Michal Pioro

Max-min fairness and its applications to routing and load-balancing in communication networks: a tutorial

This tutorial is devoted to the notion of max-min fairness (MMF), associated optimization problems, and their applications to multi-commodity flow networks.We first introduce a theoretical background for a generic MMF optimization problem and discuss its relation to lexicographic optimization. We next present resolution algorithms for convex MMF optimization, and analyze their properties. In the second half of the tutorial we discuss its applications to communication networks, in particular to routing and load-balancing. We state several properties with respect to each of the studied problems and analyze the behavior of the algorithms.

Planning fixed to flexgrid gradual migration: drivers and open issues

Flexgrid technology has recently been presented as the most promising option for upgrading the currently operating fixed grid optical networks and extending their capacity to be able to deal with the massive traffic volumes forecast for the next decade. Although the current traffic is successfully supported on fixed grid networks, flexgrid technology brings features that are not offered by the fixed grid networks, such as transporting optical connections with a capacity beyond 100 Gb/s and elasticity against time-varying traffic. In light of this, a gradual fixed grid to flexgrid migration is generally accepted in order to add these useful features to the network. In this article, we study the migration process where flexgrid is deployed in the network progressively, and review the main drivers and open issues induced by its deployment.

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.

An overview of routing methods in optical burst switching networks

In this article we present a survey of routing methods in Optical Burst Switching (OBS) networks. We begin with a description of routing approaches and follow the discussion with a detailed classification of routing algorithms in OBS. Afterwards, we discuss common OBS network loss models that are frequently used in routing optimization. As examples of such application, we present a linear and a non-linear formulation of a multi-path routing optimization problem with an indication on convenient resolution methods. The presented algorithms are appropriate for proactive load balancing routing and aim at the improvement of network-wide burst loss performance. To compare performance results, both methods are evaluated by simulation in a set of unified network scenarios.

Determining link weight system under various objectives for OSPF networks using a Lagrangian relaxation-based approach

An important traffic engineering problem for OSPF networks is the determination of optimal link weights. Certainly, this depends on the traffic engineering objective. Regardless, often a variety of performance measures may be of interest to a network provider due to their impact on the network. In this paper, we consider different objectives and discuss how they impact the determination of the link weights and different performance measures. In particular, we propose a composite objective function; furthermore, we present a Lagrangian relaxation-based dual approach to determine the link weight system. We then consider different performance measures and discuss the effectiveness of different objectives through computational studies of a variety of network topologies. We find that our proposed composite objective function with Lagrangian relaxation-based dual approach is very effective in meeting different performance measures and is computationally very fast.

Complexity of column generation in network design with path‐based survivability mechanisms

Abstract in Undetermined his survey deals with computational complexity of column generation problems arising in the design of survivable communication networks. Such problems are often modeled as linear programs based on noncompact multicommodity flow network formulations. These formulations involve an exponential number of path-flow variables, and therefore require column generation to be solved to optimality. We consider several path-based protection and restoration mechanisms and present results, both known and new, on the complexity of the corresponding column generation (also called pricing) problems. We discuss results for the case of single link or single node failures scenarios, and extend the considerations to multiple link failures. Further, we classify the design problems corresponding to different survivability mechanisms according to the structure of their pricing problem. Eventually, we show that almost all the encountered pricing problems are hard to solve for scenarios admitting multiple failures, while a great deal of them are NP-hard already for single failure scenarios. (Less)

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

Finding Failure-Disjoint Paths for Path Diversity Protection in Communication Networks

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