90B18 Communication networks [See also 68M10, 94A05]
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We consider the design of transparent optical networks from a practical perspective. Network operators aim at satisfying the communication demands at minimum cost. Such an optimization involves three interdependent planning issues: the dimensioning of the physical topology, the routing of lightpaths, and the wavelength assignment. Further topics include the reliability of the configuration and sparse wavelength conversion for efficient use of the capacities. In this paper, we investigate this extensive optical network design task. Using a flexible device-based model, we present an integer programming formulation that supports greenfield planning as well as expansion planning on top of an existing network. As solution method, we propose a suitable decomposition approach that separates the wavelength assignment from the dimensioning and routing. Our method in particular provides a lower bound on the total cost which allows to rate the solution quality. Computational experiments on realistic networks approve the solution approach to be appropriate.
Abstract The cost-efficient design of survivable optical telecommunication networks is the topic of this thesis. In cooperation with network operators, we have developed suitable concepts and mathematical optimization methods to solve this comprehensive planning task in practice. Optical technology is more and more employed in modern telecommunication networks. Digital information is thereby transmitted as short light pulses through glass fibers. Moreover, the optical medium allows for simultaneous transmissions on a single fiber by use of different wavelengths. Recent optical switches enable a direct forwarding of optical channels in the network nodes without the previously required signal retransformation to electronics. Their integration creates ongoing optical connections,which are called lightpaths. We study the problem of finding cost-efficient configurations of optical networks which meet specified communication requirements. A configuration comprises the determination of all lightpaths to establish as well as the detailed allocation of all required devices and systems. We use a flexible modeling framework for a realistic representation of the networks and their composition. For different network architectures, we formulate integer linear programs which model the design task in detail. Moreover, network survivability is an important issue due to the immense bandwidths offered by optical technology. Operators therefore request for designs which perpetuate protected connections and guarantee for a defined minimum throughput in case of malfunctions. In order to achieve an effective realization of scalable protection, we present a novel survivability concept tailored to optical networks and integrate several variants into the models. Our solution approach is based on a suitable model decomposition into two subtasks which separates two individually hard subproblems and enables this way to compute cost-efficient designs with approved quality guarantee. The first subtask consists of routing the connections with corresponding dimensioning of capacities and constitutes a common core task in the area of network planning. Sophisticated methods for such problems have already been developed and are deployed by appropriate integration. The second subtask is characteristic for optical networks and seeks for a conflict-free assignment of available wavelengths to the lightpaths using a minimum number of involved wavelength converters. For this coloring-like task, we derive particular models and study methods to estimate the number of unavoidable conversions. As constructive approach, we develop heuristics and an exact branch-and-price algorithm. Finally, we carry out an extensive computational study on realistic data, provided by our industrial partners. As twofold purpose, we demonstrate the potential of our approach for computing good solutions with quality guarantee, and we exemplify its flexibility for application to network design and analysis.
Application of Multistage Stochastic Programming in Strategic Telecommunication Network Planning
(2010)
Telecommunication is fundamental for the information society. In both, the
private and the professional sector, mobile communication is nowadays taken
for granted. Starting primarily as a service for speech communication, data
service and mobile Internet access are now driving the evolution of network
infrastructure. In the year 2009, 19 million users generated over 33
million GB of traffic using mobile data services. The 3rd generation
networks (3G or UMTS) in Germany comprises over 39,000 base stations with
some 120,000 cells. From 1998 to 2008, the four network operators in
Germany invested over 33 billion Euros in their infrastructure. A careful
allocation of the resources is thus crucial for the profitability for a
network operator: a network should be dimensioned to match customers
demand. As this demand evolves over time, the infrastructure has to evolve
accordingly. The demand evolution is hard to predict and thus constitutes a
strong source of uncertainty. Strategic network planning has to take this
uncertainty into account, and the planned network evolution should adapt to
changing market conditions. The application of superior planning methods
under the consideration of uncertainty can improve the profitability of the
network and creates a competitive advantage. Multistage stochastic
programming is a suitable framework to model strategic telecommunication
network planning.
We present mathematical models and effective optimization procedures for
strategic cellular network design. The demand evolution is modeled as a
continuous stochastic process which is approximated by a discrete scenario
tree. A tree-stage approach is used for the construction of non-uniform
scenario trees that serve as input of the stochastic program. The model is
calibrated by historical traffic observations. A realistic system model of
UMTS radio cells is used that determines coverage areas and cell capacities
and takes signal propagation and interferences into account. The network
design problem is formulated as a multistage stochastic mixed integer
linear program, which is solved using state-of-the-art commercial MIP
solvers. Problem specific presolving is proposed to reduce the problem
size. Computational results on realistic data is presented. Optimization
for the expected profit and the conditional value at risk are performed and
compared.
