Optimal Polynomial Complexity Deadlock Avoidance Policies for Manufacturing Systems with Flexible Routings

Xing, Keyi; Tian, Feng; Xu, Hongbin; Hu, Baosheng

doi:10.1109/coase.2006.326923

Cited by 4 publications

(9 citation statements)

References 10 publications

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“…Resource-transition circuits can be used to characterize deadlocks. 262 The relationship between siphons and maximal perfect resource-transition circuits is explored by Xing et al 136 An algorithm for computing all SMSs is proposed by Wang et al 263 based on resource circuits in S 3 PR. In this work, the concepts of loop resource subsets and their characteristic resource subnets are proposed, and sufficient and necessary conditions for loop resource subsets to generate SMS are established.…”

Section: Siphons Computationmentioning

confidence: 99%

“…When a deadlock occurs, it is detected and then the system is put back to a deadlock-free state. Deadlock avoidance 4,11,12,15,48,53,54,56,57,73,106,107,109,[122][123][124][125][126][127][128][129][130][131][132][133][134][135][136]319 is a resources allocation mechanism, behind which an online control policy is used to make a correct decision to proceed among the feasible evolutions. Deadlock prevention 6,49,71,72,75,77,82,91,[95][96][97][98]103,111,[137][138][139][140][141][142]…”

Section: Introductionmentioning

confidence: 99%

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Deadlock analysis and control based on Petri nets: A siphon approach review

Hou

Barkaoui

2017

Advances in Mechanical Engineering

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Deadlocks should be eliminated in highly automated manufacturing systems since their occurrence implies the stoppage of the whole or partial system operation. Over the past decades, Petri nets are increasingly becoming one of the most popular and full-fledged mathematical tools to deal with deadlock problems due to their inherent characteristics. In a Petri net formalism, liveness is an important property of system safeness, which implies the absence of global and local deadlock situations in an automated manufacturing system. The liveness assessment can be performed by verifying the satisfiability of certain predicates on siphons, a well-known structural object in Petri nets. Therefore, siphons have received much attention to analyze and control systems modeled with Petri nets. Particularly, elementary siphon theory plays a key role in the development of structurally simple liveness-enforcing Petri net supervisors, leading to a variety of deadlock control approaches. This survey studies on the state-of-the-art elementary siphon theory of Petri nets including refined concepts of elementary siphons and their extended version, computation methods of siphons and elementary ones, controllability conditions, and their application to deadlock control. As a reference, this work attempts to provide a comprehensive and updated research survey on siphons, elementary siphons, and their applications to the deadlock resolution in Petri nets.

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Section: Siphons Computationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Deadlock analysis and control based on Petri nets: A siphon approach review

Hou

Barkaoui

2017

Advances in Mechanical Engineering

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“…A resource is said to be a -resource if its capacity is one and shared by two or more MPRTcircuits that do not include each other. With the utilization of deadlock characteristic description, it is first proved that there are only two types of reachable markings that are safe ones and deadlocks, in an AMS modeled with an S 3 PR withoutresources [19]. Under the circumstance, a DAP only needs to prohibit the transitions whose firing leads a system to deadlocks.…”

Section: Introductionmentioning

confidence: 99%

“…Under the circumstance, a DAP only needs to prohibit the transitions whose firing leads a system to deadlocks. Consequently, an optimal DAP can be formulated by a one-step look-ahead policy [19,35] to check whether the forthcoming state is safe or not. Furthermore, the proposed optimal DAP is of polynomial complexity with respect to the system scale.…”

Section: Introductionmentioning

confidence: 99%

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A Multistep Look-Ahead Deadlock Avoidance Policy for Automated Manufacturing Systems

Al-Ahmari

2017

Discrete Dynamics in Nature and Society

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For an automated manufacturing system (AMS), it is a computationally intractable problem to find a maximally permissive deadlock avoidance policy (DAP) in a general case, since the decision on the safety of a reachable state is NP-hard. This paper focuses on the deadlock avoidance problem for systems of simple sequential processes with resources (S 3 PR) by using Petri nets structural analysis theory. Inspired by the one-step look-ahead DAP that is an established result, which is of polynomial complexity, for an S 3 PR without one-unit-capacity resources shared by two or more resource-transition circuits (in the Petri net model) that do not include each other, this research explores a multiple-step look-ahead deadlock avoidance policy for a system modeled with an S 3 PR that contains a shared one-unit-capacity resource in resource-transition circuits. It is shown that the development of an optimal DAP for the considered class of Petri nets is also of polynomial complexity. It is indicated that the steps needed to look ahead in a DAP depend on the structure of the net model. A number of examples are used to illustrate the proposed method.

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Combinatorics‐based estimation of reachable states for the system of simple sequential process with resources

Hong

Jing

Hou

et al. 2016

IEEJ Transactions Elec Engng

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The system of simple sequential processes with resources (S 3 PR) is a class of Petri nets that can model a typical class of resource allocation systems. This paper proposes a method to calculate the number of reachable states of an S 3 PR. First of all, an upper bound of reachable states of an S 3 PR can be obtained by combinatorics. The number of unreachable states may be counted in the upper bound because of the existence of shared resources. Hence, the next step is to subtract the number of unreachable states from the upper bound. Here, siphons with two resources derived from resource circuits are used to obtain the number of the unreachable states. The resulting number after subtracting the number of unreachable states from the upper bound is what we are looking for. Finally, example calculations and analyses are conducted to verify the effectiveness of the method.

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Optimal Polynomial Complexity Deadlock Avoidance Policies for Manufacturing Systems with Flexible Routings

Cited by 4 publications

References 10 publications

Deadlock analysis and control based on Petri nets: A siphon approach review

Deadlock analysis and control based on Petri nets: A siphon approach review

A Multistep Look-Ahead Deadlock Avoidance Policy for Automated Manufacturing Systems

Combinatorics‐based estimation of reachable states for the system of simple sequential process with resources

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