Symbolic dynamical model of average queue size of random early detection algorithm

In this paper, a symbolic dynamical model of the average queue size of the random early detection (RED) algorithm is proposed. The conditions on both the system parameters and the initial conditions that the average queue size of the RED algorithm would converge to a fixed point are derived. These results are useful for network engineers to design both the system parameters and the initial conditions so that internet networks would achieve a good performance

Learning Queuing Networks by Recurrent Neural Networks

It is well known that building analytical performance models in practice is difficult because it requires a considerable degree of proficiency in the underlying mathematics. In this paper, we propose a machine-learning approach to derive performance models from data. We focus on queuing networks, and crucially exploit a deterministic approximation of their average dynamics in terms of a compact system of ordinary differential equations. We encode these equations into a recurrent neural network whose weights can be directly related to model parameters. This allows for an interpretable structure of the neural network, which can be trained from system measurements to yield a white-box parameterized model that can be used for prediction purposes such as what-if analyses and capacity planning. Using synthetic models as well as a real case study of a load-balancing system, we show the effectiveness of our technique in yielding models with high predictive power

Iterated function systems and shape representation

We propose the use of iterated function systems as an isomorphic shape representation scheme for use in a machine vision environment. A concise description of the basic theory and salient characteristics of iterated function systems is presented and from this we develop a formal framework within which to embed a representation scheme. Concentrating on the problem of obtaining automatically generated two-dimensional encodings we describe implementations of two solutions. The first is based on a deterministic algorithm and makes simplifying assumptions which limit its range of applicability. The second employs a novel formulation of a genetic algorithm and is intended to function with general data input. Keywords: Machine Vision, Shape Representation, Iterated Function Systems, Genetic Algorithms

VI Workshop on Computational Data Analysis and Numerical Methods: Book of Abstracts

The VI Workshop on Computational Data Analysis and Numerical Methods (WCDANM) is going to be held on June 27-29, 2019, in the Department of Mathematics of the University of Beira Interior (UBI), Covilhã, Portugal and it is a unique opportunity to disseminate scientific research related to the areas of Mathematics in general, with particular relevance to the areas of Computational Data Analysis and Numerical Methods in theoretical and/or practical field, using new techniques, giving especial emphasis to applications in Medicine, Biology, Biotechnology, Engineering, Industry, Environmental Sciences, Finance, Insurance, Management and Administration. The meeting will provide a forum for discussion and debate of ideas with interest to the scientific community in general. With this meeting new scientific collaborations among colleagues, namely new collaborations in Masters and PhD projects are expected. The event is open to the entire scientific community (with or without communication/poster)

