Uncovering the evolution from finite to infinite high-priority capacity in a priority queue

Infinite capacity queues are often used as approximation for their finite real-world counterparts as they are mathematically tractable. It is generally known that tail probabilities of low-priority system content in a two-class priority queue with infinite capacity for customers of both priority classes can be non-exponential, even if the interarrival time and service time distributions are exponentially decaying. In contrast, when the capacity for the high-priority customers is finite, tail probabilities of low-priority system content are always exponentially decaying. Therefore, using the results for one as an (accurate) approximation for the other is not obvious. From an analytical point of view, the non-exponentiality in the infinite case is caused by the arisal of an implicitly defined function, a root of the kernel, in the probability generating function for the low-priority system content. However, up till now, it has been unclear how this non-exponentiality suddenly emerges when taking the limit from to the finite to the infinite case. Our main contribution is that, under the restriction of a maximum of two arrivals per slot, a recurrence relation in the high-priority capacity is constructed resulting in an explicit expression for the corresponding generating function for the finite case. Amazingly, this expression contains all roots of the kernel in the infinite case. Taking the limit of this expression leads to the well-known behavior for the infinite case as the root inside the complex unit circle dominates the other roots uncovering the evolution from the finite to the infinite case. Furthermore, we investigate under which circumstances the standard tail characterizations are inaccurate

Modeling bursts and heavy tails in human dynamics

Current models of human dynamics, used from risk assessment to communications, assume that human actions are randomly distributed in time and thus well approximated by Poisson processes. We provide direct evidence that for five human activity patterns the timing of individual human actions follow non-Poisson statistics, characterized by bursts of rapidly occurring events separated by long periods of inactivity. We show that the bursty nature of human behavior is a consequence of a decision based queuing process: when individuals execute tasks based on some perceived priority, the timing of the tasks will be heavy tailed, most tasks being rapidly executed, while a few experiencing very long waiting times. We discuss two queueing models that capture human activity. The first model assumes that there are no limitations on the number of tasks an individual can hadle at any time, predicting that the waiting time of the individual tasks follow a heavy tailed distribution with exponent alpha=3/2. The second model imposes limitations on the queue length, resulting in alpha=1. We provide empirical evidence supporting the relevance of these two models to human activity patterns. Finally, we discuss possible extension of the proposed queueing models and outline some future challenges in exploring the statistical mechanisms of human dynamics.Comment: RevTex, 19 pages, 8 figure

Study of dynamical properties of complex networks

Doutoramento em FísicaNa última década houve grandes desenvolvimentos na área de teoria de grafos e suas aplicações interdisciplinares. Teoria de grafos (ou redes) é um campo de matemática discreta, que, por abstracção dos detalhes de um problema exceptuando a ligação entre os seus elementos, é capaz de uma descrição das suas características estruturais que de outra maneira não seria possível. Muitos sistemas na natureza, e em particular na sociedade, são bem representados por, ou evoluem tendo como base, redes complexas. Neste trabalho apresentamos alguns avanços para a compreensão das características estruturais genéricas destas redes e sistemas. A tese divide-se em duas partes principais: Na primeira parte faz-se um estudo da estrutura de redes, começando com uma breve introdução histórica do desenvolvimento da teoria de redes e de conceitos básicos, continuando com um conjunto de exemplos de redes previamente estudadas bem como modelos (Capítulo 1). Seguidamente, apresentamos um estudo teórico de propriedades estruturais como a distância entre vértices e a presença de subgrafos em redes (Capítulo 2). O último capítulo desta primeira parte é dedicado a um estudo detalhado de propriedades estruturais da rede real de colaborações científicas promovida pelo V Programa Quadro da União Europeia, FP5 (Capítulo 3). Na segunda parte, dividida em três capítulos, processos dinâmicos tendo como base duas redes são investigados: primeiro, a frequência com que os números ocorrem na World-Wide Web (Capítulo 4); segundo, a estatística temporal de actividades humanas, e seus modelos baseados em teoria de filas de espera, que será aqui introduzida (Capítulo 5); e, terceiro, um modelo teórico servindo como base para o estudo de interacções em redes sociais (Capítulo 6). No Capítulo 7 apresentam-se conclusões gerais, possível trabalho futuro e a lista de publicações resultante do trabalho realizado.In the last decade there have been great developments in graph theory, namely in its interdisciplinary applications. Graph (or network) theory is a field of discrete mathematics, which, by abstracting away the details of a problem except the connectivity between its elements, is capable of describing important structural features that would be impossible with all the details retained. Many systems in nature, and in particular in society, are either well represented by, or evolve on the framework of, so called complex networks. Here we present some advances in understanding the generic structural characteristics of these networks and systems. The thesis is divided in two main parts: In the first part, we present a study of networks' structure, beginning with a brief historical introduction and of basic concepts of network research, continuing with a set of well studied network examples and models (Chapter 1). Next, we present a theoretical investigation of structural properties such as the intervertex distance and the presence of subgraphs in networks (Chapter 2). The last chapter of this first part is devoted to a detailed study of structural properties of the real-world network of scientific collaborations promoted by the European Union's Fifth Framework Programme, FP5 (Chapter 3). In the second part, divided in three chapters, dynamical processes based on two networks are investigated: First, the frequency with which numbers occur on the World-Wide Web (Chapter 4); second, the statistics of the timing of human activities, and their models based on queueing theory, which will be introduced here (Chapter 5); and third, a theoretical queueing model serving as base for the study of interactions on social networks (Chapter 6). In Chapter 7 we present general conclusions, outlook future work and the list of publications resulting from the work developed

