Max-plus algebra is a discrete algebraic system developed on the operations max () and plus src=image/13420822_03.gif>), where are defined as addition multiplication in conventional algebra. This structure semi-ring with its elements being real numbers along ε=-∞ e=0. On other hand, synchronized event problem which an scheduled to meet deadline. There two aspects ...

The theory of linear systems in the max-plus algebra is developed for the analysis of discrete event systems. The timed event graphs are one of the tools used for modelling these systems, and their behaviour can be described by (max, plus )-linear equations. This paper proposes a control structure for a public transport system. We mainly based the research of this control on the Residuation the...

In this paper we give a survey of our research on the Extended Linear Complemen-tarity Problem (ELCP). First we discuss the link between the ELCP and other generalizations of the Linear Complementarity Problem, and we present an algorithm to nd all the solutions of an ELCP. Next we introduce the max-plus algebra and show how it can be used to model a certain class of discrete event systems. Fin...

asynchronous circuit, clock schedule verification, cycle time, fixed point, max-plus algebra, min-max function Recent progress in the timing analysis of digital circuits has involved the use of maximum and minimum timing constraints. We put forward the theory of min-max functions, a non-linear generalization of max-plus algebra, as the correct framework in which to study problems with mixed con...

The main purpose of this paper is to propose five programs in C for matrix computations and solving recurrent equations systems with entries in max plus algebra. 1

Model predictive control for max-plus-linear discrete event systems * B. De Schutter and T. van den Boom If you want to cite this report, please use the following reference instead: B. De Schutter and T. van den Boom, " Model predictive control for max-plus-linear discrete event systems, " The conventional model predictive control framework is extended and adapted to max-plus-linear systems, i....

This paper aims to unify and extend existing techniques for deriving upper bounds on the transient of max-plus matrix powers. To this aim, we introduce the concept of weak CSR expansions: A = CSR⊕B. We observe that most of the known bounds (implicitly) take the maximum of (i) a bound for the weak CSR expansion to hold, which does not depend on the values of the entries of the matrix but only on...

We survey and discuss upper bounds on the length of the transient phase of max-plus linear systems and sequences of max-plus matrix powers. In particular, we explain how to extend a result by Nachtigall to yield a new approach for proving such bounds and we state an asymptotic tightness result by using an example given by Hartmann and Arguelles.

A class of queueing networks which consist of single-server fork-join nodes with infinite buffers is examined to derive a representation of the network dynamics in terms of max-plus algebra. For the networks, we present a common dynamic state equation which relates the departure epochs of customers from the network nodes in an explicit vector form determined by a state transition matrix. We sho...