A Fast Distributed Stateless Algorithm for α\alpha-Fair Packing Problems

Over the past two decades, fair resource allocation problems have received considerable attention in a variety of application areas. However, little progress has been made in the design of distributed algorithms with convergence guarantees for general and commonly used $\alpha$-fair allocations. In this paper, we study weighted $\alpha$-fair packing problems, that is, the problems of maximizing the objective functions (i) $\sum_j w_j x_j^{1-\alpha}/(1-\alpha)$ when $\alpha > 0$, $\alpha \neq 1$ and (ii) $\sum_j w_j \ln x_j$ when $\alpha = 1$, over linear constraints $Ax \leq b$, $x\geq 0$, where $w_j$ are positive weights and $A$ and $b$ are non-negative. We consider the distributed computation model that was used for packing linear programs and network utility maximization problems. Under this model, we provide a distributed algorithm for general $\alpha$ that converges to an $\varepsilon-$approximate solution in time (number of distributed iterations) that has an inverse polynomial dependence on the approximation parameter $\varepsilon$ and poly-logarithmic dependence on the problem size. This is the first distributed algorithm for weighted $\alpha-$fair packing with poly-logarithmic convergence in the input size. The algorithm uses simple local update rules and is stateless (namely, it allows asynchronous updates, is self-stabilizing, and allows incremental and local adjustments). We also obtain a number of structural results that characterize $\alpha-$fair allocations as the value of $\alpha$ is varied. These results deepen our understanding of fairness guarantees in $\alpha-$fair packing allocations, and also provide insight into the behavior of $\alpha-$fair allocations in the asymptotic cases $\alpha\rightarrow 0$, $\alpha \rightarrow 1$, and $\alpha \rightarrow \infty$.Comment: Added structural results for asymptotic cases of \alpha-fairness (\alpha approaching 0, 1, or infinity), improved presentation, and revised throughou

Multi-Path Alpha-Fair Resource Allocation at Scale in Distributed Software Defined Networks

The performance of computer networks relies on how bandwidth is shared among different flows. Fair resource allocation is a challenging problem particularly when the flows evolve over time. To address this issue, bandwidth sharing techniques that quickly react to the traffic fluctuations are of interest, especially in large scale settings with hundreds of nodes and thousands of flows. In this context, we propose a distributed algorithm based on the Alternating Direction Method of Multipliers (ADMM) that tackles the multi-path fair resource allocation problem in a distributed SDN control architecture. Our ADMM-based algorithm continuously generates a sequence of resource allocation solutions converging to the fair allocation while always remaining feasible, a property that standard primal-dual decomposition methods often lack. Thanks to the distribution of all computer intensive operations, we demonstrate that we can handle large instances at scale

Lower Bounds for the Fair Resource Allocation Problem

The $\alpha$-fair resource allocation problem has received remarkable attention and has been studied in numerous application fields. Several algorithms have been proposed in the context of $\alpha$-fair resource sharing to distributively compute its value. However, little work has been done on its structural properties. In this work, we present a lower bound for the optimal solution of the weighted $\alpha$-fair resource allocation problem and compare it with existing propositions in the literature. Our derivations rely on a localization property verified by optimization problems with separable objective that permit one to better exploit their local structures. We give a local version of the well-known midpoint domination axiom used to axiomatically build the Nash Bargaining Solution (or proportionally fair resource allocation problem). Moreover, we show how our lower bound can improve the performances of a distributed algorithm based on the Alternating Directions Method of Multipliers (ADMM). The evaluation of the algorithm shows that our lower bound can considerably reduce its convergence time up to two orders of magnitude compared to when the bound is not used at all or is simply looser.Comment: in IFIP WG 7.3 Performance 2017, New York, NY US

