MuDer Jeng

Deadlock prevention policy based on Petri nets and siphons

This paper presents a deadlock prevention method for a class of flexible manufacturing systems where deadlocks are caused by unmarked siphons in their Petri net models. This method is an iterative approach consisting of two main stages. At each iteration, a fast deadlock detection technique developed by mixed integer programming is used to find an unmarked maximal siphon. An algorithm is formalized that can efficiently obtain an unmarked minimal siphon from the maximal siphon. The first stage, called siphons control, of the proposed method is to add, for each unmarked minimal siphons, a control place to the original net with its output arcs to the sink transitions of the minimal siphon. The objective is to prevent a minimal siphon from being unmarked. The second stage, called augmented siphons control, is to add a control place to the modified net with its output arcs to the source transitions of the resultant net if the resource places are removed. The second stage is required since adding control places in the first stage may create new unmarked siphons. In addition, the second stage assures that there are no new unmarked siphons generated. The relation of the proposed method and the liveness and reversibility of the controlled net have been obtained. Finally, manufacturing examples are presented to illustrate the method and to allow comparison with earlier methods.

A Maximally Permissive Deadlock Prevention Policy for FMS Based on Petri Net Siphon Control and the Theory of Regions

This paper addresses the deadlock problems in flexible manufacturing systems (FMS) by using a Petri net siphon control method and the theory of regions. The proposed policy consists of two stages. The first one, called siphons control, is to add, for every siphon that we identify, a monitor to the original net model such that it is optimally invariant controlled. In the second stage, the theory of regions is utilized to derive the net supervisors such that deadlocks can be prevented. The first-stage work significantly lowers the computational cost compared with the approach where the theory of regions is used alone. An FMS example is presented to illustrate the technique. By varying the markings of given net structures, this paper shows its computational advantages.

A siphon-based deadlock prevention policy for flexible manufacturing systems

A siphon-based algorithm for deadlock prevention of a type of Petri nets called S3PMR, which is a subclass of S3PGR2, is presented in this correspondence. The proposed method is an iterative approach by adding two kinds of control places called ordinary control (OC) places and weighted control (WC) places to the original model to prevent siphons from being unmarked. An OC place with ordinary arcs, which optimally prevent a siphon from becoming unmarked, is employed whenever it is possible, and otherwise, the WC places that adopt a conservative policy of controlling the release of parts into the system are used. Furthermore, this algorithm is not only for the subclass Petri nets but also for S3PR, ES 3PR, S2LSPR, and S3PGR2 nets. The authors prove the liveness and reversibility of the controlled net, and hence establish the correctness of the deadlock prevention policy. Finally, numerical experiments indicate that the proposed policy appears to be more permissive than closely related approaches in the literature

Synthesis using resource control nets for modeling shared-resource systems

This paper proposes a general approach to synthesize a class of Petri nets that model shared-resource automated manufacturing systems. The approach imposes minimal restrictions on the interactions among subsystems initially so that the modeler is given significant freedom. To modularize the synthesis procedure, a shared-resource system is formulated from the processes. i.e., the subsystems, that control the system resources and the interactions among the processes. For modeling the processes. Resource control nets are defined as the basic generic modules. Then, the system model is built by merging these modules through their common transitions and common transition subnets, which denote the interactions among the processes. The merged net is proven to be conservative and thus bounded. An algorithm is also developed to check two sufficient conditions for structural liveness of the net. This algorithm examines only the nets structure, and appears to be more efficient than state enumeration techniques such as the reachability graph method. >

A review of synthesis techniques for Petri nets with applications to automated manufacturing systems

Research results in both bottom-up and top-down synthesis techniques for Petri net modeling are reviewed. These methods can be adopted for representing parallel and distributed application environments such as automated manufacturing systems. Bottom-up techniques, consisting of the merging of places and sharing of simple elementary paths, have the advantage of ease of system description since the modeled subsystems usually have real-life correspondences. Nevertheless, with current bottom-up techniques, the synthesized system may not exhibit the same control properties as the subsystems. Top-down methods, including refinement of transitions and refinement of places, have the advantage of viewing the system globally, which may generate more structured designs. However, it is difficult to apply these methods to the environments with highly shared resources. Examples in the context of automated manufacturing systems are given to demonstrate application of these techniques. Petri net reduction techniques and their relationship to synthesis methods are discussed. >

