Tight Load Balancing via Randomized Local Search

We consider the following balls-into-bins process with $n$ bins and $m$ balls: each ball is equipped with a mutually independent exponential clock of rate 1. Whenever a ball's clock rings, the ball samples a random bin and moves there if the number of balls in the sampled bin is smaller than in its current bin. This simple process models a typical load balancing problem where users (balls) seek a selfish improvement of their assignment to resources (bins). From a game theoretic perspective, this is a randomized approach to the well-known Koutsoupias-Papadimitriou model, while it is known as randomized local search (RLS) in load balancing literature. Up to now, the best bound on the expected time to reach perfect balance was $O\left({(\ln n)}^2+\ln(n)\cdot n^2/m\right)$ due to Ganesh, Lilienthal, Manjunath, Proutiere, and Simatos (Load balancing via random local search in closed and open systems, Queueing Systems, 2012). We improve this to an asymptotically tight $O\left(\ln(n)+n^2/m\right)$. Our analysis is based on the crucial observation that performing "destructive moves" (reversals of RLS moves) cannot decrease the balancing time. This allows us to simplify problem instances and to ignore "inconvenient moves" in the analysis.Comment: 24 pages, 3 figures, preliminary version appeared in proceedings of 2017 IEEE International Parallel and Distributed Processing Symposium (IPDPS'17

Load Balancing via Random Local Search in Closed and Open systems

In this paper, we analyze the performance of random load resampling and migration strategies in parallel server systems. Clients initially attach to an arbitrary server, but may switch server independently at random instants of time in an attempt to improve their service rate. This approach to load balancing contrasts with traditional approaches where clients make smart server selections upon arrival (e.g., Join-the-Shortest-Queue policy and variants thereof). Load resampling is particularly relevant in scenarios where clients cannot predict the load of a server before being actually attached to it. An important example is in wireless spectrum sharing where clients try to share a set of frequency bands in a distributed manner.Comment: Accepted to Sigmetrics 201

Load Balancing Algorithms In Software Defined Network

Compared with the traditional networks, the SDN networks have shown great advantages in many aspects, but also exist the problem of the load imbalance. If the load distribution uneven in the SDN networks, it will greatly affect the performance of network. Many SDN-based load balancing strategies have been proposed to improve the performance of the SDN networks. Therefore, in this paper a finding form comprehensive review help to improve further understanding of lead b balancing algorithms in SDN

Threshold Load Balancing with Weighted Tasks

We study threshold-based load balancing protocols for weighted tasks. We are given an arbitrary graph G with n nodes (resources, bins) and m > n tasks (balls). Initially the tasks are distributed arbitrarily over the n nodes. The resources have a threshold and we are interested in the balancing time, i.e., the time it takes until the load of all resources is below the threshold. We distinguish between resource-based and user based protocols. In the case of resource-based protocols resources with a load larger than the threshold are allowed to send tasks to neighbouring resources. In the case of user-based protocols tasks allocated to resources with a load above the threshold decide on their own whether to migrate to a neighbouring resource or not. For resource-controlled protocols we present results for arbitrary graphs. Our bounds are in terms of the mixing time (for above-average thresholds) and the hitting time (for tight thresholds) of the graph. We relate the balancing time of resource-controlled protocols for above-average thresholds in arbitrary graphs to the mixing time of the graph and to the hitting time for tight thresholds. Our bounds are tight and, surprisingly, they are independent of the weights of the tasks. For the user-controlled migration we consider complete graphs and derive bounds for both above-average and tight thresholds

