Abstract
The study of resource allocation related aspects is a fundamental issue in the design and control of Discrete Event Dynamic Systems (DEDSs) belonging to domains ranging from multithreaded software applications to Flexible Manufacturing Systems (FMSs). The formulation of this application-driven problem in terms of Petri nets leads to a family of net models with a specific structure-based characterization. These net subclasses are derived from a specific methodology to abstract the system in order to obtain its Resource Allocation System (RAS) view, which we describe in this chapter. After that, we concentrate our efforts in the characterization of the liveness of such models. The structural causes of the non-liveness (deadlock of some processes) are also discussed. These will lay the foundations to introduce control elements which forbid all the bad states enforcing the liveness property. The methods to compute the control are based on structural techniques avoiding the construction of the reachability graph.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Best, E., Voss, K.: Free Choice Systems Have Home States. Acta Informatica 21, 89–100 (1984)
Cano, E.-E., Rovetto, C.-A., Colom, J.-M.: On the Computation of the Minimal Siphons of S4PR nets from a Generating Family of Siphons. In: Proc. 15th IEEE International Conference on Emerging Technologies and Factory Automation, Bilbao, Spain (2010)
Chu, F., Xie, X.: Deadlock Analysis of Petri Nets using Siphons and Mathematical Programming. IEEE Transactions on Robotics and Automation 13(6), 793–804 (1997)
Colom, J.M., Silva, M.: Improving the Linearly Based Characterization of P/T Nets. In: Rozenberg, G. (ed.) APN 1990. LNCS, vol. 483, pp. 113–145. Springer, Heidelberg (1991)
Colom, J.-M.: The Resource Allocation Problem in Flexible Manufacturing Systems. In: van der Aalst, W.M.P., Best, E. (eds.) ICATPN 2003. LNCS, vol. 2679, pp. 23–35. Springer, Heidelberg (2003)
Ezpeleta, J., Colom, J.-M., Martínez, J.: A Petri net Based Deadlock Prevention Policy for Flexible Manufacturing Systems. IEEE Transactions on Robotics and Automation 2(11), 173–184 (1995)
Ezpeleta, J., Garcia-Vallés, F., Colom, J.-M.: A Class of Well Structured Petri Nets for Flexible Manufacturing Systems. In: Desel, J., Silva, M. (eds.) ICATPN 1998. LNCS, vol. 1420, pp. 64–83. Springer, Heidelberg (1998)
Ezpeleta, J., Tricas, F., García–Vallés, F., Colom, J.-M.: A Banker’s Solution for Deadlock Avoidance in FMS with Flexible Routing and Multiresource States. IEEE Transactions on Robotics and Automation 18(4), 621–625 (2002)
Ezpeleta, J., Recalde, L.: A Deadlock Avoidance Approach for Non–Sequential Resource Allocation Systems. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 34(1), 93–101 (2004)
Fanti, M.P., Maione, B., Mascolo, S., Turchiano, B.: Event-Based Feedback Control for Deadlock Avoidance in Flexible Production Systems. IEEE Transactions on Robotics and Automation 13(3), 347–363 (1997)
Ghaffari, A., Rezg, N., Xie, X.: Design of a Live and Maximally Permissive Petri Net Controller using the Theory of Regions. IEEE Transactions on Robotics 19(1), 137–141 (2003)
Hu, H., Zhou, M.C., Li, Z.W.: Supervisor Optimization for Deadlock Resolution in Automated Manufacturing Systems With Petri Nets. IEEE Transactions on Automation Science and Engineering 8(4), 794–804 (2011)
Jeng, M.-D., Xie, X.-L., Peng, M.-Y.: Process Nets with Resources for Manufacturing Modeling and their Analysis. IEEE Transactions on Robotics 18(6), 875–889 (2002)
Lautenbach, K., Thiagarajan, P.S.: Analysis of a Resource Allocation Problem Using Petri Nets. In: Proc. 1st European Conf. on Parallel and Distributed Processing, France (1979)
