Elementary Siphons Research Articles

Adaptive Deadlock Control for a Class of Petri Nets With Unreliable Resources

In an automated manufacturing system (AMS), resources are, in general, subject to unpredictable failures, which invalidate many existing deadlock control strategies. In this article, we propose an adaptive deadlock control policy for an AMS with multiple types of unreliable resources. The considered AMS is modeled with a system of simple sequential processes with resources. First, based on an elementary siphon control method, monitors are added for elementary siphons and some particular dependent siphons to ensure the liveness of a system if there are no resource failures. By considering the fact that an unreliable resource may fail in a system, recovery subnets are added to describe the resource failures and recoveries. Since a monitor added for a siphon may not be able to guarantee that the corresponding siphon is always marked if the failure of a resource in the siphon occurs, the concept of switch controllers is presented so as to make the siphon always remarked if it is emptied by resource failures. It is verified that the adaptive controller proposed in this article can guarantee the liveness of the controlled system no matter whether unreliable resources break down or not. More importantly, if there is no resource failure, the system can maintain predefined production without degrading planned system performance. Finally, examples are presented to illustrate the validity of the proposed method.

Robust deadlock control for automated manufacturing systems based on elementary siphon theory

Resource failures may happen from time to time in an automated manufacturing system (AMS) in production practice, leading to that most of deadlock control methods in the literature are not applicable. For a generalized system of simple sequential process with resources (GS3PR), this paper develops a robust deadlock control strategy when there exists a type of unreliable resources. To do so, after computing the system’s elementary and dependent strict minimal siphons (SMSs), by using the concept of max′-controllability of siphons, we then check whether an elementary SMS is self-max′-controlled or not, and whether it contains unreliable resources. Afterwards, a constraint set for a siphon is introduced and a monitor is designed for each non-max′-controlled elementary SMS and self-max′-controlled elementary one that contains unreliable resources. Then, if a dependent SMS is max′-controlled with respect to the control depth variables of its elementary siphons, it needs no monitor; otherwise, we add a monitor for such a dependent SMS. Finally, a robust deadlock control algorithm is developed to keep each SMS to be max′-controlled, even if there exists a type of unreliable resources. The proposed method is demonstrated by using examples.

Elementary Siphon-Based Robust Control for Automated Manufacturing Systems With Multiple Unreliable Resources

Resources in a real-world automated manufacturing system may be unreliable, thus paralyzing many existing deadlock control strategies. This paper defines robust legal markings and proposes a two-step robust deadlock control policy for systems of the simple sequential process with resources based on elementary siphons. The first step, called elementary siphons control, derives a live controlled system without considering resource failures. The second step deals with failure-induced deadlocks control issues. With resource failures taken into account, recovery subnets modeling resource failures and recoveries are added to the first-step-derived system, which may cause the occurrence of failure-induced deadlocks, resulting in an unreliable controlled system. In order to make the system reliable, the definition that a resource failure is observed by a monitor is developed. A scenario is exposed that a resource failure does not need to be observed while can be observed by the added monitors. Arcs connecting recovery places and transitions of the initial system are added based on the obtained scenario. The concept of the extend the adjoint set of a siphon is presented due to a resource failure that needs to be observed while cannot be observed by the added monitors, leading to the modification of the arcs added in the first step. Consequently, a robust controlled system is acquired. Finally, examples are presented to demonstrate the proposed method.

An elementary siphon-based deadlock control algorithm with maximally reachable number to cope with deadlock problems in ordinary Petri nets

Elementary siphons play an important role in designing deadlock prevention policies for flexible manufacturing systems modeling by Petri nets. This article proposes a deadlock control algorithm wit...

A suboptimal deadlock control policy for designing non-blocking supervisors in flexible manufacturing systems

This work aims to resolve deadlock problems in flexible manufacturing systems. A novel deadlock control policy in the frame of Petri nets formalism is presented for a class of generalized Petri nets, namely G-systems, which can usually model assembly and disassembly operations of multiple resource acquisition. Based on the concept of elementary siphons, all strict minimal siphons (SMS) in an uncontrolled net system are first divided into elementary siphons and dependent ones. After that, a set of linear inequality constraints expressed by state vectors can be formalized for elementary siphons. After being modified by utilizing the conjunctive/disjunctive resources upstream neighborhood policy, a set of generalized mutual exclusion constraints expressed by marking vectors can be obtained. Then, the additional monitors are only designed for elementary siphons, whose control depth variables can be obtained by solving a linear programming problem. As a result, the controllability of dependent ones can be ensured by properly supervising its elementary siphons. Finally, all strict minimal siphons are max′-controlled and no insufficiently marked siphon is generated, which indicates that the sequential resources are allocated reasonably to guarantee the absence of deadlock states. The proposed method can usually lead to a near-optimal non-blocking supervisor with simple structure. A G-system example prone to deadlocks is used to illustrate the applicability and the effectiveness of the proposed method.

