Reliability of Wireless Mesh Networks with directional antennas

The paper is devoted to modeling and optimization of reliable wireless mesh networks that employ directional antennas. We introduce two mixed-integer programming formulations that allow to simultaneously characterize routing patterns and transmission schedules. The first model allows for maximizing the minimal flow in a network. The second model involves reliability constraints and aims at minimizing the number of used directional antennas. In both cases locations of mesh routers are known. However, the number of installed radio interfaces and their directions are subject to optimization. We discuss a way of solving a cost minimization problem based on the introduced characterization, and present an extensive numerical study that illustrates the efficiency of the solution algorithm

A polynomial multicommodity flow problem with difficult path generation

In the paper we consider a commonly known network design problem with demand restoration assuming stub release. No compact linear programming (LP) formulation for the problem is known, and all known non-compact LP formulations of the problem require NP-hard path generation (pricing). Therefore, the problem itself is suspected to be NP-hard - this, however, is not actually known. The main result of our paper reveals a special case of the basic problem for which the resulting non-compact LP formulation still has an NP-hard pricing problem, the corresponding compact LP formulation is not known either, but the problem itself is polynomial. The considered special case assumes only one failing link so that all the links but one are assumed to be 100% reliable. The constructed case of a polynomial multicommodity flow problem with difficult path generation is of interest since no such problem is, to the best of our knowledge, widely known

Failure disjoint paths

Given a set of commodities and a network where some arcs can fail while others are reliable, we first consider the problem of computing a minimum-cost pair of paths not sharing failing links. If a reliable link belongs to both paths then its cost is counted only once. We show that this problem can be solved in strongly polynomial time. Second, we consider a routing problem where each commodity can be split among pairs of failure-disjoint paths. We present a compact linear formulation of the problem. Also three non-compact formulations solvable by column generation are introduced. All formulations are numerically compared

Elastic Multi-Layer Resilient IP-over-Flexgrid Networking: Detailed Cost Analysis with Bandwidth-Variable Transponders

We introduce a mixed-integer optimization model for two-layer IP-over-Flexgrid networks, and present a cost study performed using the CPLEX package for the introduced model. The study concerns a generic German network with 12 nodes and 20 links in the optical layer, and a set of six IP traffic matrices with increasing demand volumes. The optimization assumes a hot-standby mechanism in the optical layer to make the network resilient to cable cuts. The dominant cost drivers are bandwidth-variable transponders. The numerical results reveal that due to the huge spectral capacity of a single fiber, the spectrum allocation problem simplifies significantly in practice. However, the routing problem minimizing the total cost of employed transponders becomes a challenge, but when appropriately approached and solved, can bring reductions in costs of up to 10%

Flow adjustment methods for survivable networks

The presented study deals with a specific rerouting strategy for protecting traffic flows in communication networks called Flow Adjustment Routing. The strategy is designed to handle partial link failures. We present two variants of the strategy and analyze their pros and cons. We show that the initial strategy is not directly implementable to cope with severe link failures such as total link failures. Therefore, we propose a restricted flow adjustment version as well as its distributed variant that can be used for the total link failures case. Numerical experiments for different settings and test networks illustrate the findings

After failure repair optimization in dynamic flexgrid optical networks

We introduce the problem of reoptimizing the network after a link failure has been repaired as an effective way for reducing capacity usage and improving network performance. Numerical results show gains higher than 42%

Exact Approach to Reliability of Wireless Mesh Networks with Directional Antennas

The paper is devoted to modeling and optimization of reliable wireless mesh networks that employ directional antennas. We introduce two mixed-integer programming formulations that allow to simultaneously characterize routing patterns and transmission schedules. The first model allows for maximizing the minimal flow in a network. The second model involves reliability constraints and aims at minimizing the number of used directional antennas. In both cases locations of mesh routers are known. However, the number of installed radio interfaces and their directions are subject to optimization. We discuss a way of solving a cost minimization problem based on the introduced characterization, and present an extensive numerical study that illustrates the efficiency of the solution algorithm. We also provide an algorithm capable of verifying feasibility of obtained solutions. Moreover, in rare cases of failed verification, the algorithm provides additional constraints that should be added to the problem