Measuring and Understanding Throughput of Network Topologies

High throughput is of particular interest in data center and HPC networks. Although myriad network topologies have been proposed, a broad head-to-head comparison across topologies and across traffic patterns is absent, and the right way to compare worst-case throughput performance is a subtle problem. In this paper, we develop a framework to benchmark the throughput of network topologies, using a two-pronged approach. First, we study performance on a variety of synthetic and experimentally-measured traffic matrices (TMs). Second, we show how to measure worst-case throughput by generating a near-worst-case TM for any given topology. We apply the framework to study the performance of these TMs in a wide range of network topologies, revealing insights into the performance of topologies with scaling, robustness of performance across TMs, and the effect of scattered workload placement. Our evaluation code is freely available

Minimum-cost multicast over coded packet networks

We consider the problem of establishing minimum-cost multicast connections over coded packet networks, i.e., packet networks where the contents of outgoing packets are arbitrary, causal functions of the contents of received packets. We consider both wireline and wireless packet networks as well as both static multicast (where membership of the multicast group remains constant for the duration of the connection) and dynamic multicast (where membership of the multicast group changes in time, with nodes joining and leaving the group). For static multicast, we reduce the problem to a polynomial-time solvable optimization problem, and we present decentralized algorithms for solving it. These algorithms, when coupled with existing decentralized schemes for constructing network codes, yield a fully decentralized approach for achieving minimum-cost multicast. By contrast, establishing minimum-cost static multicast connections over routed packet networks is a very difficult problem even using centralized computation, except in the special cases of unicast and broadcast connections. For dynamic multicast, we reduce the problem to a dynamic programming problem and apply the theory of dynamic programming to suggest how it may be solved

Lagrangian-based methods for single and multi-layer multicommodity capacitated network design

Le problème de conception de réseau avec coûts fixes et capacités (MCFND) et le problème de conception de réseau multicouches (MLND) sont parmi les problèmes de conception de réseau les plus importants. Dans le problème MCFND monocouche, plusieurs produits doivent être acheminés entre des paires origine-destination différentes d’un réseau potentiel donné. Des liaisons doivent être ouvertes pour acheminer les produits, chaque liaison ayant une capacité donnée. Le problème est de trouver la conception du réseau à coût minimum de sorte que les demandes soient satisfaites et que les capacités soient respectées. Dans le problème MLND, il existe plusieurs réseaux potentiels, chacun correspondant à une couche donnée. Dans chaque couche, les demandes pour un ensemble de produits doivent être satisfaites. Pour ouvrir un lien dans une couche particulière, une chaîne de liens de support dans une autre couche doit être ouverte. Nous abordons le problème de conception de réseau multiproduits multicouches à flot unique avec coûts fixes et capacités (MSMCFND), où les produits doivent être acheminés uniquement dans l’une des couches. Les algorithmes basés sur la relaxation lagrangienne sont l’une des méthodes de résolution les plus efficaces pour résoudre les problèmes de conception de réseau. Nous présentons de nouvelles relaxations à base de noeuds, où le sous-problème résultant se décompose par noeud. Nous montrons que la décomposition lagrangienne améliore significativement les limites des relaxations traditionnelles. Les problèmes de conception du réseau ont été étudiés dans la littérature. Cependant, ces dernières années, des applications intéressantes des problèmes MLND sont apparues, qui ne sont pas couvertes dans ces études. Nous présentons un examen des problèmes de MLND et proposons une formulation générale pour le MLND. Nous proposons également une formulation générale et une méthodologie de relaxation lagrangienne efficace pour le problème MMCFND. La méthode est compétitive avec un logiciel commercial de programmation en nombres entiers, et donne généralement de meilleurs résultats.The multicommodity capacitated fixed-charge network design problem (MCFND) and the multilayer network design problem (MLND) are among the most important network design problems. In the single-layer MCFND problem, several commodities have to be routed between different origin-destination pairs of a given potential network. Appropriate capacitated links have to be opened to route the commodities. The problem is to find the minimum cost design and routing such that the demands are satisfied and the capacities are respected. In the MLND, there are several potential networks, each at a given layer. In each network, the flow requirements for a set of commodities must be satisfied. However, the selection of the links is interdependent. To open a link in a particular layer, a chain of supporting links in another layer has to be opened. We address the multilayer single flow-type multicommodity capacitated fixed-charge network design problem (MSMCFND), where commodities are routed only in one of the layers. Lagrangian-based algorithms are one of the most effective solution methods to solve network design problems. The traditional Lagrangian relaxations for the MCFND problem are the flow and knapsack relaxations, where the resulting Lagrangian subproblems decompose by commodity and by arc, respectively. We present new node-based relaxations, where the resulting subproblem decomposes by node. We show that the Lagrangian dual bound improves significantly upon the bounds of the traditional relaxations. We also propose a Lagrangian-based algorithm to obtain upper bounds. Network design problems have been the object of extensive literature reviews. However, in recent years, interesting applications of multilayer problems have appeared that are not covered in these surveys. We present a review of multilayer problems and propose a general formulation for the MLND. We also propose a general formulation and an efficient Lagrangian-based solution methodology for the MMCFND problem. The method is competitive with (and often significantly better than) a state-of-the-art mixedinteger programming solver on a large set of randomly generated instances