Update to "Extraction of elementary siphons in a class of generalized Petri nets using graph theory" [Engineering Computations (2014) 31(2)331-352

Purpose The purpose of this paper is to correct some mistakes in recently published paper (Hou, Y.F., Li, Z.W., Zhao, M., and Liu, D. (2014) “Extraction of elementary siphons in a class of generalized Petri nets using graph theory”, Engineering Computations, Vol.31, No.2, pp.331-352). Design/methodology/approach In (Hou et al., 2014), based on the concepts of initial resource weighted digraphs and restricted subgraphs, a structurally simple liveness-enforcing supervisor for WS3PR was designed. To demonstrate the effectiveness and applicability of the proposed method, a flexible manufacturing system (FMS) example was presented. However, there are some mistakes in the considered example. The derived monitors were incorrect, which caused the result that the final controlled net system is not live. Findings In order to correct the errors in (Hou et al., 2014), a liveness-enforcing Petri nets supervisor with revised monitors for the considered example was redesigned by applying the method in (Hou et al., 2014). Originality/value This paper corrected the mistakes in (Hou et al., 2014). Consequently, a liveness-enforcing Petri net supervisor is redesigned.

An Efficient Siphon-Based Deadlock Prevention Policy for a Class of Generalized Petri Nets

We propose a new deadlock prevention policy for an important class of resource allocation systems (RASs) that appear in the modeling of flexible manufacturing systems (FMSs). The model of this class in terms of generalized Petri nets is, namely, S4PR. On the basis of recent structural analysis results related to the elementary siphons in generalized Petri nets on one hand and an efficient deadlock avoidance policy proposed for the class of conjunctive/disjunctive (C/D) RASs on the other hand, we show how one can generate monitors to be added to a net system such that all its strict minimal siphons aremax′-controlled and no insufficiently marked siphon is generated. Thereby, a new, simple, and more permissive liveness-enforcing supervisor synthesis method for S4PR is established.

Utilization Elementary Siphons of Petri Net to Solved Deadloaks in Flexible Manufacturing Systems

Utilization Elementary Siphons of Petri Net to Solved Deadloaks in Flexible Manufacturing Systems

Flexible Manufacturing System Design and Optimization using Petri Net-based Elementary Siphons

computer simulation system, which is based-siphon Petri net for control of concurrent processes of the reusable resources, that is mainly aimed to provide guidelines for control and management engineering of flexible manufacturing systems (FMSs) is presented in this work. We present an important technique for the analysis of siphon Petri net (PN) based on structural analysis, control, and simulation of the reachability tree used PN-tool with MATLAB. We are representing the deadlock prevention problem, which can be solved using the concept of Petri nets based siphons. Structural deadlock prevention is presenting for supervisors a class of FMS in simulating the system behaviour and elementary siphons control rule's inference. We are recovering the satiation of the liveness system from the consequence of analysis net by adding control place (monitor). Our experiment, a few monitors is added to the net for every minimal siphon taken from the consequence of the siphon in order to be liveness (i.e. deadlock-freeness), proposing extensions of the structural analysis of Petri nets, where deadlocks are regarding to the unmarked siphons. The siphon is recognized in the structural analysis of PN and can be used to control deadlocks in resource systems modelled.

A Petri Net Approach Based Elementary Siphons Supervisor for Flexible Manufacturing Systems

A Petri Net Approach Based Elementary Siphons Supervisor for Flexible Manufacturing Systems

Controllability of weakly dependent siphons under elementary-siphon control

Monitors are added to problematic siphons to avoid deadlocks. Li and Zhou (2004, 2006a,b, 2008a,b,c) add monitors to elementary siphons only while controlling the rest-dependent siphons to save on costs. After failing a marking linear inequality (MLI) test, Li and Zhou perform a linear integer programming (LIP) test (NP-hard). We proposed a new MLI test earlier to avoid the LIP and extended it to systems of simple sequential processes with general resource requirements (S3PGR2) for strongly dependent siphons (SDSs). The control policy for weakly dependent siphons (WDSs) is rather conservative due to some negative terms in the MLI. This paper shows that WDS and SDS have the same controllability (i.e. MLI). As a result, the control for WDS need no longer be that conservative. We also develop an optimization (by redundancy elimination) of the computation required for the LIP test to ensure deadlock prevention of systems of simple sequential processes with resources (S3PR). A favourable result for this policy is that any n-dependent ( n > 2) WDS (similar to SDS) needs no monitor and hence the complexity for synthesizing a controller becomes polynomial. Application to a slight variant of a well-known benchmark is illustrated.