Li, Z.-W., Zhou, M.-C.: Control of Elementary and Dependent Siphons in Petri Nets and Their Application. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 38(1), 133–148 (2008)
Li, Z.-W., Zhou, M.-C.: Deadlock Resolution in Automated Manufacturing Systems: A Novel Petri Net Approach. Springer, New York (2009)
López-Grao, J.-P., Colom, J.-M.: Resource Allocation Systems: Some Complexity Results on the S4PR Class. In: Najm, E., Pradat-Peyre, J.-F., Donzeau-Gouge, V.V. (eds.) FORTE 2006. LNCS, vol. 4229, pp. 323–338. Springer, Heidelberg (2006)
López–Grao, J.-P., Colom, J.-M.: Lender Processes Competing for Shared Resources: Beyond the S4PR Paradigm. In: Proc. 2006 IEEE Int. Conf. on Systems, Man and Cybernetics, Taipei, Taiwan (2006)
López–Grao, J.-P., Colom, J.-M.: On the Deadlock Analysis of Multithreaded Control Software. In: Proc. 16th IEEE Int. Conf. on Emerging Technologies and Factory Automation, Toulouse, France (2006)
López-Grao, J.-P., Colom, J.-M.: A Petri Net Perspective on the Resource Allocation Problem in Software Engineering. In: Jensen, K., Donatelli, S., Kleijn, J. (eds.) Transactions on Petri Nets and Other Models of Concurrency V. LNCS, vol. 6900, pp. 181–200. Springer, Heidelberg (2012)
López–Grao, J.-P.: Contributions to the Deadlock Problem in Multithreaded Software Applications Observed as Resource Allocation Systems. PhD Thesis. University of Zaragoza, Spain (2012)
Park, J., Reveliotis, S.A.: Deadlock Avoidance in Sequential Resource Allocation Systems with Multiple Resource Acquisitions and Flexible Routings. IEEE Transactions on Automatic Control 46(10), 1572–1583 (2001)
Piroddi, L., Cordone, R., Fumagalli, I.: Combined Siphon and Marking Generation for Deadlock Prevention in Petri Nets. IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans 39(3), 650–661 (2009)
Reveliotis, S.A.: Real-Time Management of Resource Allocation Systems: A Discrete Event Systems Approach. International Series in Operations Research & Management Science (2004)
Rovetto, C.-A.: Métodos Basados en Redes de Petri para el Diseño de Algoritmos de Encaminamiento Adaptativos Mínimos Libres de Bloqueos. PhD Thesis. University of Zaragoza, Spain (2011)
Silva, M., Colom, J.-M.: On the Computation of Structural Synchronic Invariants in P/T Nets. In: Rozenberg, G. (ed.) APN 1988. LNCS, vol. 340, pp. 386–417. Springer, Heidelberg (1988)
Tricas, F.: Deadlock Analysis, Prevention and Avoidance in Sequential Resource Allocation Systems. PhD Thesis. University of Zaragoza, Spain (2003)
Tricas, F., García–Valles, F., Colom, J.-M., Ezpeleta, J.: A Petri net Structure-Based Deadlock Prevention Solution for Sequential Resource Allocation Systems. In: Proc. 2005 Int. Conf. on Robotics and Automation, Barcelona, Spain (2005)
Xie, X., Jeng, M.-D.: ERCN-merged Nets and Their Analysis using Siphons. IEEE Transactions on Robotics and Automation 29(4), 692–703 (1999)
Wang, Y., Liao, H., Reveliotis, S.A., Kelly, T., Mahlke, S., Lafortune, S.: Gadara Nets: Modeling and Analyzing Lock Allocation for Deadlock Avoidance in Multithreaded Software. In: Proc. 49th IEEE Conf. on Decision and Control, Atlanta, Georgia, USA (2009)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag London
About this chapter
Cite this chapter
López-Grao, JP., Colom, JM. (2013). Structural Methods for the Control of Discrete Event Dynamic Systems – The Case of the Resource Allocation Problem. In: Seatzu, C., Silva, M., van Schuppen, J. (eds) Control of Discrete-Event Systems. Lecture Notes in Control and Information Sciences, vol 433. Springer, London. https://doi.org/10.1007/978-1-4471-4276-8_13
Download citation
DOI: https://doi.org/10.1007/978-1-4471-4276-8_13
Publisher Name: Springer, London
Print ISBN: 978-1-4471-4275-1
Online ISBN: 978-1-4471-4276-8
eBook Packages: EngineeringEngineering (R0)