In this paper, an optimal deadlock prevention policy for flexible manufacturing systems (FMSs) is proposed. In an FMS, deadlocks can arise because of a limited number of shared resources, i.e. machines, robots, buffers, fixtures etc. Deadlock is a highly undesirable situation, where each of a set of two or more jobs keeps waiting indefinitely for the other jobs in the set to release resources. The proposed optimal deadlock prevention policy is based on the use of reachability graph analysis of a 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, which is a formal synthesis technique to derive Petri nets from automaton-based models. The policy proposed is optimal in the sense that it allows the maximal use of resources in the system according to the production requirements. Two examples are provided for illustration.

An Optimal Deadlock Prevention Policy for Flexible Manufacturing Systems Using Petri Net Models with Resources and the Theory of Regions

ion, however, has a meaningful interpretation. To give an example, consider the fragment of a net in Figure 2.13a. Intuitively the abstraction in 2.4 Refinement and Composition 21 Figure 2.13d has a corresponding behaviour ("a token is passed through"). Figure 2.13d is also an abstraction of Figure 2.13b, but now the behaviour is different. In Figure 2.13d a token can pass, but not so in Figure 2.13b. Note that the set Y to be abstracted is not necessarily connected as a subgraph. However, Figure 2.13d can be interpreted as a merge of two places. This operation is called a fusion of places or place fusion. It will be used in Part II of this book to create larger nets from smaller ones. This kind of abstraction will be represented graphically as shown in Figure 2.13c. The dual situation for a transition-bordered set is shown in Figures 2.13e-h. Thus Figures 2.13f, g and h describe a fusion of transitions or transition fusion. -1 -I

Petri nets for systems engineering

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.

The use of the Petri net reduction approach for an optimal deadlock prevention policy for flexible manufacturing systems

This paper shows how two of the most important analysis methods for Petri nets can be performed in a modular way. We illustrate our techniques by means of modular Place/Transitions nets (modular PT-nets) in which the individual modules interact via shared places and shared transitions. For place invariants we show that it is possible to construct invariants of the total modular PT-net from invariants of the individual modules. For state spaces, we show that it is possible to decide behavioural properties of the modular PT-net from state spaces of the individual modules plus a synchronization graph, without unfolding to the ordinary state space. The generalization of our techniques to high-level Petri nets is rather straightforward.

Modular Analysis of Petri Nets

We present timing constraint Petri nets (or TCPN's for short) and describe how to use them to model a real-time system specification and determine whether the specification is schedulable with respect to imposed timing constraints. The strength of TCPN's over other time-related Petri nets is in the modeling and analysis of conflict structures. Schedulability analysis is conducted in three steps: specification modeling, reachability simulation, and timing analysis. First, we model a real-time system by transforming its system specification along with its imposed timing constraints into a TCPN; we call this net N/sub s/. Then we simulate the reachability of N/sub s/ to verify whether a marking, M/sub n/, is reachable from an initial marking, M/sub o/. It is important to note that a reachable marking in Petri nets is not necessarily reachable in TCPN's due to the imposed timing constraints, Therefore, in the timing analysis step, a reachable marking M/sub n/, found in the reachability simulation step is analyzed to verify whether M/sub n/, is reachable with the timing constraints. M/sub n/ is said to be reachable in the TCPN's if and only if we can find at least one firing sequence /spl sigma/ so that all transitions in /spl sigma/ are strongly schedulable with respect to M/sub o/ under the timing constraints. If such M/sub n/ can be found, then we can assert that the specification is schedulable under the imposed timing constraints, otherwise the system specification needs to be modified or the timing constraints need to be relaxed. We also present a synthesis method for determining the best approximation of the earliest fire beginning time (EFBT) and the latest fire ending time (LFET) of each strongly schedulable transition. >

Timing constraint Petri nets and their application to schedulability analysis of real-time system specifications

Petri nets have been proposed as a promising tool for modeling and analyzing concurrent-software systems such as Ada programs and communication protocol software. Among analysis techniques available for Petri nets, the most general approach is to generate all possible states (markings) of the system in a form of a so-called reachability graph. However, this conventional reachability graph approach is inefficient or intractable, even for a bounded Petri net, due to state explosion in many practical applications. To cope with this problem, this paper proposes a method for constructing a hierarchically organized state space called the hierarchical reachability graph (HRG). Using the HRG, we obtain necessary and sufficient conditions for reachability and deadlock, as well as algorithms to test whether a given state or marking is reachable from the initial state and whether there is a deadlock state (a state with no successor states). >

M. Notomi

Papers

Hierarchical reachability graph of bounded Petri nets for concurrent-software analysis