Process nets with resources for manufacturing modeling and their analysis

This paper presents a new class of Petri nets, called process nets with resources (PNRs), for modeling manufacturing systems where only parts can interact with resources, and resources alone cannot interact with one another. PNRs properly include S/sup 3/PR, augmented marked graphs, and some subclasses of resource control net (RCN) merged nets and ERCN merged nets. As a result, PNRs can model far more complex manufacturing process flows and resource sharing than these nets. To construct a PNR, we first build a process net to specify the process flow for each part type. A process net is a consistent, conservative, strongly connected, and live Petri net that satisfies three conditions, including strong reversibility. Then resource places denoting the availability of resource types are added to the process nets. We generalize strong reversibility for PNRs in order to check a sufficient condition for reversibility of PNRs. It is shown that strong reversibility and reversibility of a PNR depends on the siphons. Liveness of a PNR can be verified by checking the potential firing ability of all transitions of each isolated process net, which is, informally speaking, a process net with all resources allocated to it. A manufacturing example is given to show the applicability of PNRs.

A Petri net synthesis theory for modeling flexible manufacturing systems

A theory that synthesizes Petri nets for modeling flexible manufacturing systems is presented. The theory adopts a bottom-up or modular-composition approach to construct net models. Each module is modeled as a resource control net (RCN), which represents a subsystem that controls a resource type in a flexible manufacturing system. Interactions among the modules are described as the common transition and transition subnets. The net obtained by merging the modules with two minimal restrictions is shown to be conservative and thus bounded. An algorithm is developed to detect two sufficient conditions for structural liveness of the net. The algorithm examines only the nets structure and the initial marking, and appears to be more efficient than state enumeration techniques such as the reachability tree method. In this paper, the sufficient conditions for liveness are shown to be related to some structural objects called siphons. To demonstrate the applicability of the theory, a flexible manufacturing system of a moderate size is modeled and analyzed using the proposed theory.

ERCN-merged nets and their analysis using siphons

This paper generalizes the modular approach proposed by Jeng and DiCesare (1995) for modeling manufacturing systems with shared resources. First, the-dynamic behavior of each resource is modeled separately using extended resource control nets (ERCNs). An important feature of ERCNs is their capability to express explicitly assembly operations and parallel processes, which is not possible with resource control nets. Interactions among the resources are then modeled through merging of common transitions and common transition subnets. This paper provides conditions, expressed in terms of siphons, under which reversibility and liveness of the integrated model are obtained. Relations between siphons, circular structure and circular-wait are formally established.

Analysis of modularly composed nets by siphons

This paper uses siphons to analyze the class of Petri nets constructed by a modular approach by Jeng and DiCesare (1995) for modeling manufacturing systems with shared resources. A resource point of view is taken. First the behavior of each resource is modeled using resource control nets, strongly connected state machines with one place being marked initially. Interactions among the resources are modeled through merging of common transition subnets. This paper provides conditions, expressed in terms of siphons, under which reversibility and liveness of the integrated model are obtained. Relations between siphons and circular-wait are formally established. Superiority of the siphon-based analysis over a previous analysis using circular wait is shown.

A deadlock prevention policy for flexible manufacturing systems using siphons

We present a new deadlock prevention algorithm for a class Petri nets. A new class of net that is extended from S/sup 3/PR, called ES/sup 3/PR, where deadlocks are related to unmarked siphons. This method is an iterative approach by adding two kinds of control places, called the ordinary control place and weighted control place, to the original model to prevent siphons from being unmarked. We obtained the relation of the algorithm, liveness and reversibility of the controlled net. Finally, a flexible manufacturing example is presented for illustrating the method.