Christian Raack

Saving energy in IP-over-WDM networks by switching off line cards in low-demand scenarios

We estimate potential energy savings in IP-over-WDM networks achieved by switching off router line cards in low-demand hours. We compare three approaches to react on dynamics in the IP traffic over time, FUFL, DUFL and DUDL. They provide different levels of freedom in adjusting the routing of lightpaths in the WDM layer and the routing of demands in the IP layer. Using MILP models based on realistic network topologies and node architectures as well as realistic demands, power, and cost values, we show that already a simple monitoring of the lightpath utilization in order to deactivate empty line cards (FUFL) brings substantial benefits. The most significant savings, however, are achieved by rerouting traffic in the IP layer (DUFL), which allows emptying and deactivating lightpaths together with the corresponding line cards. A sophisticated reoptimization of the virtual topologies and the routing in the optical domain for every demand scenario (DUDL) yields nearly no additional profits in the considered networks.

DISCUS: an end-to-end solution for ubiquitous broadband optical access

Fiber to the premises has promised to increase the capacity in telecommunications access networks for well over 30 years. While it is widely recognized that optical-fiber-based access networks will be a necessity in the short to medium-term future, its large upfront cost and regulatory issues are pushing many operators to further postpone its deployment, while installing intermediate unambitious solutions such as fiber to the cabinet. Such high investment cost of both network access and core capacity upgrade often derives from poor planning strategies that do not consider the necessity to adequately modify the network architecture to fully exploit the cost benefit that a fiber-centric solution can bring. DISCUS is a European Framework 7 Integrated Project that, building on optical-centric solutions such as long-reach passive optical access and flat optical core, aims to deliver a cost-effective architecture for ubiquitous broadband services. DISCUS analyzes, designs, and demonstrates end-to-end architectures and technologies capable of saving cost and energy by reducing the number of electronic terminations in the network and sharing the deployment costs among a larger number of users compared to current fiber access systems. This article describes the network architecture and the supporting technologies behind DISCUS, giving an overview of the concepts and methodologies that will be used to deliver our end-to-end network solution.

Dynamic routing at different layers in IP-over-WDM networks - Maximizing energy savings

We estimate potential energy savings in IP-over-WDM networks achieved by switching off router line cards in low-demand hours. We compare three approaches to react on dynamics in the IP traffic over time, Fufl, Dufl and Dudl. They provide different levels of freedom in adjusting the routing of lightpaths in the WDM layer and the routing of demands in the IP layer. Using MILP models based on three realistic network topologies as well as realistic demands, power, and cost values, we show that already a simple monitoring of the lightpath utilization in order to deactivate empty line cards (Fufl) may bring substantial benefits. The most significant savings, however, are achieved by rerouting traffic in the IP layer (Dufl). A sophisticated reoptimization of the virtual topology and the routing in the optical and electrical domains for every demand scenario (Dudl) yields nearly no additional profits in the considered networks. These results are independent of the ratio between the traffic demands and capacity granularity, the time scale, distribution of demands, and the network topology for Dufl and Dudl. The success of Fufl, however, depends on the spatial distribution of the traffic as well as on the ratio of traffic demands and lightpath capacity.

On cut-based inequalities for capacitated network design polyhedra

In this article, we study capacitated network design problems. We unify and extend polyhedral results for directed, bidirected, and undirected link capacity models. Valid inequalities based on a network cut are known to be strong in several special cases. We show that regardless of the link model, facets of the polyhedra associated with such a cut translate to facets of the original network design polyhedra if the two subgraphs defined by the network cut are (strongly) connected. Our investigation of the facial structure of the cutset polyhedra allows to complement existing polyhedral results for the three variants by presenting facet-defining flow-cutset inequalities in a unifying way. In addition, we present a new class of facet-defining inequalities, showing as well that flow-cutset inequalities alone do not suffice to give a complete description for single-commodity, single-module cutset polyhedra in the bidirected and undirected case – in contrast to a known result for the directed case. The practical importance of the theoretical investigations is highlighted in an extensive computational study on 27 instances from the Survivable Network Design Library (SNDlib).