Lower Bounds for the Fair Resource Allocation Problem

International audienceThe α-fair resource allocation problem has received remarkable attention and has been studied in numerous application fields. Several algorithms have been proposed in the context of α-fair resource sharing to distributively compute its value. However, little work has been done on its structural properties. In this work, we present a lower bound for the optimal solution of the weighted α-fair resource allocation problem and compare it with existing propositions in the literature. Our derivations rely on a localization property verified by optimization problems with separable objective that permit one to better exploit their local structures. We give a local version of the well-known midpoint domination axiom used to axiomatically build the Nash Bargaining Solution (or proportionally fair resource allocation problem). Moreover, we show how our lower bound can improve the performances of a distributed algorithm based on the Alternating Directions Method of Multipliers (ADMM). The evaluation of the algorithm shows that our lower bound can considerably reduce its convergence time up to two orders of magnitude compared to when the bound is not used at all or is simply looser

Multi-Path Alpha-Fair Resource Allocation at Scale in Distributed Software Defined Networks

International audienceThe performance of computer networks relies on how bandwidth is shared among different flows. Fair resource allocation is a challenging problem particularly when the flows evolve over time. To address this issue, bandwidth sharing techniques that quickly react to the traffic fluctuations are of interest, especially in large scale settings with hundreds of nodes and thousands of flows. In this context, we propose a distributed algorithm based on the Alternating Direction Method of Multipliers (ADMM) that tackles the multi-path fair resource allocation problem in a distributed SDN control architecture. Our ADMM-based algorithm continuously generates a sequence of resource allocation solutions converging to the fair allocation while always remaining feasible, a property that standard primal-dual decomposition methods often lack. Thanks to the distribution of all computer intensive operations, we demonstrate that we can handle large instances at scale

Partage équitable de ressources en temps réel dans les Software Defined Networks distribués

The performance of computer networks relies on how bandwidth is shared among different flows. Fair resource allocation is a challenging problem particularly when the flows evolve over time.To address this issue, bandwidth sharing techniques that quickly react to the traffic fluctuations are of interest, especially in large scale settings with hundreds of nodes and thousands of flows. In this context, we propose a distributed algorithm that tackles the fair resource allocation problem in a distributed SDN control architecture. Our algorithm continuously generates a sequence of resource allocation solutions converging to the fair allocation while always remaining feasible, a property that standard primal-dual decomposition methods often lack. Thanks to the distribution of all computer intensive operations, we demonstrate that we can handle large instances in real-time.La performance des réseaux informatiques est fortement liée au partage équitable de la bande-passante entre les différents flux.Lorsque la taille de ces flux varie constamment dans le temps, le problème de partage des ressources est non-trivial. Afin d'aborder ce problème, des techniques de partage pouvant réagir rapidement aux fluctuations de trafic sont désirables, en particulier pour le contrôle de grands réseaux avec des centaines de noeuds et des milliers de flux. Nous proposons un algorithme distribué qui s'attaque au problème de partage de ressources équitable dans le contexte des architectures Software-Defined Networks (SDN) distribuées. Cet algorithme génère en chaque instant des solutions convergeant vers le partage équitable en respectant toujours l'ensemble des contraintes, une propriété non satisfaite par les méthodes classiques de décomposition primale-duale. Grâce à la distribution des calculs, nous montrons que notre algorithme peut contrôler de grands réseaux en temps réel

Real-Time Fair Resource Allocation in Distributed Software Defined Networks

International audienceThe performance of computer networks relies on how bandwidth is shared among different flows. Fair resource allocation is a challenging problem particularly when the flows evolve over time. To address this issue, bandwidth sharing techniques that quickly react to the traffic fluctuations are of interest, especially in large scale settings with hundreds of nodes and thousands of flows. In this context, we propose a distributed algorithm based on the Alternating Direction Method of Multipliers (ADMM) that tackles the fair resource allocation problem in a distributed SDN control architecture. Our ADMM-based algorithm continuously generates a sequence of resource allocation solutions converging to the fair allocation while always remaining feasible, a property that standard primal-dual decomposition methods often lack. Thanks to the distribution of all computer intensive operations, we demonstrate that we can handle large instances in real-time