In this paper we study capacitated network design problems, differentiating directed, bidirected and undirected link capacity models. We complement existing polyhedral results for the three variants by new classes of facet-defining valid inequalities and unified lifting results. For this, we study the restriction of the problems to a cut of the network. First, we show that facets of the resulting cutset polyhedra translate into facets of the original network design polyhedra if the two subgraphs defined by the network cut are (strongly) connected. Second, we provide an analysis of the facial structure of cutset polyhedra, elaborating the differences caused by the three different types of capacity constraints. We present flow-cutset inequalities for all three models and show under which conditions these are facet-defining. We also state a new class of facets for the bidirected and undirected case and it is shown how to handle multiple capacity modules by Mixed Integer Rounding (MIR).
This paper deals with directed, bidirected, and undirected capacitated network design problems. Using mixed integer rounding (MIR), we generalize flow-cutset inequalities to these three link types and to an arbitrary modular link capacity structure, and propose a generic separation algorithm. In an extensive computational study on 54 instances from the Survivable Network Design Library (SNDlib), we show that the performance of cplex can significantly be enhanced by this class of cutting planes. The computations reveal the particular importance of the subclass of cutset-inequalities.
Affinely-Adjustable Robust Counterparts provide tractable alternatives to (two-stage) robust
programs with arbitrary recourse. We apply them to robust network design with polyhedral demand
uncertainty, introducing the affine routing principle.
We compare the affine routing to the well-studied static and dynamic routing schemes for robust
network design.
All three schemes are embedded into the general framework of two-stage network design with recourse.
It is shown that affine routing can be seen as a generalization of the widely used static
routing still being tractable and providing cheaper solutions. We investigate properties on 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.
We provide information on the Survivable Network Design Library (SNDlib), a data library for fixed telecommunication network design that can be accessed at http://sndlib.zib.de. In version 1.0, the library contains data related to 22 networks which, combined with a set of selected planning parameters, leads to 830 network planning problem instances. In this paper, we provide a mathematical model for each planning problem considered in the library and describe the data concepts of the SNDlib. Furthermore, we provide statistical information and details about the origin of the data sets.
This paper deals with MIP-based primal heuristics to be used within a branch-and-cut approach for solving multi-layer telecommunication network design problems. Based on a mixed-integer programming formulation for two network layers, we present three heuristics for solving important subproblems, two of which solve a sub-MIP. On multi-layer planning instances with many parallel logical links, we show the effectiveness of our heuristics in finding good solutions early in the branch-and-cut search tree.
In this paper, we study the influence of technology, traffic properties and price trends on optimized
design of a reference IP-over-WDM network with rich underlying fiber topology. In each network node,
we investigate the optimal degree of traffic switching in an optical (lambda) domain versus an electrical
(packet) domain, also known as measure of \emph{node transparency}. This measure is studied in connection to changes in
traffic volume,
demand affinity, optical circuit speeds and equipment cost. By applying variable design constraints,
we assess the relative roles of the two distinct equipment groups, IP routers and optical
cross-connects, with respect to resulting changes in cost-sensitive network architectures.
In the problem of \emph{Online Call Admission in Optical Networks}, briefly called \textsc{oca}, we are given a graph $G=(V,E)$ together with a set of wavelengths~$W$ and a finite sequence $\sigma=r_1,r_2,\dots$ of calls which arrive in an online fashion. Each call~$r_j$ specifies a pair of nodes to be connected and an integral demand indicating the number of required lightpaths. A lightpath is a path in~$G$ together with a wavelength~$\lambda \in W$. Upon arrival of a call, an online algorithm must decide immediately and irrevocably whether to accept or to reject the call without any knowledge of calls which appear later in the sequence. If the call is accepted, the algorithm must provide the requested number of lightpaths to connect the specified nodes. The essential restriction is the wavelength conflict constraint: each wavelength is available only once per edge, which implies that two lightpaths sharing an edge must have different wavelengths. Each accepted call contributes a benefit equal to its demand to the overall profit. The objective in \textsc{oca} is to maximize the overall profit. Competitive algorithms for \textsc{oca} have been known for the special case where every call requests just a single lightpath. In this paper we present the first competitive online algorithms for the general case of larger demands.