Elementary Siphons of Petri Nets and Deadlock Control in FMS

For responsiveness, in the Petri nets theory framework deadlock prevention policies based elementary siphons control are often utilized to deal with deadlocks caused by the sharing of resources in flexible manufacturing system (FMS) which is developing the theory of efficient strict minimal siphons of an S3PR. Analyzer of Petri net models and their P-invariant analysis, and deadlock control are presented as tools for modelling, efficiency structure analysis, control, and investigation of the FMSs when different policies can be implemented for the deadlock prevention. We are to show an effective deadlock prevention policy of a special class of Petri nets namely elementary siphons. As well, both structural analysis and reachability graph analysis and simulation are used for analysis and control of Petri nets. This work is successfully applied Petri nets to deadlock analysis using the concept of elementary siphons, for design of supervisors of some supervisory control problems of FMS and simulation of Petri net tool with MATLAB.

Improvement on ‘structure of weakly 2-dependent siphons’

Li and Zhou propose simpler Petri net controllers based on the concept of elementary siphons (generally much smaller than the set of all strict minimum siphons (SMSs) in large Petri nets) to minimise the addition of control places. SMSs can be divided into two groups: elementary and dependant; characteristic T-vectors of the latter are linear combinations of that of the former. A T-vector η is associated with each siphon S such that η(i) is the number of tokens gained in or lost from S by firing transition ti once. A dependent siphon S0 strongly depends on elementary siphons S1, S2, … , Sk if η0 = a1η1 + a2η2 + ⋅⋅⋅ + akηk with all ai (i = 1, 2, 3, … , k) positive. S0 is a weakly dependent siphon if some ai is negative. The T-vectors (resp. number) for elementary siphons are mutually independent (linear to the size of the net). In an earlier paper, we show that there exists a third siphon S3 such that ηβ = η1 + η2 - η3. This equation (called η relationship) plays an important role for optimal control of weakly dependent siphons. However, it assumes that all above S span between exactly two processes. For a well-known benchmark, however, most dependent siphons span more than two processes. This paper improves by removing this restriction and shows that ηβ = η1 + η2 - η3 holds as long as S1∩S2 is another emptiable siphon.

Elementary‐Siphon‐Based Control Policy for Flexible Manufacturing Systems with Partial Observability and Controllability of Transitions

AbstractElementary siphons have been extensively studied to solve deadlock problems in Petri nets. However, most of the existing approaches based on elementary siphons can deal with the Petri nets in which all the transitions are supposed to be controllable and observable. This paper develops an elementary‐siphon‐based deadlock control policy for flexible manufacturing systems with uncontrollable and unobservable transitions. For elementary siphons, their complementary sets are successively expanded by considering unobservability and uncontrollability of transitions. Monitors are designed for the expanded complementary sets. The proposed method permits that there are arcs from monitors to a set of special uncontrollable transitions. Moreover, we show that the dependent siphons are always marked in the controlled system that is derived from the proposed method when there exist uncontrollable and unobservable transitions.

Extraction of elementary siphons in a class of generalized Petri nets using graph theory

Purpose – Siphon-based deadlock control in a flexible manufacturing system (FMS) suffers from the problems of computational and structural complexity since the number of siphons grows exponentially with respect to the size of its Petri net model. In order to reduce structural complexity of a supervisor, a set of elementary siphons derived from all strict minimal siphons (SMS) is explicitly controlled. The purpose of this paper is through fully investigating the structure of a class of generalized Petri nets, WS3PR, to compute all SMS and a compact set of elementary siphons. Design/methodology/approach – Based on graph theory, the concepts of initial resource weighted digraphs and restricted subgraphs are proposed. Moreover, the concept of augmented siphons is proposed to extend the application of elementary siphons theory for WS3PR. Consequently, the set of elementary siphons obtained by the proposed method is more compact and well suits for WS3PR. Findings – In order to demonstrate the proposed method, an FMS example is presented. All SMS and elementary siphons can be derived from initial resource weighted digraphs. Compared with those obtained by the method in Li and Zhou, the presented method is more effective to design a structural simple liveness-enforcing supervisor for WS3PR. Originality/value – This work presents an effective method of computing SMS and elementary siphons for WS3PR. Monitors are added for the elementary siphons only, and the controllability of every dependent siphon is ensured by properly supervising its elementary ones. A same set of elementary siphons can be admitted by different WS3PR with isomorphic structures.

Extended Elementary Siphons and Their Application to Liveness‐Enforcement of Generalized Petri Nets

AbstractAs a significant structural object, siphons are extensively employed to implement a large number of deadlock prevention and liveness‐enforcing methods for flexible manufacturing systems modeled by Petri nets. By linear combinations, a set of elementary siphons is chosen from all strict minimal ones to be controlled and thus the structural complexity of a supervisor is greatly reduced. The concept of elementary siphons is originally proposed for ordinary Petri nets. When applied to generalized Petri nets, their selection and controllability require an additional study. In this work, the concept of augmented siphons is proposed to extend the application of the elementary ones to a class of generalized Petri nets, GLS3PR. Based on graph theory, a siphon extraction algorithm is developed to obtain all strict minimal siphons, from which augmented elementary ones are computed. In addition, the controllability conditions of dependent siphons are developed. Through fully investigating the net structure, especially weight information, the set of augmented elementary siphons is more compact and well suits for generalized Petri net models under consideration. Some examples are used to illustrate the proposed method.

