This paper describes Nancy, a Network Calculus (NC) library that allows users to perform complex min-plus and max-plus algebra operations efficiently. To the best of our knowledge, Nancy is only open-source implements working on arbitrary piecewise affine functions, as well implement some them (e.g. sub-additive closure function composition). researchers compute NC results using straightforward...

This paper proposes an online scheduling method considering no-concurrency of resource with subsequent event. We focus on repetitive discrete event systems with MIMO (Multiple Inputs and Multiple Outputs)-FIFO structure. The behavior of such kind of systems can be described by linear equations in max-plus algebra, which is also called the MPL (Max-Plus Linear) systems. Conventional MPL represen...

The topic of this paper is state space realization of impulse responses in the max-plus algebra, which is one of the modeling frameworks that can be used to model discrete event systems. We use the fact that a system of multivariate max-algebraic polynomial equalities and inequalities can be transformed into an Extended Linear Complementarity Problem to find all equivalent fixed order state spa...

Max-plus-linear (MPL) systems are a class of event-driven nonlinear dynamic systems that can be described by models that are “linear” in the max-plus algebra. In this paper we derive a solution to a finite-horizon model predictive control (MPC) problem for MPL systems where the cost is designed to provide a trade-off between minimizing the due date error and a just-in-time production. In genera...

Max-Plus-Linear (MPL) system is known as a solution for scheduling problems of a class of discrete event systems. Typical systems include: manufacturing system and project management, etc. In such systems, the initial schedule is frequently changed due to unpredictable disturbances. Critical Chain Project Management (CCPM) method is a management method that can shorten the time required to comp...

The ecologist H. T. Odum introduced a principle of physics, called Maximum Empower, in order to explain self-organization in a system (e.g. physical, biological, social, economical, mathematical, ...). The concept of empower relies on emergy, which is a second notion introduced by Odum for comparing energy systems on the same basis. The roots of these notions trace back to the 50’s (with the wo...

Let us consider a parametric weighted directed graph in which every arc (j,i) has weight of the form w((j,i))=max(Pij+λ,Iij−λ,Cij), where λ is real parameter and P, I C are arbitrary square matrices with elements R∪{−∞}. In this paper, we design an algorithm that solves Non-positive Circuit Problem (NCP) on class graphs, consists finding all values such does not contain circuits positive weight...