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...

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...

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...

Feedback mechanisms in Switching Max-Plus Linear systems

The class of Discrete Event Systems (DES) are systems of which the dynamics consist of the occurrences of discrete events in the time domain. Typical examples of DES from everyday life are transport systems , production facilities or communication systems. Recently legged locomotion has been adressed from the point of view of DES. Here, the...