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Data Uncertainty in Virtual Network Embedding: Robust Optimization and Protection Levels

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Abstract

We address the virtual network embedding problem (VNE) which, given a physical (substrate) network and a collection of virtual networks (VNs), calls for an embedding of the most profitable subset of VNs onto the physical substrate, subject to capacity constraints. In practical applications, node and link demands of the different VNs are, typically, uncertain and difficult to know a priori. To face this issue, we first model VNE as a chance-constrained Mixed-Integer Linear Program (MILP) where the uncertain demands are assumed to be random variables. We then propose a \(\varGamma \)-robust optimization approach to approximate the original chance-constrained formulation, capable of yielding solutions with a large profit that are feasible for almost all the possible realizations of the uncertain demands. To solve larger scale instances, for which the exact approach is computationally too demanding, we propose two MILP-based heuristics: a parametric one, which relies on a parameter setting chosen a priori, and an adaptive one, which does not. We conclude by reporting on extensive computational experiments where the different methods and approaches are compared.

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Notes

  1. We assume that each task which can be parallelized on multiple physical nodes is described in a VN request via as many virtual nodes as the number of parallel threads it can use. This way, a task will be split only if, by splitting it, a more profitable embedding can be obtained. On the contrary, splitting a single virtual node would force us to split both the node and the traffic demands over the physical network in a not well defined way, see Fig. 1b.

  2. The works in [11, 18] constitute the, to our knowledge, only notable exceptions where VNE is not tackled in a deterministic setting. Differently from the setting we assume in this paper though, both works tackle (heuristically) the online version of VNE where the VN requests arrive over time one by one (or, at most, in batches), whereas, in this work, we assume that the whole set of requests is known beforehand and that admission control is in place. Although our work can clearly be used for the case where a single VN request has to be embedded, we recall that, in this paper, embedding costs are not considered.

  3. A preliminary version of this work appeared in [1].

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Acknowledgments

This work is supported by the German Federal Ministry of Education and Research (BMBF Grant 05M13PAA, joint Project 05M2013—VINO: Virtual Network Optimization).

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Author notes

  1. S. Coniglio

    Present address: Department of Mathematical Sciences, University of Southampton, Southampton, UK

Authors and Affiliations

  1. Lehrstuhl II für Mathematik, RWTH Aachen University, Aachen, Germany

    S. Coniglio, A. Koster & M. Tieves

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  1. S. Coniglio
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Correspondence to S. Coniglio.

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The paper is an extended version of [1]. In its extended form, is has not been published or accepted for publication elsewhere, nor it has been submitted to any other journal.

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Coniglio, S., Koster, A. & Tieves, M. Data Uncertainty in Virtual Network Embedding: Robust Optimization and Protection Levels. J Netw Syst Manage 24, 681–710 (2016). https://doi.org/10.1007/s10922-016-9376-x

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  • DOI: https://doi.org/10.1007/s10922-016-9376-x

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