Converging an Overlay Network to a Gradient Topology

In this paper, we investigate the topology convergence problem for the gossip-based Gradient overlay network. In an overlay network where each node has a local utility value, a Gradient overlay network is characterized by the properties that each node has a set of neighbors with the same utility value (a similar view) and a set of neighbors containing higher utility values (gradient neighbor set), such that paths of increasing utilities emerge in the network topology. The Gradient overlay network is built using gossiping and a preference function that samples from nodes using a uniform random peer sampling service. We analyze it using tools from matrix analysis, and we prove both the necessary and sufficient conditions for convergence to a complete gradient structure, as well as estimating the convergence time and providing bounds on worst-case convergence time. Finally, we show in simulations the potential of the Gradient overlay, by building a more efficient live-streaming peer-to-peer (P2P) system than one built using uniform random peer sampling.Comment: Submitted to 50th IEEE Conference on Decision and Control (CDC 2011

Consensus Algorithms in Dynamical Network Systems

Dynamical network systems are complex interconnected systems describing many real world problems. The current trend is to connect more and more systems together, and at the same time requiring continuous availability. To this end, it is crucial to understand the dynamic behaviors of networked systems.This thesis makes three contributions in this area. First, we study the important problem of gathering data that are distributed among the nodes in a network. Two specific tasks are considered: to estimate the size of the network, and to aggregate the distribution of local measurements generated by the nodes. We consider a framework where the nodes require anonymity, and restricted computational resources. We propose probabilistic algorithms with low resource requirements, that quickly generate arbitrarily accurate estimates. For dynamical networks, we improve the accuracy through a regularization term which captures the trade-off between the gathered data and a-priori assumptions on the dynamics. In the second part of this thesis, we consider a dynamical network system where one node is misbehaving due to a failure. We specifically seek robustness conditions that guarantee that the entire network system is still functional. The nodes' dynamics is governed by consensus updates, and we present thresholds on the interaction strengths that determines if the system will reach consensus, or if the system will diverge. Finally, a P2P network is utilized to improve a live-streaming media application. In particular, we study how an overlay network, constructed from simple preference functions, can be used to build efficient topologies that reduce both network latency and interruptions. We present necessary and sufficient convergence conditions, as well as convergence speed estimates, and demonstrate the improvements for a real P2P video streaming application.QC 20131111</p

Optimization and Control in Dynamical Network Systems

Dynamical network systems are complex interconnected systems useful to describe many real world problems. The advances in information technology has led the current trend towards connecting more and more systems, creating "intelligent" systems, where the intelligence originates in the scale and complexity of the network. With the growing scale of networked systems comes also higher demands on performance and continuous availability and this creates the need for optimization and control of network systems. This thesis makes four important contributions in this area. In the first contribution, we consider a collaborative road freight transportation system. An efficiency measure for the road utilization in collaborative transportation scenarios is introduced, which evaluates the performance of collaboration strategies in comparison to an optimal central planner. The efficiency measure is used to study a freight transport simulation in Germany and taxi trips using real data from New York City. This is followed by a study of the optimal idling locations for trucks, and the optimal locations for distribution centers. These locations are then exploited in a simulation of a realistic collaborative freight transport system. The second contribution studies the important problem of gathering data that are distributed among the nodes in an anonymous network, i.e., a network where the nodes are not endowed with unique identifies. Two specific tasks are considered: to estimate the size of the network, and to aggregate the distribution of local measurements generated by the nodes. We consider a framework where the nodes require anonymity and have restricted computational resources. We propose probabilistic algorithms with low resource requirements, that quickly generate arbitrarily accurate estimates. For dynamical networks, we improve the accuracy through a regularization term which captures the trade-off between the reliability of the gathered data and a-priori assumptions for the dynamics. In the third contribution, a peer-to-peer network is utilized to improve a live-streaming media application. In particular, we study how an overlay network, constructed from simple preference functions, can be used to build efficient topologies that reduce both network latency and interruptions. We present necessary and sufficient convergence conditions, as well as convergence rate estimates, and demonstrate the improvements for a real peer-to-peer video streaming application. The final contribution is a distributed optimization algorithm. We consider a distributed multi-agent optimization problem of minimizing the sum of convex objective functions. A decentralized optimization algorithm is introduced, based on dual decomposition, together with the subgradient method for finding the optimal solution. The convergence rate is analyzed for different step size rules, constant and time-varying communication delays, and noisy communication channels.Dynamiska nätverkssystem är komplexa sammankopplade system med många praktiska tillämpningar. Den snabba utvecklingen inom informationsteknologin har drivit trenden att sammankoppla större och större system till nätverk av "intelligenta" system, där intelligensen kommer från komplexiteten av nätverken. Med den ökande storleken på nätverkssystemen kommer också ökade krav på dess prestanda och tillgänglighet, vilket är drivkraften bakom utvecklingen av optimering och styrning av nätverkssystem. Den här avhandlingen presenterar fyra viktiga bidrag inom detta område. Det första bidraget handlar om kooperativ lastbilstransport. Först introduceras ett mått som mäter effektiviteten i systemet jämfört med en central planerare. Detta mått används sedan för att utvärdera vinsterna med kooperativa transporter, men används också för att utvärdera taxiförarnas vägval med verkliga data från New York City. Detta följs av en studie av de optimala vänteplatserna för lastbilar och de optimal placeringarna av distributionscentraler. Dessa positioner används sedan för att förbättra transportprestandan i ett kooperativt transportsystem. I det andra bidraget studeras informationsaggregering i anonyma nätverkssystem, det vill säga nätverk där noderna saknar unika identiteter. Två specifika problem hanteras: att estimera storleken på nätverket, och att sammanställa fördelningen av lokala mätvärden i nätverket. Noderna i detta nätverk kräver anonymitet, men antas också ha strikt begränsad beräkningskapacitet. Vi presenterar stokastiska algoritmer med låga beräkningskrav, som dessutom har snabb konvergens och som kan justeras till att ge godtycklig precision. För dynamiska nätverk förbättras prestandan genom att en regulariseringsterm används för att väga observerad data mot förväntat beteende hos systemet. I tredje bidraget analyseras ett peer-to-peer nätverk för direktsänd videodistribution. Speciellt studeras konvergensen av nätverkstopologin som genereras från lokala preferensfunktioner, och hur resultaten kan används för att minska fördröjningarna och avbrotten under videouppspelning. Vi ger nödvändiga och tillräckliga villkor för konvergens, samt karakteriserar gränsvärden för hur snabbt användare kan ansluta eller lämna nätverket utan att påverka prestandan. Det sista bidraget är en distribuerad optimeringsalgoritm. Problemet består i att minimera summan av konvexa funktioner för varje nod i ett nätverk. En decentraliserad optimeringsalgoritm presenteras som baseras på det duala optimeringsproblemet tillsammans med subgradient-metoden. Konvergenshastigheten analyseras för olika val av steglängder, konstanta samt tidsberoende kommunikationsfördröjningar och brusiga kommunikationskanaler.QC 20161020</p

