from the Sousse Bab Jdid station (departure at 05 : 41 : 22; see Table _{es1⟶es3} = 620 s. This delay may involve an illegal behavior and can lead to a degraded service. In fact, according to Figure _{S18,S1}). This delay can affect the stability of the studied railway network: according to Table _{S18,S1} (planned arrival time 06 : 10 : 00/measured arrival time at 06 : 21 : 25). Consequently, the distributed monitoring, based on chronicle, allows an early detection of traffic disturbance, to avoid catastrophic scenarios and preserve stability and security of the studied railway networks.

Possibility function considering Φ_{es1⟶es3}.

In this study, we investigate the monitoring of a railway network. The proposed monitoring architecture is a distributed architecture, based on monitoring sites. To each site is associated a subsystem receiving a set of events and providing a detection function. Abnormal behaviors and traffic disturbances are recognized with the cooperation of local detection functions. The verification of the global constraints supposes the existence of communication tools allowing event exchanges between monitoring sites. The chronicle recognition is exploited for the detection of traffic disturbances.

The problem of the distributed recognition of subchronicles through the verification of local and global time constraints has been pointed out. This recognition is based on time constraints verification performed with a possibility evaluation. The results obtained for the illustrative example are promising. They show that the distributed monitoring improves the prevention of temporal disruption and traffic management by performing an early detection.

In our future works, a comparative study based upon several cases should be developed. A comparison with the proposed monitoring architecture and results with the works based on Causal Time Signature (CTS) should also be considered. Likewise, it would be interesting to apply a robust control strategy facing disturbances in railway transport systems in order to compensate the disturbances once they have been detected [

The data used to support the findings of this study are included within the article.

The authors declare that there are no conflicts of interest regarding the publication of this paper.