A sufficient condition for the liveness of weighted event graphs

Abstract

International audienceWeighted event graphs (in short WEG) are widely used to model industrial problems and embedded systems. In an optimization context, fast algorithms checking the liveness of a marked WEG must be developed. The purpose of this paper is to develop a sufficient condition of liveness of a WEG. We first show that any unitary WEG can be transformed into a graph in which the values of the arcs adjacent to any transition depend on the transition. Then, a simple sufficient condition of liveness can be expressed on this new graph and polynomially computed. This condition is shown to be necessary for a circuit with two transitions

Minimizing Place Capacities of Weighted Event Graphs for Enforcing Liveness

“…MWEG) G is normalized if there exists a vector Z ∈ N n such that, for every transition t i ∈ T, The proof of this theorem and a polynomial algorithm to perform this transformation are presented in Marchetti and Munier-Kordon (2004). However, we illustrate intuitively this transformation using the MWEG G = (T, P, M 0 ) pictured by Fig.…”

“…The question is: is it possible to compute for each place p of a given WEG G, a capacity M ( p) and an initial marking M 0 ( p) such that G is live, the number of tokens of any place p remains at anytime bounded by M ( p) and f (M ( p 1 ), · · · , M ( p m )) is minimum? We develop an original (to our best knowledge) polynomial algorithm solving exactly this problem based on a sufficient condition of liveness proved in Marchetti and Munier-Kordon (2004). This paper is structured as follows: Section 2 recalls basic concepts of WEG.…”

A polynomial algorithm for the computation of buffer capacities with throughput constraint for embedded system design

“…, Z n ) = 1. This assumption is not restrictive: if it is not true, it is proved in [23] that the integers Z i , t i ∈ T can be replaced by Z i gcd(Z 1 , . .…”

“…It has been proved in [23] that the initial marking M 0 (p) of any place p = (t i , t j ) may be replaced by…”

A Software Tool for Live-Lock Avoidance in Systems Modelled Using a Class of Petri NETS

“…Reveliotis et al [18] and Ghaffariet al [19] used the theory of regions to identify minimally restrictive LESPs forResource Allocation Systems. Marchetti et al [20] presented a polynomial time sufficient condition for liveness, for the class of Unitary Weighted Event Graphs. Ferrariniet al [21] compare the performance of a selection of deadlock avoidance policies inPN models of flexible manufacturing systems.…”