Distributed Multi-Agent Optimization via Dual Decomposition

In this master thesis, a new distributed multi-agent optimization algorithm is introduced. The algorithm is based upon the dual decomposition of the optimization problem, together with the subgradient method for finding the optimal dual solution. The convergence of the new optimization algorithm is proved for communication networks with bounded time-varying delays, and noisy communication. Further, an explicit bound on the convergence rate is given, that shows the dependency on the network parameters. Finally, the new optimization algorithm is also compared to an earlier known primal decomposition algorithm, with extensive numerical simulations

On the optimal location of distribution centers for a one-dimensional transportation system

 Transportation service providers are pressurized to enable real-time logistics planning from a constantly changing demand. This paper focus on a real-time transportation service provider operating along a one-dimensional highway. Transportation assignments arrive following a Poisson process, and the transportation service provider is operating on this road system with a fleet of vehicles, trying to minimize the expected delivery time. Specifically, the optimal locations for idle vehicles, and the optimal locations for construction of distribution centers are considered. The strategies are evaluated with numerical simulations along a Swedish highway system.QC 20170202</p

An efficiency measure for road transportation networks with application to two case studies

Enabling efficient transportation is a major challenge for large cities, as the transportation need is increasing, while the environmental impact has to be minimized.In this paper, we define an efficiency measure that shows how much of the current transportation mileage that is really necessary to meet all the transportation assignments.We show that the efficiency measure can be computed efficiently as a minimum cost flow, and we apply it on two case studies. The first case demonstrate the efficiency measure on a freight transportation system, and the second case computes the measure for a large real-world data set from the New York City taxis.QC 20160615</p

Decentralized Multi-Agent Optimization via Dual Decomposition

We study a distributed multi-agent optimization problem of minimizing the sum of convex objective functions. A new decentralized optimization algorithm is introduced, based on dual decomposition, together with the subgradient method for finding the optimal solution. The iterative algorithm is implemented on a multi-hop network and is designed to handle communication delays.The convergence of the algorithm is proved for communication networks with bounded delays. An explicit bound, which depends on the communication delays, on the convergence rate is given.A numerical comparison with a decentralized primal algorithm shows that the dual algorithm converges faster, and with less communication.QC 20111124</p

Ce que les controverses nous apprennent sur l'activité de restauration des peintures au musée du Louvre

We study a distributed multi-agent optimization problem of minimizing the sum of convex objective functions. A new decentralized optimization algorithm is introduced, based on dual decomposition, together with the subgradient method for finding the optimal solution. The iterative algorithm is implemented on a multi-hop network and is designed to handle communication delays.The convergence of the algorithm is proved for communication networks with bounded delays. An explicit bound, which depends on the communication delays, on the convergence rate is given.A numerical comparison with a decentralized primal algorithm shows that the dual algorithm converges faster, and with less communication.QC 20111124</p

Distributed size estimation of dynamic anonymous networks

We consider the problem of estimating the size of dynamic anonymous networks, motivated by network maintenance. The proposed algorithm is based on max-consensus information exchange protocols, and extends a previous algorithm for static anonymous networks. A regularization term is accounting for a-priori assumptions on the smoothness of the estimate, and we specifically consider quadratic regularization terms since they lead to closed-form solutions and intuitive design laws. We derive an explicit estimation scheme for a particular peer-to-peer service network, starting from its statistical model. To validate the accuracy of the algorithm, we perform numerical experiments and show how the algorithm can be implemented using finite precision arithmetics as well as small communication burdensQC 20130116</p

Memory-enhancing techniques in pedagogical process for pre-school children

We consider the problem of estimating the size of dynamic anonymous networks, motivated by network maintenance. The proposed algorithm is based on max-consensus information exchange protocols, and extends a previous algorithm for static anonymous networks. A regularization term is accounting for a-priori assumptions on the smoothness of the estimate, and we specifically consider quadratic regularization terms since they lead to closed-form solutions and intuitive design laws. We derive an explicit estimation scheme for a particular peer-to-peer service network, starting from its statistical model. To validate the accuracy of the algorithm, we perform numerical experiments and show how the algorithm can be implemented using finite precision arithmetics as well as small communication burdensQC 20130116</p