Distance Transformation for Network Design Problems

International audienceWe propose a new generic way to construct extended formulations for a large class of network design problems with given connectivity requirements. The approach is based on a graph transformation that maps any graph into a layered graph according to a given distance function. The original connectivity requirements are in turn transformed into equivalent connectivity requirements in the layered graph. The mapping is extended to the graphs induced by fractional vectors through an extended linear integer programming formulation. While graphs induced by binary vectors are mapped to isomorphic layered graphs, those induced by fractional vectors are mapped to a set of graphs having worse connectivity properties. Hence, the connectivity requirements in the layered graph may cut off fractional vectors that were feasible for the problem formulated in the original graph. Experiments over instances of the Steiner Forest and Hop-constrained Survivable Network Design problems show that significant gap reductions over the state-of-the art formulations can be obtained

Analysis and optimization of highly reliable systems

In the field of network design, the survivability property enables the network to maintain a certain level of network connectivity and quality of service under failure conditions. In this thesis, survivability aspects of communication systems are studied. Aspects of reliability and vulnerability of network design are also addressed. The contributions are three-fold. First, a Hop Constrained node Survivable Network Design Problem (HCSNDP) with optional (Steiner) nodes is modelled. This kind of problems are N P-Hard. An exact integer linear model is built, focused on networks represented by graphs without rooted demands, considering costs in arcs and in Steiner nodes. In addition to the exact model, the calculation of lower and upper bounds to the optimal solution is included. Models were tested over several graphs and instances, in order to validate it in cases with known solution. An Approximation Algorithm is also developed in order to address a particular case of SNDP: the Two Node Survivable Star Problem (2NCSP) with optional nodes. This problem belongs to the class of N P-Hard computational problems too. Second, the research is focused on cascading failures and target/random attacks. The Graph Fragmentation Problem (GFP) is the result of a worst case analysis of a random attack. A fixed number of individuals for protection can be chosen, and a non-protected target node immediately destroys all reachable nodes. The goal is to minimize the expected number of destroyed nodes in the network. This problem belongs to the N P-Hard class. A mathematical programming formulation is introduced and exact resolution for small instances as well as lower and upper bounds to the optimal solution. In addition to exact methods, we address the GFP by several approaches: metaheuristics, approximation algorithms, polytime methods for specific instances and exact methods in exponential time. Finally, the concept of separability in stochastic binary systems is here introduced. Stochastic Binary Systems (SBS) represent a mathematical model of a multi-component on-off system subject to independent failures. The reliability evaluation of an SBS belongs to the N P-Hard class. Therefore, we fully characterize separable systems using Han-Banach separation theorem for convex sets. Using this new concept of separable systems and Markov inequality, reliability bounds are provided for arbitrary SBS

Layered graph approaches for combinatorial optimization problems

Extending the concept of time-space networks, layered graphs associate information about one or multiple resource state values with nodes and arcs. While integer programming formulations based on them allow to model complex problems comparably easy, their large size makes them hard to solve for non-trivial instances. We detail and classify layered graph modeling techniques that have been used in the (recent) scientific literature and review methods to successfully solve the resulting large-scale, extended formulations. Modeling guidelines and important observations concerning the solution of layered graph formulations by decomposition methods are given together with several future research directions