Robust network design: Formulations, valid inequalities, and computations

Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks, operators highly overestimate the traffic volume during network planning. In this article we consider telecommunication network design under traffic uncertainty, adapting the robust optimization approach of Bertsimas and Sim [Oper Res 52 (2004), 35‐53]. We present two different mathematical formulations for this problem, provide valid inequalities, study the computational implications, and evaluate the realized robustness. To enhance the performance of the mixed-integer programming solver, we derive robust cutset inequalities generalizing their deterministic counterparts. Instead of a single cutset inequality for every network cut, we derive multiple valid inequalities by exploiting the extra variables available in the robust formulations. We show that these inequalities define facets under certain conditions and that they completely describe a projection of the robust cutset polyhedron if the cutset consists of a single edge. For realistic networks and live traffic measurements, we compare the formulations and report on the speed-up achieved by the valid inequalities. We study the “price of robustness” and evaluate the approach by analyzing the real network load. The results show that the robust optimization approach has the potential to support network planners better than present methods.

Affine recourse for the robust network design problem: Between static and dynamic routing

Affinely Adjustable Robust Counterparts provide tractable alternatives to (two-stage) robust programs with arbitrary recourse. Following Ouorou and Vial, we apply them to robust network design with polyhedral demand uncertainty, introducing the notion of affine routing. We compare the new affine routing scheme to the well-studied static and dynamic routing schemes for robust network design. It is shown that affine routing can be seen as a generalization of the widely used static routing while still being tractable and providing cheaper solutions. We investigate properties of the demand polytope under which affine routings reduce to static routings and also develop conditions on the uncertainty set leading to dynamic routings being affine. We show however that affine routings suffer from the drawback that (even totally) dominated demand vectors are not necessarily supported by affine solutions. Uncertainty sets have to be designed accordingly. Finally, we present computational results on networks from SNDlib. We conclude that for these instances the optimal solutions based on affine routings tend to be as cheap as optimal network designs for dynamic routings. In this respect the affine routing principle can be used to approximate the cost for two-stage solutions with free recourse which are hard to compute

Single-layer Cuts for Multi-layer Network Design Problems

We study a planning problem arising in SDH/WDM multi-layer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixed-integer programming formulation for a predefined set of admissible logical links that takes many practical side constraints into account, including node hardware, several bit-rates, and survivability against single physical node or link failures. This model is solved using a branch-and-cut approach with cutting planes based on either of the two layers. On several realistic two-layer planning scenarios, we show that these cutting planes are still useful in the multi-layer context, helping to increase the dual bound and to reduce the optimality gaps.

On the Robustness of Optimal Network Designs

Robust optimization is an emerging field in telecommunication network design which takes future traffic uncertainty into account. This yields optimal robust network designs which are optimal for all traffic realizations within a pre-defined set of uncertainty. In 2003, Bertsimas and Sim have introduced an adjustable uncertainty set for general optimization problems which preserves the computational complexity of the original non-robust problem. Recently, Koster et al. (NGI2010) have applied this approach to network design problems. In this paper, we consider this so-called Gamma-robust network design problem. We investigate the importance of statistical input data analysis to determine reasonable parameter settings for robust network planning. Using detailed real-life traffic measurements of two backbone networks (Abilene and GEANT), we determine optimal robust network designs for 495 different parameter settings per network. Afterwards, we evaluate the realized robustness (i.e., the percentage of supported traffic matrices) w.r.t. the planning data and a larger set of historical data to simulate uncertain future traffic.

Towards robust network design using integer linear programming techniques

Traffic in communication networks fluctuates heavily over time. Thus, to avoid capacity bottlenecks, operators highly overestimate the traffic volume during network planning. In this paper we consider telecommunication network design under traffic uncertainty, adapting the robust optimization approach of [11]. We present three different mathematical formulations for this problem, provide valid inequalities, study the computational implications, and evaluate the realized robustness.

The MCF-separator: detecting and exploiting multi-commodity flow structures in MIPs

Given a general mixed integer program, we automatically detect block structures in the constraint matrix together with the coupling by capacity constraints arising from multi-commodity flow formulations. We identify the underlying graph and generate cutting planes based on cuts in the detected network. Our implementation adds a separator to the branch-and-cut libraries of Scip and Cplex. We make use of the complemented mixed integer rounding framework but provide a special purpose aggregation heuristic that exploits the network structure. Our separation scheme speeds-up the computation for a large set of mixed integer programs coming from network design problems by a factor two on average. We show that almost 10% of the instances in general testsets contain consistent embedded networks. For these instances the computation time is decreased by 18% on average.