An Algebraic Approach to Timed Petri Nets with Applications to Communication Networks -- Extended Version (original) (raw)

Optimization Techniques

Petri-nets have been found an adequate tool to describe the state transitions of rather complicated systems (as asynchronous systems). Many cocrdinatio~ problems have been modeled successfully with them. However, these models need more information in order to study some quantitative aspects as utilisation rates , delays ..... which are of main interest for a practical point of view. 8o, we are interested in more sophisticated models called Timed Petri-Nets (TPN) in which the time dimension is introduced. In this paper, we first give a formal and rigorous definition of the execution of a TPN ; then, we give some general results on what we call "a program" ; finally, we extend Ramachandani previous results on strongly periodic event graphs to general Petri-nets.

Timed-Arc Petri Nets vs. Networks of Timed Automata

Lecture Notes in Computer Science, 2005

We establish mutual translations between the classes of 1safe timed-arc Petri nets (and its extension with testing arcs) and networks of timed automata (and its subclass where every clock used in the guard has to be reset). The presented translations are very tight (up to isomorphism of labelled transition systems with time). This provides a convenient characterization from the theoretical point of view but is not always satisfactory from the practical point of view because of the possible non-polynomial blow up in the size (in the direction from automata to nets). Hence we relax the isomorphism requirement and provide efficient (polynomial time) reductions between networks of timed automata and 1-safe timed-arc Petri nets preserving the answer to the reachability question. This makes our techniques suitable for automatic translation into a format required by tools like UPPAAL and KRONOS. A direct corollary of the presented reductions is a new PSPACE-completeness result for reachability in 1-safe timed-arc Petri nets, reusing the region/zone techniques already developed for timed automata.

Timed Processes of Interval-Timed Petri Nets

HAL (Le Centre pour la Communication Scientifique Directe), 2016

In this paper we use partial order semantics to express the truly concurrent behaviour of interval-timed Petri nets (ITPNs) in their most general setting, i.e. with autoconcurrency and zero duration, as studied with its standard maximal step semantics in [8]. First we introduce the notion of timed processes for ITPNs inductively. Then we investigate if the equivalence of inductive and axiomatic process semantics-true for classical Petri nets-could hold for ITPNs too. We will see that the notions of independence and immediate firing obligation seem to be antagonistic ones, and that local axioms, adequate to define processes of classical Petri nets, are not sufficient to caracterize timed Processes of IITPNs. We propose several original "global" axioms which reveal to be an effective solution. Thus we yield finally a full axiomatic definition of timed processes for ITPNs.

Full Axiomatisation of Timed Processes of Interval-Timed Petri Nets

Fundamenta Informaticae, 2018

Timed Mobility in process algebra and Petri nets

The Journal of Logic and Algebraic Programming, 2011

We present a process algebra called TiMo in which timeouts of interactions and adaptable migrations in a distributed environment with explicit locations can be specified. Timing constraints allow to control the communication between co-located mobile processes, and a migration action with variable destination supports flexible movement from one location to another. The model of time is based on local clocks rather than a global clock. We provide a structural translation of TiMo into behaviourally equivalent high level timed Petri nets. As a result, we obtain a formal net semantics for timed interaction and migration which is both structural and allows one to deal directly with concurrency and causality.

Time Process Equivalences for Time Petri Nets

2014

In the core of every theory of systems lies a notion of equivalence between systems: it indicates which particular aspects of systems behaviors are considered to be observable. In concurrency theory, a variety of observational equivalences has been promoted, and the relationships between them have been quite wellunderstood. In order to investigate the performance of systems (e.g. the maximal time used for the execution of certain activities and average waiting time for certain requests), many time extensions have been de ned for a non-interleaving model of Petri nets. On the other hand, there are few mentions of a fusion of timing and partial order semantics, in the Petri net literature. In [9], processes of timed Petri nets (under the asap hypothesis) have been de ned by an algebra of the so-called weighted pomsets. The paper [8] has provided and compared timed step sequence and timed process semantics for timed Petri nets. A method to compute all valid timings for a causal net pro...

Comparing the Expressiveness of Timed Automata and Timed Extensions of Petri Nets

Lecture Notes in Computer Science

Time dependant models have been intensively studied for many reasons, among others because of their applications in software verification and due to the development of embedded platforms where reliability and safety depend to a large extent on the time features. Many of the time dependant models were suggested as real-time extensions of several well-known untimed models. The most studied formalisms include Networks of Timed Automata which extend the model of communicating finite-state machines with a finite number of real-valued clocks, and timed extensions of Petri nets where the added time constructs include e.g. time intervals that are assigned to the transitions (Time Petri Nets) or to the arcs (Timed-Arc Petri Nets). In this paper, we shall semiformally introduce these models, discuss their strengths and weaknesses, and provide an overview of the known results about the relationships among the models.

Towards a Notion of Distributed Time for Petri Nets

Lecture Notes in Computer Science, 2001

We set the ground for research on a timed extension of Petri nets where time parameters are associated with tokens and arcs carry constraints that qualify the age of tokens required for enabling. The novelty is that, rather than a single global clock, we use a set of unrelated clocks-possibly one per place-allowing a local timing as well as distributed time synchronisation. We give a formal definition of the model and investigate properties of local versus global timing, including decidability issues and notions of processes of the respective models.

Formalization of petri nets with clocks

Journal of Computational Methods in Sciences and Engineering, 2005

PN (PN) are tools for the analysis and design of concurrent systems. There is a formal theory, which supports PN. An extension of PN is Petri Nets with Clocks (PNwC). PNwC are useful to model systems with temporal requirements via specification of clocks, using temporal invariants for the places and temporal conditions in the transitions. Using invariants in places allows the specifications of hard deadlines constrains (upper bound constrains): when a deadline is reached the progress of time is blocked by the invariant and the action becomes urgent. An algorithm for the analysis of a PNwC has been proposed in [1]. The algorithm is oriented to the verification and correction of errors in the modelling of the time variable. The algorithm generates information about temporal unreachable states and process deadlocks with temporal blocks. Also, it corrects places invariants and transitions conditions. We present here a formalism for PNwC based on Timed Graphs. The analysis algorithm is presented here using the formalism. We show here how Petri Net theory can be joined with Timed Graph theory to construct a formalism, which supports a tool for the analysis of models of concurrent process with real time specification.

An Algebraic Approach to Timed Petri Nets with Applications to Communication Networks -- Extended Version (original) (raw)

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