Stable routing scheduling algorithms in multi-hop wireless networks

Stability is an important issue in order to characterize the performance of a network, and it has become a major topic of study in the last decade. Roughly speaking, a communication network system is said to be stableif the number of packets waiting to be delivered (backlog) is finitely bounded at any one time. In this paper we introduce a number of routing scheduling algorithms which, making use of certain knowledge about the network’s structure, guarantee stability for certain injection rates. First, we introduce two new families of combinatorial structures, which we call universally strong selectorsand generalized universally strong selectors, that are used to provide a set of transmission schedules. Making use of these structures, we propose two local-knowledgepacket-oblivious routing scheduling algorithms. The first proposed routing scheduling algorithm onlyneeds to know some upper bounds on the number of links and on the network’s degree, and is asymptotically optimal regarding the injection rate for which stability is guaranteed. The second proposed routing scheduling algorithm isclose to be asymptotically optimal, but it only needs to know an upper bound on the number of links. For such algorithms, we also provide some results regarding both the maximum latencies and queue lengths. Furthermore, we also evaluate how the lack of global knowledge about the system topology affects the performance of the routing scheduling algorithms.Funding for open access charge: CRUE-Universitat Jaume

Optimal Control of Distributed Computing Networks with Mixed-Cast Traffic Flows

Distributed computing networks, tasked with both packet transmission and processing, require the joint optimization of communication and computation resources. We develop a dynamic control policy that determines both routes and processing locations for packets upon their arrival at a distributed computing network. The proposed policy, referred to as Universal Computing Network Control (UCNC), guarantees that packets i) are processed by a specified chain of service functions, ii) follow cycle-free routes between consecutive functions, and iii) are delivered to their corresponding set of destinations via proper packet duplications. UCNC is shown to be throughput-optimal for any mix of unicast and multicast traffic, and is the first throughput-optimal policy for non-unicast traffic in distributed computing networks with both communication and computation constraints. Moreover, simulation results suggest that UCNC yields substantially lower average packet delay compared with existing control policies for unicast traffic

Algorithmic issues in queueing systems and combinatorial counting problems

Includes bibliographical references (leaves 111-118).Thesis (Ph. D.)--Massachusetts Institute of Technology, Sloan School of Management, Operations Research Center, 2008.(cont.) However, these randomized algorithms can never provide proven upper or lower bounds on the number of objects they are counting, but can only give probabilistic estimates. We propose a set of deterministic algorithms for counting such objects for three classes of counting problems. They are interesting both because they give an alternative approach to solving these problems, and because unlike MCMC algorithms, they provide provable bounds on the number of objects. The algorithms we propose are for special cases of counting the number of matchings, colorings, or perfect matchings (permanent), of a graph.Multiclass queueing networks are used to model manufacturing, computer, supply chain, and other systems. Questions of performance and stability arise in these systems. There is a body of research on determining stability of a given queueing system, which contains algorithms for determining stability of queueing networks in some special cases, such as the case where there are only two stations. Yet previous attempts to find a general characterization of stability of queueing networks have not been successful.In the first part of the thesis, we contribute to the understanding of why such a general characterization could not be found. We prove that even under a relatively simple class of static buffer priority scheduling policies, stability of deterministic multiclass queueing network is, in general, an undecidable problem. Thus, there does not exist an algorithm for determining stability of queueing networks, even under those relatively simple assumptions. This explains why such an algorithm, despite significant efforts, has not been found to date. In the second part of the thesis, we address the problem of finding algorithms for approximately solving combinatorial graph counting problems. Counting problems are a wide and well studied class of algorithmic problems, that deal with counting certain objects, such as the number of independent sets, or matchings, or colorings, in a graph. The problems we address are known to be #P-hard, which implies that, unless P = #P, they can not be solved exactly in polynomial time. It is known that randomized approximation algorithms based on Monte Carlo Markov Chains (MCMC) solve these problems approximately, in polynomial time.by Dmitriy A. Katz-Rogozhnikov.Ph.D

