**5. Conclusions**

16 Will-be-set-by-IN-TECH

If the transitions occur in a time interval [*tmin*, *tmax*] the timeline is said to be flexible. In this case we can represent the transition in a Timed Petri Net by an interval, as proposed in the first section. If we want to deal with deterministic time transition it is enough to make *tmin* = *tmax*

Timeline models can be very useful in some critical problem applications such as intelligent planning and scheduling. Some of those applications could be used in spatial projects [14]5. In other applications Petri Nets were used to perform requirements analysis including deterministic time, as in the one proposed by Vaquero et al.[40][41]. In that case the idea of solving real life planning problems starts with the elicitation and specification of requirements using UML, goes through the analysis of this requirements using Timed Petri Nets, synthesizes a model also in Petri Nets and finally uses a specific language, PDDL, to transfer the model to software planners which will provide the final result. Also, a modeling

A specific state lifetime were developed to model and analyze the timelines for the agents and

Based on this time diagram Petri Nets could be synthesized to make the proper validation of the model. It is important to notice that there are a large number of approaches and tools that claim to perform a good analysis of models directly associated to a planer software with good results. However, most of this systems address only model problems which are well behaved and/or have a limited size and complexity. When the challenge is to model a large system, such as the space project mentioned before or a port to get and deliver petroleum, the

Therefore the combination UML/Timed Petri Nets could be successful in the modeling of large and complex problems also in the planning area, with the possibility to be applied in

<sup>5</sup> See also the Mexar 2 Project and the use of intelligent software application in the link mexar.istc.cnr.it/mexar2.

design environment were developed to perform this process[41][40].

and the same net framework could be used.

**Figure 8.** Language structure in itSIMPLE 3.1

practice to real systems.

objects that would compose the plan, as shown in Figure 8.

challenge could be too big to be faced by these proposals.

In conclusion it is important to remark that the evolution of Petri Nets towards a formal representation, capable to treat complex systems should be based in two basis: the extension to model timed systems; and the development of a unified net that includes all extensions besides the timed approach - hierarchy, gates, not controled elements, always respecting the recent published ISO/IEC standard and its next release to appear in 2013. This is the fundamental concepts to have new environments that could support a complementary treatment of timed systems, that is, that could deal with deterministic timed net as well as with time PN in the same environment. That is the focus of the present work.

Besides, it would be advisable that the same environment could deal, also in a complementary way, with classic P/T nets as well as with high level (HLPN) nets or even with simetric nets, which is also part of the ISO/IEC standard. The novelty would be to use a unified net system as a platform to reach the further challenge which would be the introduction of abstract nets.

In what concerns the unified net to treat time intervals and dense time, we achieve a good point with the system GHENeSys where the present work focus most in the first part. However, in [17] a more detailed description of the state class algorithm is given and the basic concepts that lead to a modeling and simulation approach to dense time nets. Therefore the unification with timed PN is a promising result in the near future. Also the system GHENeSys is being developed to implement a unified net as we described above, dealing with P/T and HLPN in the same environment. That is a good combination, capable to model and simulate timed and time nets (in that case using model checking) in the same environment, with the advantage to have a sound and formal representation supporting all process.

[10] Bodbar, B, Giacomini, L, Holding, DJ (2000) UML and Petri Nets for the Design and Analysis of Distributed Systems, Proc. of the IEEE Int. Conf. on Control Applications,

Timed Petri Nets 377

[11] Boucheneb, H., Alger, U. and Berthelot, G. (1993) . Towards a simplified building of time petri nets reachability graph, *Proc. 5th International Workshop on Petri Nets and Performance*

[12] Boucheneb, H. and Mullins, J. (2003). Analyse des réseaux temporels. calcul des classes en o(n2) et des temps de chemin en o(m x n), *Technique et Science Informatiques*

[13] Cerone, A. and Maggiolo-Schettini, A. (1999). Time-based expressivity of time petri nets

[14] Cesta, A, Finzi, A, Fratini, S, Orlandini, A, Ronci, E (2010) Validation and verification issues in a temiline-bsed planning system, Knowledge Engineering Review, vol. 25, no.

[15] Ciufudean C, Filote C (2010) Workflow Diagnosis Using Petri Net Charts, in Petri Nets

[16] Daws, C., Olivero, A., Tripakis, S. and Yovine, S. (1995). The tool KRONOS, *Hybrid Systems III: Verification and Control*, Vol. 1066, Springer, Rutgers University, New

[17] del Foyo, P. M. G. and Silva, J. R. (2011). Some issues in real-time systems verification using time petri nets, *Journal of the Braz. Soc. of Mech. Sci. & Eng.* XXXIII(4): 467–474. [18] del Foyo, P. M. G., Salmon, A. Z. O., Silva, J. R. (2011) Requirements Analysis of

[20] Gardey, G., Lime, D., Magnin, M. and Roux, O. H. (2005). Romeo: A tool for analyzing time petri nets, *in* K. Etessami and S. Rajamani (eds), *CAV2005*, Vol. 3576,

[21] Hadjidj, R. and Boucheneb, H. (2006). On-the-fly tctl model checking for time petri nets

[22] Hadjidj, R. and Boucheneb, H. (2008). Improving state class constructions for ctl\* model

[23] ISO/IEC (2002) High-Level Petri Nets: Concepts, Definitions and Graphical Notation,

[24] ISO/IEC (2005) Software and Systems Engineering - High-Level Petri Nets, Part 2:

[25] Kindler, E (2006) PNML: Concepts, Status and Future Directions, Invited paper, Proc. of

[26] Kordic, V (ed.) (2008) Petri Nets: Theory and Applications, I-Tech Education and Pub,

[27] Lafortune, S. and Cassandras, C. G. (2008). *Introduction to Discrete Event Systems*, second

[28] Larsen, K. G., Pettersson, P. and Yi, W. (2000). Uppaal - validation and verification of real

for system specification, *Theoretical Computer Science* 216(1): 1–53.

Automated Projects Using UML/Petri Nets, Proc. of COBEM 2011. [19] Girault, C, Valk, R (2003) Petri Nets for System Engineering, Springer, 607 p.

Applications, Pauwel Pawlewski (ed.), InTech, 752 p.

pp. 610-615.

22(4): 435–459.

3, pp. 299-318.

*Models*, Toulouse, France, pp. 46–55.

Brunswick, NJ, USA, pp. 208–219.

Springer-Verlag, pp. 418–423.

EKA 2006, pp. 35-55.

208 p.

using state class graphs, *acsd* 0: 111–122.

time systems - status & developments.

checking of time petri nets, *STTT* 10(2): 167–184.

International Standard Final Draft, ISO/IEC 15909.

Transfer Format, International Standard WD ISO/IEC 15909.

edn, Springer, 233 Spring Street, New York, NY 10013, USA.

Thus, it would be possible to have performance analysis that really fits the complexity of the problem addressed, adapting very easily to discrete or dense time approach.
