Scheduling Multi-Vessel Placement in Multi-Chamber Inland Waterway Locks Using Switching Max-Plus Algebra

Inland waterway transport is a low CO2 emission alternative to road transport. A shift towards more inland waterway transport could also help reduce road congestion and noise pollution. Infrastructure bottlenecking, particularly at locks, is part of the reasons preventing this shift. Congestion is leading to delays. Locks can be physically...

Modeling and scheduling an autonomous sorting system using a switching max-plus linear model

Sorting systems form an example of event driven systems. These types of systems are referred to as discrete event systems (DES), and they consist of jobs that need to be performed at available resources. In an autonomous sorting system, jobs consist of robots receiving and delivering parcels at the correct locations. With scheduling, optimal...

Predicting Processing Time of Stochastic Switching Max-Plus Systems

The goal in this thesis is to make a prediction on the total processing time for logistical systems to complete their tasks. For simple systems that can be described using a regular max plus state space model this is done by calculating the systems eigenvalue and multiplying that by the number of iterations required. But, for more complex...

Modelling and Optimal Scheduling of Inland Waterway Transport Systems: A Switching Max-Plus-Linear Systems Approach

Inland waterways form a natural network infrastructure with the capacity for waterborne transport of people and goods for moving freight from seaports to the hinterland. Recently, Inland Waterway Transport (IWT) has been promoted more extensively by the European Union and various governments as it plays a crucial role in reducing road congestion...

Scheduling Inland Waterway Transport Vessels and Locks Using a Switching Max-Plus-Linear Systems Approach

This paper considers the inland waterborne transport (IWT) problem, and presents a scheduling approach for inland vessels and locks to generate optimal vessel and lock timetables. The scheduling strategy is designed in the switching max-plus-linear (SMPL) systems framework, as these are characterized by a number of features that make them...

Model predictive scheduling of semi-cyclic discrete-event systems using switching max-plus linear models and dynamic graphs

In this paper we discuss scheduling of semi-cyclic discrete-event systems, for which the set of operations may vary over a limited set of possible sequences of operations. We introduce a unified modeling framework in which different types of semi-cyclic discrete-event systems can be described by switching max-plus linear (SMPL) models. We use...

Matrix spans in max-plus algebra and a graph-theoretic approach to switching max-plus linear systems

The relation between graph theory and max-plus algebra has been well studied since the inception of max-plus algebra. It has been shown that any square matrix over the maxplus semiring can be represented as a weighted directed graph. Furthermore, properties of these matrices, such as irreducibility and its (unique) eigenvalue, can be determined...

The interaction between scheduling and control of semi-cyclic hybrid systems

In this paper a new iterative approach is proposed for the design of a combined real-time scheduling and control algorithm that can be applied to industrial systems that are described by a hybrid model with a (semi-)cyclic behavior. Traditionally scheduling and control problems are considered in a sequential way. First the scheduling problem...

Turning of a Legged Robot via a Switching Max-Plus Linear System: Simulation and Implementation

Legged locomotion is an example of a discrete event system (DES) with only synchronization and no concurrency. This particular kind of DES can be framed in max-plus algebra, which consists of maximization and addition as its basic operations. Utilizing the max-plus operations between matrices, max-plus linear (MPL) system is constructed.<br/><br...

Modeling and Control of Switching Max-Plus-Linear Systems: Rescheduling of railway traffic and changing gaits in legged locomotion

The operation of many systems can be described by the timing of events. When the system behavior can be described by equations that are "linear'' in the max-plus algebra, which has maximization and addition as its basic operations, the system is called a max-plus-linear system. In many of these systems the order of the events may need to be...

Approximation Methods in Stochastic Max-Plus Systems

Stochastic max-plus systems belong to a special class of discrete-event systems. This class consists of systems with synchronization but no choice and the models of such systems are defined using the operators maximization and addition. Stochastic max-plus systems can be further extended to stochastic switching max-plus systems and stochastic...

Modeling and control of switching max-plus-linear systems with random and deterministic switching

Switching max-plus-linear (SMPL) systems are discrete-event systems that can switch between different modes of operation. In each mode the system is described by a max-plus-linear state equation and a max-plus-linear output equation, with different system matrices for each mode. The switching may depend on the inputs and the states, or it may be...