Quelques propriétés topologiques des graphes et applications à Internet et aux réseaux

This thesis focuses on topological properties of graphs and their application on communication networks, specif- ically on graphs reflecting Internet structure. We first look how far from a tree a graph may be by the study of two parameters : hyperbolicity and treewidth. For hyperbolicity, we analyse the relation with others graph parameters, we also show that some graph decom- positions allow its efficient computation. We compute both parameters on Internet snapshots at different levels of granularity and time periods. We propose some structural and algorithmic consequences of obtained values. Then, we study the graph clustering problem from the perspective of modularity, which measures a clustering quality and is largely studied in the literature. We analyse modularity from a theoretical point of view and [describe] its asymptotic behaviour for some graph families. Finally, we deal with adversarial queueing theory, a combinatorial framework derived from classic queueing theory where injection process is under the control of an adversary. We propose a new model generalisation by considering request of distinct types.Ce travail étudie des propriétés topologiques des graphes et leurs applications aux réseaux de communications, notamment aux graphes représentant la structure d'Internet. Dans un premier temps, on s'intéresse à l'arborescence des graphes par l'étude de deux paramètres : l'hyperbolicité et la largeur arborescente (treewidth). Pour l'hyperbolicité, on analyse sa relation avec d'autres paramètres de graphes et on montre que certaines décompositions de graphes en permettent un calcul efficace. On calcule ces deux paramètres dans des instantanés d'Internet pour différents niveaux hiérarchiques et différentes périodes de temps. On y apporte des interprétations structurelles et algorithmiques pour les valeurs obtenues. On aborde ensuite le problème de partitionnement de graphes (clustering) sous l'angle de la modularité, paramètre qui mesure la qualité d'un partitionnement, largement utilisé dans la littérature. On analyse la modularité du point de vue théorique et son comportement asymptotique pour certaines familles de graphes. Enfin, on s'intéresse à une approche combinatoire de la théorie des files d'attente où les injections de paquets sont effectuées par un adversaire. On propose une généralisation de ce modèle par l'introduction de différentes classes de requêtes

Generalized asset integrity games

Generalized assets represent a class of multi-scale adaptive state-transition systems with domain-oblivious performance criteria. The governance of such assets must proceed without exact specifications, objectives, or constraints. Decision making must rapidly scale in the presence of uncertainty, complexity, and intelligent adversaries. This thesis formulates an architecture for generalized asset planning. Assets are modelled as dynamical graph structures which admit topological performance indicators, such as dependability, resilience, and efficiency. These metrics are used to construct robust model configurations. A normalized compression distance (NCD) is computed between a given active/live asset model and a reference configuration to produce an integrity score. The utility derived from the asset is monotonically proportional to this integrity score, which represents the proximity to ideal conditions. The present work considers the situation between an asset manager and an intelligent adversary, who act within a stochastic environment to control the integrity state of the asset. A generalized asset integrity game engine (GAIGE) is developed, which implements anytime algorithms to solve a stochastically perturbed two-player zero-sum game. The resulting planning strategies seek to stabilize deviations from minimax trajectories of the integrity score. Results demonstrate the performance and scalability of the GAIGE. This approach represents a first-step towards domain-oblivious architectures for complex asset governance and anytime planning

Operational Research: Methods and Applications

Throughout its history, Operational Research has evolved to include a variety of methods, models and algorithms that have been applied to a diverse and wide range of contexts. This encyclopedic article consists of two main sections: methods and applications. The first aims to summarise the up-to-date knowledge and provide an overview of the state-of-the-art methods and key developments in the various subdomains of the field. The second offers a wide-ranging list of areas where Operational Research has been applied. The article is meant to be read in a nonlinear fashion. It should be used as a point of reference or first-port-of-call for a diverse pool of readers: academics, researchers, students, and practitioners. The entries within the methods and applications sections are presented in alphabetical order. The authors dedicate this paper to the 2023 Turkey/Syria earthquake victims. We sincerely hope that advances in OR will play a role towards minimising the pain and suffering caused by this and future catastrophes