More than sixteen years after the beginning of a linear theory for certain discrete event systems in which max-plus algebra and similar algebraic tools play a central role, this paper attempts to summarize some of the main achievements in an informal style based on examples. By comparison with classical linear system theory, there are areas which are practically untouched, mostly because the co...

Ultradiscretization with negative values is a long-standing problem and several attempts have been made to solve it. Among others, we focus on the symmetrized max-plus algebra, with which we ultradiscretize the discrete sine-Gordon equation. Another ultradiscretization of the discrete sine-Gordon equation has already been proposed by previous studies, but the equation and the solutions obtained...

In this paper we explore computing max-plus algebra operations and discrete event simulations on parallel hierarchal heterogeneous platforms. When performing such tasks on heterogeneous platforms parameters such as the total volume of communication and the top-level data partitioning strategy must be carefully taken into account. Choice of the partitioning strategy is shown to greatly affect th...

Abstract. This paper proposes an approach to monitoring and scheduling methods for repetitive MIMO-FIFO DESs. We use max-plus algebra for modeling and formulation, known as an effective approach for controller design for this type of system. Because a certain type of linear equations in max-plus algebra can represent the system’s behavior, the principal concerns in past researches were how to s...

This research aims to accelerate the computation of the Kleene star in max-plus algebra using CUDA technology on graphics processing units (GPUs). The target module is the Kleene star of a weighted adjacency matrix for directed acyclic graph (DAGs) which plays an essential role in calculating the earliest and/or latest schedule for a class of discrete event systems. In recent NVIDIA GPU cards, ...

This paper establishes a link between three areas, namely Max-Plus Linear System Theory as used for dealing with certain classes of discrete event systems, Network Calculus for establishing time bounds in communication networks, and real-time scheduling. In particular, it is shown that important results from scheduling theory can be easily derived and unified using Max-Plus Algebra. Based on th...

Max-plus-linear (MPL) systems are a class of discrete-event systems that can be described by models that are “linear” in the max-plus algebra. MPL systems arise in the context of e.g. manufacturing systems, telecommunication networks, railway networks, and parallel computing. We derive a receding horizon control scheme for MPL systems that guarantees a priori stability (in the sense of boundedn...

Stochastic max-plus linear systems, i.e., perturbed systems that are linear in the max-plus algebra, belong to a special class of discrete-event systems that consists of systems with synchronization but no choice. In this paper, we study the identification problem for such systems, considering two different approaches. One approach is based on exact computation of the expected values and consis...

Discrete-event systems with synchronization but no concurrency can be described by models that are “linear” in the max-plus algebra, and they are called max-plus-linear (MPL) systems. Examples of MPL systems often arise in the context of manufacturing systems, telecommunication networks, railway networks, parallel computing, etc. In this paper we provide a solution to a finite-horizon model pre...

The statistical leverage scores of a complex matrix A ∈ Cn×d record the degree of alignment between col(A) and the coordinate axes in Cn. These score are used in random sampling algorithms for solving certain numerical linear algebra problems. In this paper we present a max-plus algebraic analogue for statistical leverage scores. We show that max-plus statistical leverage scores can be used to ...