Stochastic spreading on complex networks

Complex interacting systems are ubiquitous in nature and society. Computational modeling of these systems is, therefore, of great relevance for science and engineering. Complex networks are common representations of these systems (e.g., friendship networks or road networks). Dynamical processes (e.g., virus spreading, traffic jams) that evolve on these networks are shaped and constrained by the underlying connectivity. This thesis provides numerical methods to study stochastic spreading processes on complex networks. We consider the processes as inherently probabilistic and analyze their behavior through the lens of probability theory. While powerful theoretical frameworks (like the SIS-epidemic model and continuous-time Markov chains) already exist, their analysis is computationally challenging. A key contribution of the thesis is to ease the computational burden of these methods. Particularly, we provide novel methods for the efficient stochastic simulation of these processes. Based on different simulation studies, we investigate techniques for optimal vaccine distribution and critically address the usage of mathematical models during the Covid-19 pandemic. We also provide model-reduction techniques that translate complicated models into simpler ones that can be solved without resorting to simulations. Lastly, we show how to infer the underlying contact data from node-level observations.Komplexe, interagierende Systeme sind in Natur und Gesellschaft allgegenwärtig. Die computergestützte Modellierung dieser Systeme ist daher von immenser Bedeutung für Wissenschaft und Technik. Netzwerke sind eine gängige Art, diese Systeme zu repräsentieren (z. B. Freundschaftsnetzwerke, Straßennetze). Dynamische Prozesse (z. B. Epidemien, Staus), die sich auf diesen Netzwerken ausbreiten, werden durch die spezifische Konnektivität geformt. In dieser Arbeit werden numerische Methoden zur Untersuchung stochastischer Ausbreitungsprozesse in komplexen Netzwerken entwickelt. Wir betrachten die Prozesse als inhärent probabilistisch und analysieren ihr Verhalten nach wahrscheinlichkeitstheoretischen Fragestellungen. Zwar gibt es bereits theoretische Grundlagen und Paradigmen (wie das SIS-Epidemiemodell und zeitkontinuierliche Markov-Ketten), aber ihre Analyse ist rechnerisch aufwändig. Ein wesentlicher Beitrag dieser Arbeit besteht darin, die Rechenlast dieser Methoden zu verringern. Wir erforschen Methoden zur effizienten Simulation dieser Prozesse. Anhand von Simulationsstudien untersuchen wir außerdem Techniken für optimale Impfstoffverteilung und setzen uns kritisch mit der Verwendung mathematischer Modelle bei der Covid-19-Pandemie auseinander. Des Weiteren führen wir Modellreduktionen ein, mit denen komplizierte Modelle in einfachere umgewandelt werden können. Abschließend zeigen wir, wie man von Beobachtungen einzelner Knoten auf die zugrunde liegende Netzwerkstruktur schließt

34th Midwest Symposium on Circuits and Systems-Final Program

Organized by the Naval Postgraduate School Monterey California. Cosponsored by the IEEE Circuits and Systems Society. Symposium Organizing Committee: General Chairman-Sherif Michael, Technical Program-Roberto Cristi, Publications-Michael Soderstrand, Special Sessions- Charles W. Therrien, Publicity: Jeffrey Burl, Finance: Ralph Hippenstiel, and Local Arrangements: Barbara Cristi

Mathematical Model and Cloud Computing of Road Network Operations under Non-Recurrent Events

Optimal traffic control under incident-driven congestion is crucial for road safety and maintaining network performance. Over the last decade, prediction and simulation of road traffic play important roles in network operation. This dissertation focuses on development of a machine learning-based prediction model, a stochastic cell transmission model (CTM), and an optimisation model. Numerical studies were performed to evaluate the proposed models. The results indicate that proposed models are helpful for road management during road incidents

Discrete-time queueing model for responsive network traffic and bottleneck queues

The Internet has been more and more intensively used in recent years. Although network infrastructure has been regularly upgraded, and the ability to manage heavy traffic greatly increased, especially on the core networks, congestion never ceases to appear, as the amount of traffic that flow on the Internet seems to be increasing at an even faster rate. Thus, congestion control mechanisms play a vital role in the functioning of the Internet. Active Queue Management (AQM) is a popular type of congestion control mechanism that is implemented on gateways (most notably routers), which can predict and avoid the congestion before it happens. When properly configured, AQMs can effectively reduce the congestion, and alleviate some of the problems such as global synchronisation and unfairness to bursty traffic. However, there are still many problems regarding AQMs. Most of the AQM schemes are quite sensitive to their parameters setting, and these parameters may be heavily dependent on the network traffic profile, which the administrator may not have intensive knowledge of, and is likely to change over time. When poorly configured, many AQMs perform no better than the basic drop-tail queue. There is currently no effective method to compare the performance of these AQM algorithms, caused by the parameter configuration problem. In this research, the aim is to propose a new analytical model, which mainly uses discrete-time queueing theory. A novel transient modification to the conventional equilibrium-based method is proposed, and it is utilised to further develop a dynamic interactive model of responsive traffic and bottleneck queues. Using step-by-step analysis, it represents the bursty traffic and oscillating queue length behaviour in practical network more accurately. It also provides an effective way of predicting the behaviour of a TCP-AQM system, allowing easier parameter optimisation for AQM schemes. Numerical solution using MATLAB and software simulation using NS-2 are used to extensively validate the proposed models, theories and conclusions