Topology-Constrained Network Design

International audienc

Performance Analysis and Design of Mobile Ad-Hoc Networks

We focus on the performance analysis and design of a wireless ad-hoc network using a virtual-circuit or reservation based medium access layer. In a reservation based MAC network, source nodes reserve a session's link capacity end-to-end over the entire path before sending traffic over the established path. An example of a generic reservation based MAC protocol is Unifying Slot Assignment Protocol (USAP). Any reservation based medium access protocol (including USAP) uses a simple set of rules to determine the cells or timeslots available at a node to reserve link capacity along the path to the next node. Given inputs of node locations, traffic pattern between nodes and link propagation matrices, we develop models to estimate blocking probability and throughput for reservation based wireless ad-hoc networks. These models are based on extending reduced load loss network models for a wireless network. For generic USAP with multiple frequency channels, the key effect of multiuser interference on a link is modeled via reduced available link capacity where the effects of transmissions and receptions in the link neighborhood are modeled using USAP reservation rules. We compare our results with simulation and obtain good results using our extended reduced load loss network models but with reduced available link capacity distribution obtained by simulation. For the case of generic USAP using a single frequency channel, we develop models for unicast traffic using reduced load loss network models but with the sharing of the wireless medium between a node and its neighbors modeled by considering cliques of neighboring interfering links around a particular link. We compare results of this model with simulation and show good match. We also develop models to calculate source-destination throughput for the reservation MAC as used in the Joint Tactical Radio System to support both unicast and multicast traffic. These models are based on extending reduced load loss network models for wireless multicast traffic with the sharing of the wireless medium between a node and its (upto 2 hop) neighbors modeled by considering cliques of interfering nodes around a particular node. We compare results of this model with simulation and show good match with simulation. Once we have developed models to estimate throughput and blocking probabilities, we use these models to optimize total network throughput. In order to optimize total throughput, we compute throughput sensitivities of the reduced load loss network model using an implied cost formulation and use these sensitivities to choose the routing probabilities among multiple paths so that total network throughput is maximized. In any network scenario, MANETs can get disconnected into clusters. As part of the MANET design problem, we look at the problem of establishing network connectivity and satisfying required traffic capacity between disconnected clusters by placing a minimum number of advantaged high flying Aerial Platforms (APs) as relay nodes at appropriate places. We also extend the connectivity solution in order to make the network single AP survivable. The problem of providing both connectivity and required capacity between disconnected ground clusters (which contain nodes that can communicate directly with each other) is formulated as a summation-form clustering problem of the ground clusters with the APs along with inter-AP distance constraints that make the AP network connected and with complexity costs that take care of ground cluster to AP capacity constraints. The resultant clustering problem is solved using Deterministic Annealing to find (near) globally optimal solutions for the minimum number and locations of the APs to establish connectivity and provide required traffic capacity between disconnected clusters. The basic connectivity constraints are extended to include conditions that make the resultant network survivable to a single AP failure. In order to make the network single AP survivable, we extend the basic connectivity solution by adding another summation form constraint so that the AP network forms a biconnected network and also by making sure that each ground cluster is connected to atleast two APs. We establish the validity of our algorithms by comparing them with optimal exhaustive search algorithms and show that our algorithms are near-optimal for the problem of establishing connectivity between disconnected clusters

IP modeling of the survivable hop constrained connected facility location problem

Abstract We consider a generalized version of the rooted connected facility location problem which occurs in planning of telecommunication networks with both survivability and hop-length constraints. Given a set of client nodes, a set of potential facility nodes including one predetermined root facility, a set of optional Steiner nodes, and the set of the potential connections among these nodes, that task is to decide which facilities to open, how to assign the clients to the open facilities, and how to interconnect the open facilities in such a way, that the resulting network contains at least λ edge-disjoint paths, each containing at most H edges, between the root and each open facility and that the total cost for opening facilities and installing connections is minimal. We study two IP models for this problem and present a branch-and-cut algorithm based on Benders decomposition for finding its solution. Finally, we report computational results

Energy management in communication networks: a journey through modelling and optimization glasses

The widespread proliferation of Internet and wireless applications has produced a significant increase of ICT energy footprint. As a response, in the last five years, significant efforts have been undertaken to include energy-awareness into network management. Several green networking frameworks have been proposed by carefully managing the network routing and the power state of network devices. Even though approaches proposed differ based on network technologies and sleep modes of nodes and interfaces, they all aim at tailoring the active network resources to the varying traffic needs in order to minimize energy consumption. From a modeling point of view, this has several commonalities with classical network design and routing problems, even if with different objectives and in a dynamic context. With most researchers focused on addressing the complex and crucial technological aspects of green networking schemes, there has been so far little attention on understanding the modeling similarities and differences of proposed solutions. This paper fills the gap surveying the literature with optimization modeling glasses, following a tutorial approach that guides through the different components of the models with a unified symbolism. A detailed classification of the previous work based on the modeling issues included is also proposed

WDM optical network: Efficient techniques for fault-tolerant logic topology design

The rapid increase of bandwidth intensive applications has created an unprecedented demand for bandwidth on the Internet. With recent advances in optical technologies, especially the development of wavelength division multiplexing (WDM) techniques, the amount of raw bandwidth available on the fibre links has increased by several orders of magnitude. Due to the large volume of traffic these optical networks carry, there is one very important issue---design of robust networks that can survive faults. Two common mechanisms to protect against the network failure: one is protection and another is restoration. My research focuses on studying the efficient techniques for fault-tolerant logical topology design for the WDM optical network. In my research, the goal is to determine a topology that accommodates the entire traffic flow and provides protection against any single fiber failure. I solve the problem by formulating the logical topology design problem as a MILP optimization problem, which generates the optimum logical topology and the optimum traffic routing scheme. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .S54. Source: Masters Abstracts International, Volume: 43-01, page: 0244. Adviser: Arunita Jaekel. Thesis (M.Sc.)--University of Windsor (Canada), 2004