Mateusz Żotkiewicz

On max-min fair flow optimization in wireless mesh networks

The paper is devoted to modeling wireless mesh networks (WMN) through mixed-integer programming (MIP) formulations that allow to precisely characterize the link data rate capacity and transmission scheduling using the notion of time slots. Such MIP models are formulated for several cases of the modulation and coding schemes (MCS) assignment. We present a general way of solving the max-min fairness (MMF) traffic objective for WMN using the formulated capacity models. Thus the paper combines WMN radio link modeling with a non-standard way of dealing with uncertain traffic, a combination that has not, to our knowledge, been treated so far by exact optimization models. We discuss several ways, including a method based on the so called compatible or independent sets, of solving the arising MIP problems. We also present an extensive numerical study that illustrates the running time efficiency of different solution approaches, and the influence of the MCS selection options and the number of time slots on traffic performance of a WMN. Exact joint optimization modeling of the WMN capacity and the MMF traffic objectives forms the main contribution of the paper.

Column generation algorithm for RSA problems in flexgrid optical networks

Finding optimal routes and spectrum allocation in flexgrid optical networks, known as the RSA problem, is an important design problem in transport communication networks. The problem is

Multipolar robust optimization

\mathcal{NP }

Generalized elastic flow rerouting scheme

NP-hard, and its intractability becomes profound when network instances with several tens of nodes and several hundreds of demands are to be solved to optimum. In order to deal with such instances, large-scale optimization methods need to be considered. In this work, we present a column (more precisely, path) generation-based method for the RSA problem. The method is capable of finding reasonable sets of lightpaths, avoiding large sets of precomputed paths, and leading to high-quality solutions. Numerical results illustrating effectiveness of the proposed method for obtaining solutions for large RSA problem instances are presented.

Elastic multi-layer resilient IP-over-Flexgrid networking: Detailed cost analysis with bandwidth-variable transponders

In this paper we consider the problem of optimal partitioning of a traffic demand polytope using a hyperplane. In our model all possible demand matrices belong to a polytope. The polytope can be divided into parts, and different routing schemes can be applied while dealing with traffic matrices from different parts of the polytope. We consider three basic models: Robust-Routing, No-Sharing and Dynamic-Routing. We apply two different partitioning strategies depending on whether the reservation vectors on opposite sides of the hyperplane are required to be identical, or allowed to differ. We provide efficient algorithms that solve these problems. Moreover, we prove polynomiality of some of the considered cases. Finally, we present numerical results proving the applicability of the introduced algorithms and showing differences between the routing strategies.

Resilient arcs and node disjointness in diverse routing

We consider linear programs involving uncertain parameters and propose a new tractable robust counterpart which contains and generalizes several other models including the existing Affinely Adjustable Robust Counterpart and the Fully Adjustable Robust Counterpart. It consists in selecting a set of poles whose convex hull contains some projection of the uncertainty set, and computing a recourse strategy for each data scenario as a convex combination of some optimized recourses (one for each pole). We show that the proposed multipolar robust counterpart is tractable and its complexity is controllable. Further, we show that under some mild assumptions, two sequences of upper and lower bounds converge to the optimal value of the fully adjustable robust counterpart. We numerically investigate a couple of applications in the literature demonstrating that the approach can effectively improve the affinely adjustable policy.

Volume-oriented routing and its modifications

We deal with a natural integer-linear programming formulation of the routing and spectrum allocation (RSA) problem in elastic optical networks. We focus on strengthening the formulation with valid inequalities (cuts). For this purpose we apply clique inequalities that proved to be useful in other applications of this kind. We develop and combine a clique cut generation procedure with a column generation algorithm with the aim to improve the quality of generated columns. The presented results, obtained for a set of problem instances, illustrate the effectiveness of the optimization algorithm.

Uncertainty in FTTH splitter installation

The present study deals with Elastic Flow Rerouting EFR-an original traffic restoration strategy for protecting traffic flows in communication networks including wireless networks against multiple link failures. EFR aims at alleviating the trade-off between practicability of traffic restoration and the cost of network resources observed in existing networking solutions. We present an extension of EFR capable of managing multiple partial link failures. We describe EFR and its extension, formulate the EFR related optimization problems, and discuss approaches for their resolution. We also discuss numerical results illustrating effectiveness of EFR in terms of the link capacity cost.