Structure of weakly 2-dependent siphons

Deadlocks arising from insufficiently marked siphons in flexible manufacturing systems can be controlled by adding monitors to each siphon – too many for large systems. Li and Zhou add monitors to elementary siphons only while controlling the rest of (called dependent) siphons by adjusting control depth variables of elementary siphons. Only a linear number of monitors are required. The control of weakly dependent siphons (WDSs) is rather conservative since only positive terms were considered. The structure for strongly dependent siphons (SDSs) has been studied earlier. Based on this structure, the optimal sequence of adding monitors has been discovered earlier. Better controllability has been discovered to achieve faster and more permissive control. The results have been extended earlier to S3PGR2 (systems of simple sequential processes with general resource requirements). This paper explores the structures for WDSs, which, as found in this paper, involve elementary resource circuits interconnecting at more than (for SDSs, exactly) one resource place. This saves the time to compute compound siphons, their complementary sets and T-characteristic vectors. Also it allows us (1) to improve the controllability of WDSs and control siphons and (2) to avoid the time to find independent vectors for elementary siphons. We propose a sufficient and necessary test for adjusting control depth variables in S3PR (systems of simple sequential processes with resources) to avoid the sufficient-only time-consuming linear integer programming test (LIP) (Nondeterministic Polynomial (NP) time complete problem) required previously for some cases.

Controllability of Weakly Dependent Siphons under Elementary-Siphon Control

Monitors are added upon problematic siphons to avoid deadlocks. Li and Zhou add monitors to elementary siphons only while controlling the rest dependent siphons to save cost. After failing a Marking Linear Inequality (MLI) test, they perform a Linear Integer Programming (LIP) test (NP-hard). We proposed a new MLI test earlier to avoid the LIP and extended it to S3PGR2 (systems of simple sequential processes with general resource requirements) for strongly dependent siphons (SDS). The control policy for weakly dependent siphons (WDS) is rather conservative due to some negative terms in the MLI. This paper shows that WDS and SDS have the same controllability (i.e., MLI). As a result, the control for WDS needs no longer be that conservative. We also develop an optimization (by redundancy elimination) of the computation required for LIP test to ensure deadlock prevention of S3PR (Systems of Simple Sequential Processes with Resources). A favorable result for this policy is that any n-dependent (n>2) WDS (similar to SDS) needs no monitor and hence the complexity for synthesizing a controller becomes polynomial.

Controllability of control and mixture weakly dependent siphons in S3PR

Deadlocks in a flexible manufacturing system modelled by Petri nets arise from insufficiently marked siphons. Monitors are added to control these siphons to avoid deadlocks rendering the system too complicated since the total number of monitors grows exponentially. Li and Zhou propose to add monitors only to elementary siphons while controlling the other (strongly or weakly) dependent siphons by adjusting control depth variables. To avoid generating new siphons, the control arcs are ended at source transitions of process nets. This disturbs the original model more and hence loses more live states. Negative terms in the controllability make the control policy for weakly dependent siphons rather conservative. We studied earlier on the controllability of strongly dependent siphons and proposed to add monitors in the order of basic, compound, control, partial mixture and full mixture (strongly dependent) siphons to reduce the number of mixed integer programming iterations and redundant monitors. This article further investigates the controllability of siphons derived from weakly 2-compound siphons. We discover that the controllability for weakly and strongly compound siphons is similar. It no longer holds for control and mixture siphons. Some control and mixture siphons, derived from strongly 2-compound siphons are not redundant – no longer so for those derived from weakly 2-compound siphons; that is all control and mixture siphons are redundant. They do not need to be the conservative one as proposed by Li and Zhou. Thus, we can adopt the maximally permissive control policy even though new siphons are generated.

Deadlock prevention policy for a class of petri nets based on complementary places and elementary siphons

For a class of Petri nets called Systems of Simple Sequential Processes with Resources $$(\mathrm{{S}}^{3}\mathrm{{PR}})$$ ( S 3 PR ) , this paper proposes a sufficient condition under which there exists a complementary-place supervisor to enforce their liveness. Moreover, an algorithm is proposed to design liveness-enforcing supervisors based on complementary places and elementary siphons. The significance of the proposed policy lies in its design simplicity. A flexible manufacturing system example shows that in some cases, the proposed policy can obtain a structurally simpler supervisor with 99.9 % maximal permissive behavior.