Algorithms For Discovering Communities In Complex Networks

It has been observed that real-world random networks like the WWW, Internet, social networks, citation networks, etc., organize themselves into closely-knit groups that are locally dense and globally sparse. These closely-knit groups are termed communities. Nodes within a community are similar in some aspect. For example in a WWW network, communities might consist of web pages that share similar contents. Mining these communities facilitates better understanding of their evolution and topology, and is of great theoretical and commercial significance. Community related research has focused on two main problems: community discovery and community identification. Community discovery is the problem of extracting all the communities in a given network, whereas community identification is the problem of identifying the community, to which, a given set of nodes belong. We make a comparative study of various existing community-discovery algorithms. We then propose a new algorithm based on bibliographic metrics, which addresses the drawbacks in existing approaches. Bibliographic metrics are used to study similarities between publications in a citation network. Our algorithm classifies nodes in the network based on the similarity of their neighborhoods. One of the drawbacks of the current community-discovery algorithms is their computational complexity. These algorithms do not scale up to the enormous size of the real-world networks. We propose a hash-table-based technique that helps us compute the bibliometric similarity between nodes in O(m ?) time. Here m is the number of edges in the graph and ?, the largest degree. Next, we investigate different centrality metrics. Centrality metrics are used to portray the importance of a node in the network. We propose an algorithm that utilizes centrality metrics of the nodes to compute the importance of the edges in the network. Removal of the edges in ascending order of their importance breaks the network into components, each of which represent a community. We compare the performance of the algorithm on synthetic networks with a known community structure using several centrality metrics. Performance was measured as the percentage of nodes that were correctly classified. As an illustration, we model the ucf.edu domain as a web graph and analyze the changes in its properties like densification power law, edge density, degree distribution, diameter, etc., over a five-year period. Our results show super-linear growth in the number of edges with time. We observe (and explain) that despite the increase in average degree of the nodes, the edge density decreases with time

Sixth Workshop and Tutorial on Practical Use of Coloured Petri Nets and the CPN Tools Aarhus, Denmark, October 24-26, 2005

This booklet contains the proceedings of the Sixth Workshop on Practical Use of Coloured Petri Nets and the CPN Tools, October 24-26, 2005. The workshop is organised by the CPN group at the Department of Computer Science, University of Aarhus, Denmark. The papers are also available in electronic form via the web pages: http://www.daimi.au.dk/CPnets/workshop0

Quality embedded intelligent remanufacturing

This thesis is motivated from the four keywords: remanufacturing, quality, multi-agent and intelligence. Recent years' environmental problems caused tightening the regulations and legislations for used products. Therefore remanufacturing is getting more attention. The quality of used products is uncertain and even dynamically changes during the remanufacturing process, and each used product should be individually handled in a different way depending on its quality. Fortunately recent developing wireless technologies like radio frequency identification (RFID) may enable remanufacturing control systems to identify, track, and control each used product and disassembled subassembly/part (PDSP) automatically. The multi-agent approach can be a good solution for the individual control of each PDSP, because a centralized control system is not eligible to managing so many elements in the remanufacturing system. The objective of this thesis is to propose a quality embedded remanufacturing system (QRS) which comprises a multi-agent framework and a scheduling mechanism. First, this thesis discusses the fundamental concepts for the proposed modeling tools and scheduling mechanism: the QRS quality characteristics and the multi-agent framework. As the second step, this thesis proposes QRS modeling tools which support the PDSP/resource quality representation and comprise: intuitive remanufacturing system representation (IRSR) and dynamic token two-level colored Petri-nets (DTPN). The former is designed from the user-side perspective and the latter is from the system-side perspective. The multi-agent framework is constructed based on the model represented with the proposed tools. Last, this thesis proposes a real-time scheduling mechanism for the QRS which enables the constructed framework to execute. The scheduling mechanism embeds a communication protocol among agents and dispatching rules formulated depending on the PDSP/resource quality. A knowledge-based approach is adopted to increase efficiency of the scheduling mechanism, where the knowledge is learned by simulations. A heuristic method is also proposed to reduce the simulation time

A Survey on Data Plane Programming with P4: Fundamentals, Advances, and Applied Research

With traditional networking, users can configure control plane protocols to match the specific network configuration, but without the ability to fundamentally change the underlying algorithms. With SDN, the users may provide their own control plane, that can control network devices through their data plane APIs. Programmable data planes allow users to define their own data plane algorithms for network devices including appropriate data plane APIs which may be leveraged by user-defined SDN control. Thus, programmable data planes and SDN offer great flexibility for network customization, be it for specialized, commercial appliances, e.g., in 5G or data center networks, or for rapid prototyping in industrial and academic research. Programming protocol-independent packet processors (P4) has emerged as the currently most widespread abstraction, programming language, and concept for data plane programming. It is developed and standardized by an open community and it is supported by various software and hardware platforms. In this paper, we survey the literature from 2015 to 2020 on data plane programming with P4. Our survey covers 497 references of which 367 are scientific publications. We organize our work into two parts. In the first part, we give an overview of data plane programming models, the programming language, architectures, compilers, targets, and data plane APIs. We also consider research efforts to advance P4 technology. In the second part, we analyze a large body of literature considering P4-based applied research. We categorize 241 research papers into different application domains, summarize their contributions, and extract prototypes, target platforms, and source code availability.Comment: Submitted to IEEE Communications Surveys and Tutorials (COMS) on 2021-01-2