numerous algorithms have been proposed to solve the shortest-pathproblem; many of them consider a single-mode network and crispcosts. other attempts have addressed the problem of fuzzy costs ina single-mode network, the so-called fuzzy shortest-path problem(fspp). the main contribution of the present work is to solve theoptimum path problem in a multimodal transportation network, inwhich the co...

Abstract: The (max,+) algebra is usually used to model Timed event graph. In this paper, we show that P-time event graphs which extend Timed event graph, can be modelled using maximum, minimum and addition operations. The result is a new model called interval descriptor system where the time evolution is not strictly deterministic but belongs to intervals. The cycle-time vector allows us to to ...

This chapter deals with the control of discrete-event systems which admit linear models in dioids (or idempotent semirings), introduced in the previous chapter (see also the books [1, 19]). These systems are characterized by synchronization and delay phenomena. Their modeling is focused on the evaluation of the occurrence dates of events. The outputs correspond to the occurrence dates of events...

This paper deals with feedback controller synthesis for timed event graphs, where the number of initial tokens and time delays are only known to belong to intervals. We discuss here the existence and the computation of a robust controller set for uncertain systems that can be described by parametric models, the unknown parameters of which are assumed to vary between known bounds. Each controlle...

Continuous Event Graphs (CEGs), a subclass of Continuous Petri Nets, are defined as the limiting cases of timed event graphs and Timed Event Multigraphs. A set of dioid algebraic linear equations will be inferred as a novel method of analyzing a special class of CEG, if treated the cumulated token consumed by transitions as state-variables, endowed the monotone nondecreasing functions pointwise...

In this paper we propose a notion of weak bisimulation for a class of weighted automata with unobservable transitions where weights are taken from an idempotent semiring. In particular the (max/+), (min/+) or (max/min) dioid are considered. The proposed bisimulation is a natural extension of Milner’s well known weak bisimulation for untimed automata (i. e., weighted automata over the boolean se...

In this paper we introduce extensions of Kleinberg’s Hubs & Authorities (HITS) algorithm to calculate the influence of nodes in a network whose adjacency matrix takes values over dioids, zerosumfree semirings with a natural order. We relate these extensions to both the Singular Value Problem and the Eigen Problem of matrices in these semirings. We show the original HITS algorithm to be a partic...