Abstract The desire for configuring well‐managed open shortest path first (OSPF) routes to handle the communication needs in the contemporary business world with larger networks and changing service requirements has opened the way to use traffic engineering tools with the OSPF protocol. Moreover, anticipating possible shifts in expected traffic demands while using network resources efficiently has started to gain more attention. We take these two crucial issues into consideration and study the weight setting problem for OSPF routing problem with polyhedral demands. Our motivation is to optimize the link weight metric such that the minimum cost routing uses shortest paths with equal cost multipath splitting and the routing decisions are robust to possible fluctuations in demands. In addition to a compact mixed integer programming model, we provide an algorithmic approach with two variations to tackle the problem. We present several test results for these two strategies and discuss whether we could make our weight‐managed OSPF comparable to unconstrained routing under polyhedral demand uncertainty. © 2012 Wiley Periodicals, Inc. NETWORKS, 2012

We consider the network loading problem (NLP) under a polyhedral uncertainty description of traffic demands. After giving a compact multicommodity flow formulation of the problem, we state a decomposition property obtained from projecting out the flow variables. This property considerably simplifies the resulting polyhedral analysis and computations by doing away with metric inequalities. Then we focus on a specific choice of the uncertainty description, called the “hose model,” which specifies aggregate traffic upper bounds for selected endpoints of the network. We study the polyhedral aspects of the NLP under hose demand uncertainty and use the results as the basis of an efficient branch-and-cut algorithm. The results of extensive computational experiments on well-known network design instances are reported.

Abstract We investigate a network design problem under traffic uncertainty that arises when provisioning Virtual Private Networks (VPNs): given a set of terminals that must communicate with one another, and a set of possible traffic matrices, sufficient capacity has to be reserved on the links of the large underlying public network to support all possible traffic matrices while minimizing the total reservation cost. The problem admits several versions depending on the desired topology of the reserved links, and the nature of the traffic data uncertainty. We present compact linear mixed‐integer programming formulations for the problem with the classical hose traffic model and for a less conservative robust variant relying on the traffic statistics that are often available. These flow‐based formulations allow us to solve optimally medium‐to‐large instances with commercial MIP solvers. We also propose a combined branch‐and‐price and cutting‐plane algorithm to tackle larger instances. Computational results obtained for several classes of instances are reported and discussed. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(1), 100–115 2007