Bernard Fortz

Internet traffic engineering by optimizing OSPF weights

Open shortest path first (OSPF) is the most commonly used intra-domain Internet routing protocol. Traffic flow is routed along shortest paths, splitting flow at nodes where several outgoing links are on shortest paths to the destination. The weights of the links, and thereby the shortest path routes, can be changed by the network operator. The weights could be set proportional to their physical distances, but often the main goal is to avoid congestion, i.e., overloading of links, and the standard heuristic recommended by Cisco is to make the weight of a link inversely proportional to its capacity. Our starting point was a proposed AT&T WorldNet backbone with demands projected from previous measurements. The desire was to optimize the weight setting based on the projected demands. We showed that optimizing the weight settings for a given set of demands is NP-hard, so we resorted to a local search heuristic. Surprisingly it turned out that for the proposed AT&T WorldNet backbone, we found weight settings that performed within a few percent from that of the optimal general routing where the flow for each demand is optimally distributed over all paths between source and destination. This contrasts the common belief that OSPF routing leads to congestion and it shows that for the network and demand matrix studied we cannot get a substantially better load balancing by switching to the proposed more flexible multi-protocol label switching (MPLS) technologies. Our techniques were also tested on synthetic internetworks, based on a model of Zegura et al., (1996), for which we did not always get quite as close to the optimal general routing.

Optimizing OSPF/IS-IS weights in a changing world

A system of techniques is presented for optimizing open shortest path first (OSPF) or intermediate system-intermediate system (IS-IS) weights for intradomain routing in a changing world, the goal being to avoid overloaded links. We address predicted periodic changes in traffic as well as problems arising from link failures and emerging hot spots.

Traffic engineering with traditional IP routing protocols

Traffic engineering involves adapting the routing of traffic to network conditions, with the joint goals of good user performance and efficient use of network resources. We describe an approach to intradomain traffic engineering that works within the existing deployed base of interior gateway protocols, such as Open Shortest Path First and Intermediate System-Intermediate System. We explain how to adapt the configuration of link weights, based on a networkwide view of the traffic and topology within a domain. In addition, we summarize the results of several studies of techniques for optimizing OSPF/IS-IS weights to the prevailing traffic. The article argues that traditional shortest path routing protocols are surprisingly effective for engineering the flow of traffic in large IP networks.

Increasing Internet Capacity Using Local Search

Open Shortest Path First (OSPF) is one of the most commonly used intra-domain internet routing protocol. Traffic flow is routed along shortest paths, splitting flow evenly at nodes where several outgoing links are on shortest paths to the destination. The weights of the links, and thereby the shortest path routes, can be changed by the network operator. The weights could be set proportional to the physical lengths of the links, but often the main goal is to avoid congestion, i.e. overloading of links, and the standard heuristic recommended by Cisco (a major router vendor) is to make the weight of a link inversely proportional to its capacity.We study the problem of optimizing OSPF weights for a given a set of projected demands so as to avoid congestion. We show this problem is NP-hard, even for approximation, and propose a local search heuristic to solve it. We also provide worst-case results about the performance of OSPF routing vs. an optimal multi-commodity flow routing. Our numerical experiments compare the results obtained with our local search heuristic to the optimal multi-commodity flow routing, as well as simple and commonly used heuristics for setting the weights. Experiments were done with a proposed next-generation AT&T WorldNet backbone as well as synthetic internetworks.

An improved Benders decomposition applied to a multi-layer network design problem

Benders decomposition has been widely used for solving network design problems. In this paper, we use a branch-and-cut algorithm to improve the separation procedure of Gabrel et al. and Knippel et al. for capacitated network design. We detail experiments on bi-layer networks, comparing with Knippels previous results.

Benders Decomposition for the Hop-Constrained Survivable Network Design Problem

Given a graph with nonnegative edge weights and node pairs Q, we study the problem of constructing a minimum weight set of edges so that the induced subgraph contains at least K edge-disjoint paths containing at most L edges between each pair in Q. Using the layered representation introduced by Gouveia [Gouveia, L. 1998. Using variable redefinition for computing lower bounds for minimum spanning and Steiner trees with hop constraints. INFORMS J. Comput.102 180--188], we present a formulation for the problem valid for any K, L ≥ 1. We use a Benders decomposition method to efficiently handle the large number of variables and constraints. We show that our Benders cuts contain constraints used in previous studies to formulate the problem for L = 2, 3, 4, as well as new inequalities when L ≥ 5. Whereas some recent works on Benders decomposition study the impact of the normalization constraint in the dual subproblem, we focus here on when to generate the Benders cuts. We present a thorough computational study of various branch-and-cut algorithms on a large set of instances including the real-based instances from SNDlib. Our best branch-and-cut algorithm combined with an efficient heuristic is able to solve the instances significantly faster than CPLEX 12 on the extended formulation.

Design and Dimensioning of Survivable SDH/Sonet Networks

Basically, a telecommunications network may be represented as a graph where the edges correspond to transmission cables carrying information (signals) between nodes that represent users. Associated to each pair of users there is an integer valued traffic demand which must flow through this network. Building a network in which all customers are directly connected to one another is clearly not a realistic solution due to the huge amount of cables needed to convey all the demands. Consequently, individual signals are grouped into larger aggregate signals, also called frames, and high capacity transmission equipments may then be used to transport demands more efficiently. In technical language, this grouping operation is called multiplexing and the opposite operation which consists in extracting initial information from a high capacity frame is called demultiplexing.

Intra-domain traffic engineering with shortest path routing protocols

Throughout the last decade, extensive deployment of popular intra-domain routing protocols such as open shortest path first and intermediate system–intermediate system, has drawn an ever increasing attention to Internet traffic engineering. This paper reviews optimization techniques that have been deployed for managing intra-domain routing in networks operated with shortest path routing protocols, and the state-of-the-art research that has been carried out in this direction.

A tabu search algorithm for self-healing ring network design

We consider the problem of designing self-healing rings in order to protect the transmission of telecommunication demands in a zonal network. This problem stems from a real application with operational constraints such as dual homing and hop limit per ring. A modeling approach taking into account ring interactions is proposed as well as a tabu search heuristic for solving it. Computational results for a comprehensive set of real and randomly generated instances are presented.

Two-edge connected subgraphs with bounded rings: Polyhedral results and Branch-and-Cut

We consider the network design problem which consists in determining at minimum cost a 2-edge connected network such that the shortest cycle (a “ring”) to which each edge belongs, does not exceed a given length K. We identify a class of inequalities, called cycle inequalities, valid for the problem and show that these inequalities together with the so-called cut inequalities yield an integer programming formulation of the problem in the space of the natural design variables. We then study the polytope associated with that problem and describe further classes of valid inequalities. We give necessary and sufficient conditions for these inequalities to be facet defining. We study the separation problem associated with these inequalities. In particular, we show that the cycle inequalities can be separated in polynomial time when K≤4. We develop a Branch-and-Cut algorithm based on these results and present extensive computational results.