An Improved Mixed-Integer Programming Method to Compute Emptiable Minimal Siphons in S3PR Nets

Emptiable minimal siphons (EMSs) play a key role in the development of many deadlock control policies for resource allocation systems modeled with Petri nets. Recent research results show that siphon-based deadlock prevention methods can avoid complete siphon enumeration by using mixed-integer progr...

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Veröffentlicht in:IEEE transactions on control systems technology Jg. 26; H. 6; S. 2135 - 2140
Hauptverfasser: Gan, MengDi, Wang, ShouGuang, Ding, ZhiJun, Zhou, MengChu, Wu, Wenhui
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York IEEE 01.11.2018
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Schlagworte:
Computational complexity
Computing time
Deadlocks
Enumeration
Integer programming
liveness
Mixed integer linear programming
mixed-integer programming (MIP)
Petri nets
Resource allocation
Siphons
Solution space
System recovery
ISSN:1063-6536, 1558-0865
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Zusammenfassung:Emptiable minimal siphons (EMSs) play a key role in the development of many deadlock control policies for resource allocation systems modeled with Petri nets. Recent research results show that siphon-based deadlock prevention methods can avoid complete siphon enumeration by using mixed-integer programming (MIP). This brief proposes a novel MIP approach, called MIP<inline-formula> <tex-math notation="LaTeX">' </tex-math></inline-formula> for short, to compute EMSs for deadlock control in a class of Petri nets, i.e., a system of simple sequential processes with resources (S 3 PR). Compared with classical MIP, since MIP<inline-formula> <tex-math notation="LaTeX">' </tex-math></inline-formula> utilizes the structural characteristics of S 3 PR nets to compute EMSs and more constraints are included in it, its solution space is drastically narrowed. As a result, the number of iterations to solve the MIP<inline-formula> <tex-math notation="LaTeX">' </tex-math></inline-formula> problem is significantly reduced, and the computational efficiency is considerably improved. Comparisons are provided on several S 3 PR nets to show its superior efficiency.
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ISSN:1063-6536
1558-0865
DOI:10.1109/TCST.2017.2754982