Some results and open problems concerning elementary siphons of Petri nets

Siphons are related to the liveness property of Petri net models of concurrent systems. Elementary siphons, an important concept proposed in our previous work, has been proved to be an effective way to characterize, analyze, and control deadlocks in these systems. This paper first surveys the existing results on elementary siphons of Petri nets. It is proved that the number of elementary siphons in a Petri net is bounded by the smaller of place count and transition count. We investigate the conditions under which there is no weakly dependent siphon in a Petri net. A polynomial algorithm is developed to decide the set of elementary siphons for the deadlock control purpose. Some interesting and open problems on elementary siphons are finally discussed.

[1]  Javier Martínez,et al.  A Petri net based deadlock prevention policy for flexible manufacturing systems , 1995, IEEE Trans. Robotics Autom..

[2]  Hoda A. ElMaraghy,et al.  Deadlock prevention and avoidance in FMS: A Petri net based approach , 1998 .

[3]  Jörg Desel,et al.  Free choice Petri nets , 1995 .

[4]  K. Lautenback Linear algebraic calculation of deadlocks and traps , 1987 .

[5]  Kamel Barkaoui,et al.  On Liveness and Controlled Siphons in Petri Nets , 1996, Application and Theory of Petri Nets.

[6]  Nidhal Rezg,et al.  Design of a live and maximally permissive Petri net controller using the theory of regions , 2003, IEEE Trans. Robotics Autom..

[7]  Joaquín Ezpeleta,et al.  An Iterative Method for Deadlock Prevention in FMS , 2000 .

[8]  K. Barkaoui,et al.  A deadlock prevention method for a class of FMS , 1995, 1995 IEEE International Conference on Systems, Man and Cybernetics. Intelligent Systems for the 21st Century.

[9]  Mengchu Zhou,et al.  Elementary Siphons of Petri Nets and Deadlock Control , 2004 .

[10]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[11]  Kurt Lautenbach,et al.  The Linear Algebra of Deadlock Avoidance - A Petri Net Approach , 1996 .

[12]  MengChu Zhou,et al.  Elementary siphons of Petri nets and their application to deadlock prevention in flexible manufacturing systems , 2004, IEEE Trans. Syst. Man Cybern. Part A.

[13]  MuDer Jeng,et al.  ERCN merged nets for modeling degraded behavior and parallel processes in semiconductor manufacturing systems , 2003, 2003 IEEE International Conference on Robotics and Automation (Cat. No.03CH37422).

[14]  Kamel Barkaoui,et al.  Supervisory control of discrete event systems based on structure theory of Petri nets , 1997, 1997 IEEE International Conference on Systems, Man, and Cybernetics. Computational Cybernetics and Simulation.

[15]  Panos J. Antsaklis,et al.  Synthesis of deadlock prevention supervisors using Petri nets , 2002, IEEE Trans. Robotics Autom..

[16]  MuDer Jeng,et al.  Deadlock prevention policy based on Petri nets and siphons , 2001 .

[17]  Feng Chu,et al.  Deadlock analysis of Petri nets using siphons and mathematical programming , 1997, IEEE Trans. Robotics Autom..

[18]  Spyros A. Reveliotis,et al.  On the Siphon-Based Characterization of Liveness in Sequential Resource Allocation Systems , 2003, ICATPN.

[19]  MengChu Zhou,et al.  Deadlock control methods in automated manufacturing systems , 2004, IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans.