Liveness of an extended S3PR

Acta Polytechnica Hungarica, 2023

Correct allocation of resources in Automated Manufacturing Systems (AMS) is very important, especially in order to avoid deadlocks and their consequences. Petri Nets (PN) are frequently used for modeling AMS. S 3 PR (Systems of Simple Sequential Processes with Resources) model of Resource Allocation Systems (RAS) based on PN are defined, analyzed and controlled here. S 3 PR are modeled by Ordinary PN (OPN). After defining and creation of such models the deadlock prevention will be performed by two deadlock prevention methods, namely (i) the method based on elementary siphons, and (ii) the method based on preventing strict minimal siphons from being emptied in another way (by means of circuits, holders of resources and complementary siphons). For illustration, two practical examples will be introduced. Both approaches are very useful not only for reliable deadlockfree control of existing AMS, but also at design of new AMS of such kind.

… and Automation, 2005 …, 2005

A new method for the deadlock prevention problem in concurrent systems where a set of processes share a set of common resources in a conservative way is proposed. It can be applied to flexible manufacturing systems, modeled with Petri nets. In this paper, we present a set of important results related to the deadlock prevention problem in Ë È Ê nets. First, a liveness characterization is introduced, establishing how deadlocks can be studied in terms of circular waits. Second, we show how a circular wait situation corresponds to a particular marking related to a siphon of the Petri net model. Finally, this last characterization is used to obtain an iterative method that successively forbids deadlock related states, synthesizing the control necessary to ensure a final live behavior. The method can be implemented by means of the solutions of a set of integer linear programming problems.

IEEE Transactions on Robotics and Automation, 1995

In this paper we illustrate a compositional method for modeling the concurrent execution of working processes in flexible manufacturing systems (FMS) through a special class of Petri Nets that we call S 'PI?. In essence, this class is built from state machines sharing a set of places modeling the availability of system resources. The analysis of S ' P R leads us to characterize deadlock situations in terms of a zero marking for some structural objects called siphons. In order to prevent the system from deadlocks, we propose a policy for resource allocation based on the addition of new places to the net imposing restrictions that prevent the presence of unmarked siphons (direct cause of deadlocks). Finally, we present the application of this technique to a realistic FMS case.

IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans, 2004

A variety of important Petri net-based methods to prevent deadlocks arising in flexible manufacturing systems (FMS) are to add some control places and related arcs to strict minimal siphons (SMS) such that no siphon can be emptied. Since the number of minimal siphons grows in general exponentially with respect to a Petri net size, their disadvantages lie in that they often add too many additional places to the net, thereby making the resulting net model much more complex than the original one. This paper explores ways to minimize the new additions of places while achieving the same control purpose. It proposes for the first time the concept of elementary siphons that are a special class of siphons. The set of elementary siphons in a Petri net is generally a proper subset of the set of all SMS. Its smaller cardinality becomes evident in large Petri net models. This paper proves that by adding a control place for each elementary siphon to make sure that it is marked, deadlock can be successfully prevented. Compared with the existing methods, the new method requires a much smaller number of control places and, therefore, is suitable for large-scale Petri nets. An FMS example is used to illustrate the proposed concepts and policy, and show the significant advantage over the previous methods.

IET Control Theory & Applications, 2009

Deadlocks are a highly undesired situation in automated production systems including flexible manufacturing systems. Based on a Petri net formalism, a novel deadlock prevention policy is proposed for a class of Petri nets, S 3 PR, by using an MIP-based deadlock detection method and elementary siphons of Petri nets. Deadlock prevention is achieved by synthesising a set of monitors that are added to the plant net model. The concept of dominated transitions is proposed, to which the output arcs of the monitors are led. The monitors are computed according to a set of elementary siphons in a plant net model, which is found by using an established algorithm in the literature. When compared with the existing policies, the proposed method leads to a liveness-enforcing Petri net supervisor with a small number of monitors but more permissive behaviour. Examples are used to demonstrate the proposed method.

IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2015

Siphons are a kind of special structural objects in a Petri net, and plays a key role in synthesizing a live Petri net controller for flexible manufacturing systems. In order to obtain a small size Petri net controller, this paper introduces the concept of a controllable siphon basis. It then proves that a live Petri net controller can be established by adding a control place and related arcs to each strict minimal siphon (SMS) in a controllable siphon basis. The initial markings of control places are determined by an integer linear program. The number of control places in the obtained controllers is the same as the number of SMSs in the controllable siphon basis, while the latter is no more than that of the activity places in a Petri net model. An algorithm for constructing a controllable siphon basis is proposed, and a new deadlock prevention policy based on it is established. A few examples are provided to demonstrate the proposed concepts and policy and used to compare them with the state-of-the-art methods. Index Terms-Discrete event systems, flexible manufacturing systems, integer linear program (ILP), Petri nets. I. INTRODUCTION A FLEXIBLE manufacturing system (FMS) handles multiple concurrent flows of job processes that can make different products at the same time, and often exploits shared

Siphons are special structures of a Petri net. Their number grows exponentially with the net size. Hence, the traditional siphon-based deadlock control policies have two problems, that is, generating very structurally complex supervisory controllers and requiring intractable computation efforts. This paper intends to use the newly proposed concept, elementary siphons, and a mixed integer programming (MIP) method to design structurally simple supervisory controllers and reduce the computational burden. This method is applicable to a class of Petri nets, System of Simple Sequential Processes with Resources that can well model a wide class of discrete manufacturing systems. Siphons are divided into elementary and dependent ones. The proposed policy consists of three stages: siphon control, control-induced siphon control, and the elimination of control-redundant monitors. First, a monitor (control place) is added for each elementary siphon such that it is invariant-controlled. Because of the addition of monitors to the plant model, control-induced siphons are possibly generated in the augmented net. Next, monitors are added to make control-induced siphons in the augmented net always marked sufficiently without generating new problematic siphons. A MIP technique is used to guarantee that no siphon is insufficiently marked. Finally, we systematically remove control-redundant monitors. Compared with previous work in the literature, the deadlock prevention policy developed in this paper can lead to a structurally simple liveness-enforcing Petri net supervisor with more permissive behaviour by adding only a small number of monitors and arcs. Moreover, complete siphon enumeration is avoided. A manufacturing system example is utilised to illustrate the proposed methods.

The International Journal of Advanced Manufacturing Technology, 2004

In a flexible manufacturing system (FMS) with multiple products, deadlocks can arise due to limited shared resources, such as machines, robots, buffers, fixtures etc. The development of efficient deadlock prevention policies, which can optimise the use of system resources, while preventing deadlocks from occurring, has long been an important issue to be addressed. In [1], an optimal deadlock prevention policy was proposed, based on the use of reachability graph (RG) analysis of the Petri net model (PNM) of a given FMS and the synthesis of a set of new net elements, namely places with initial marking and related arcs, to be added to the PNM, using the theory of regions. The policy proposed in [1] is optimal in the sense that it allows the maximal use of resources in the system according to the production requirements. For very big PNMs, the reachability graph of the PNMs becomes very large and the necessary computations to obtain an optimal deadlock prevention policy become more difficult. In this paper, we propose the use of the Petri net reduction approach to simplify very big PNMs so as to make necessary calculations easily in order to obtain an optimal deadlock prevention policy for FMSs. An example is provided for illustration.

Information Sciences, 2017

The International Journal of Advanced Manufacturing Technology, 2009

In this paper a novel policy is proposed to solve the deadlock problem in a class of flexible manufacturing systems based on the notion that each shared buffer is partitioned into parts to store different types of products, respectively. A subclass of Petri nets called resource-shared net with buffers (RSNB) is defined. An RSNB is constructed by synthesizing some marked graphs, and each marked graph can model the process of manufacturing one type of product. RSNB cannot only model the concurrent execution of manufacturing processes, but also ensure that the modeled system is live. The process of constructing RSNB is described in detail, and a minimal siphon based necessary and sufficient condition is provided to characterize the liveness of RSNB.