Game theoretic approaches to parallel machine scheduling

Tesis (Ingeniero Industrial)En un problema de programación de máquinas idénticas en paralelo que persigue minimizar dos criterios en particular, lapso y tiempo de terminación total, un mecanismo basado en la teoría de juegos es propuesto para solucionarlo. Se considera un juego bipersonal no-cooperativo de 2x2 en el que cada jugador busca minimizar alguno de estos criterios que propone el problema de producción. Cada escenario implica que los jugadores jueguen de manera simultanea y busquen minimizar los costos que están relacionados con los criterios a optimizar. El jugador que representa al trabajo tiene la opción de dejar al trabajo en su posición actual o moverlo a una posición previa, buscando minimizar su tiempo de terminación; mientras que el otro jugador, un agente controlador, toma la decisión de dejar al trabajo en la máquina actual o moverlo a otra, esperando balancear la carga de la máquina y minimizar el lapso. Como resultado de una serie de juegos repetidos entre estos agentes, el Frente de Pareto es construido, mostrando un conjunto de soluciones eficientes al problema.Universidad del Norte. Programa de Ingeniería Industrial

Embedding Games

Large scale distributed computing infrastructures pose challenging resource management problems, which could be addressed by adopting one of two perspectives. On the one hand, the problem could be framed as a global optimization that aims to minimize some notion of system-wide (social) cost. On the other hand, the problem could be framed in a game-theoretic setting whereby rational, selfish users compete for a share of the resources so as to maximize their private utilities with little or no regard for system-wide objectives. This game-theoretic setting is particularly applicable to emerging cloud and grid environments, testbed platforms, and many networking applications. By adopting the first, global optimization perspective, this thesis presents NetEmbed: a framework, associated mechanisms, and implementations that enable the mapping of requested configurations to available infrastructure resources. By adopting the second, game-theoretic perspective, this thesis defines and establishes the premises of two resource acquisition mechanisms: Colocation Games and Trade and Cap. Colocation Games enable the modeling and analysis of the dynamics that result when rational, selfish parties interact in an attempt to minimize the individual costs they incur to secure shared resources necessary to support their application QoS or SLA requirements. Trade and Cap is a market-based scheduling and load-balancing mechanism that facilitates the trading of resources when users have a mixture of rigid and fluid jobs, and incentivizes users to behave in ways that result in better load-balancing of shared resources. In addition to developing their analytical underpinnings, this thesis establishes the viability of NetEmbed, Colocation Games, and Trade and Cap by presenting implementation blueprints and experimental results for many variants of these mechanisms. The results presented in this thesis pave the way for the development of economically-sound resource acquisition and management solutions in two emerging, and increasingly important settings. In pay-as-you-go settings, where pricing is based on usage, this thesis anticipates new service offerings that enable efficient marketplaces in the presence of non-cooperative, selfish agents. In settings where pricing is not a function of usage, this thesis anticipates the development of service offerings that enable trading of usage rights to maximize the utility of a shared infrastructure to its tenants

Randomised Algorithms on Networks

Networks form an indispensable part of our lives. In particular, computer networks have ranked amongst the most influential networks in recent times. In such an ever-evolving and fast growing network, the primary concern is to understand and analyse different aspects of the network behaviour, such as the quality of service and efficient information propagation. It is also desirable to predict the behaviour of a large computer network if, for example, one of the computers is infected by a virus. In all of the aforementioned cases, we need protocols that are able to make local decisions and handle the dynamic changes in the network topology. Here, randomised algorithms are preferred because many deterministic algorithms often require a central control. In this thesis, we investigate three network-based randomised algorithms, threshold load balancing with weighted tasks, the pull-Moran process and the coalescing-branching random walk. Each of these algorithms has extensive applicability within networks and computational complexity within computer science. In this thesis we investigate threshold-based load balancing protocols. We introduce a generalisation of protocols in [2, 3] to weighted tasks. This thesis also analyses an evolutionary-based process called the death-birth update, defined here as the Pull-Moran process. We show that a class of strong universal amplifiers does not exist for the Pull-Moran process. We show that any class of selective amplifiers in the (standard) Moran process is a class of selective suppressors under the Pull-Moran process. We then introduce a class of selective amplifiers called Punk graphs. Finally, we improve the broadcasting time of the coalescing-branching (COBRA) walk analysed in [4], for random regular graphs. Here, we look into the COBRA approach as a randomised rumour spreading protocol