Optimization in Telecommunication Networks

Network design and network synthesis have been the classical optimization problems intelecommunication for a long time. In the recent past, there have been many technologicaldevelopments such as digitization of information, optical networks, internet, and wirelessnetworks. These developments have led to a series of new optimization problems. Thismanuscript gives an overview of the developments in solving both classical and moderntelecom optimization problems.We start with a short historical overview of the technological developments. Then,the classical (still actual) network design and synthesis problems are described with anemphasis on the latest developments on modelling and solving them. Classical results suchas Menger’s disjoint paths theorem, and Ford-Fulkerson’s max-flow-min-cut theorem, butalso Gomory-Hu trees and the Okamura-Seymour cut-condition, will be related to themodels described. Finally, we describe recent optimization problems such as routing andwavelength assignment, and grooming in optical networks.operations research and management science;

Multicasting in All-Optical WDM Networks

n this dissertation, we study the problem of (i) routing and wavelength assignment, and (ii) traffic grooming for multicast traffic in Wavelength Division Multiplexing (WDM) based all-optical networks. We focus on the 'static' case where the set of multicast traffic requests is assumed to be known in advance. For the routing and wavelength assignment problem, we study the objective of minimizing the number of wavelengths required; and for the traffic grooming problem, we study the objectives of minimizing (i) the number of wavelengths required, and (ii) the number of electronic components required. Both the problems are known to be hard for general fiber network topologies. Hence, it makes sense to study the problems under some restrictions on the network topology. We study the routing and wavelength assignment problem for bidirected trees, and the traffic grooming problem for unidirectional rings. The selected topologies are simple in the sense that the routing for any multicast traffic request is trivially determined, yet complex in the sense that the overall problems still remain hard. A motivation for selecting these topologies is that they are of practical interest since most of the deployed optical networks can be decomposed into these elemental topologies. In the first part of the thesis, we study the the problem of multicast routing and wavelength assignment in all-optical bidirected trees with the objective of minimizing the number of wavelengths required in the network. We give a 5/2-approximation algorithm for the case when the degree of the bidirected tree is at most 3. We give another algorithm with approximation ratio 10/3, 3 and 2 for the case when the degree of the bidirected tree is equal to 4, 3 and 2, respectively. The time complexity analysis for both these algorithms is also presented. Next we prove that the problem is hard even for the two restricted cases when the bidirected tree has (i) depth 2, and (ii) degree 2. Finally, we present another hardness result for a related problem of finding the clique number for a class for intersection graphs. In the second part of the thesis, we study the problem of multicast traffic grooming in all-optical unidirectional rings. For the case when the objective is to minimize the number of wavelengths required in the network, given an 'a'-approximation algorithm for the circular arc coloring problem, we give an algorithm having asymptotic approximation ratio 'a' for the multicast traffic grooming problem. We develop an easy to calculate lower bound on the minimum number of electronic components required to support a given set of multicast traffic requests on a given unidirectional ring network. We use this lower bound to analyze the worst case performance of a pair of simple grooming schemes. We also study the case when no grooming is carried out in order to get an estimate on the maximum number of electronic components that can be saved by applying intelligent grooming. Finally, we present a new grooming scheme and compare its average performance against other grooming schemes via simulations. The time complexity analysis for all the grooming schemes is also presented

Wavelength assignment in all-optical networks for mesh topologies

All-Optical Networks employing Dense Wavelength Division Multiplexing (DWDM) are believed to be the next generation networks that can meet the ever-increasing demand for bandwidth of the end users. This thesis presents some new heuristics for wavelength assignment and converter placement in mesh topologies. Our heuristics try to assign the wavelengths in an efficient manner that results in very low blocking probability. We propose novel static and dynamic assignment schemes that outperform the assignments reported in the literature even when converters are used. The proposed on-line scheme called Round-Robin assignment outperforms previously proposed strategies such as first-fit and random assignment schemes. The performance improvement obtained with the proposed static assignments is very significant when compared with the dynamic schemes. We designed and developed a simulator in the C language that supports the 2D mesh topology with DWDM. We ran extensive simulations and compared our heuristics with those reported in the literature. We have examined converter placement in mesh topologies and proposed that placing converters at the center yields better results than uniform placement when dimension order routing is employed. We introduced a new concept called wavelength assignment with second trial that results in extremely low blocking probabilities when compared to schemes based on a single trial. Our proposed schemes are simple to implement and do not add to the cost. Thus we conclude that wavelength assignment plays more significant role in affecting the blocking probability than wavelength converters. We further conclude that static schemes without converters could easily outperform dynamic schemes thus resulting in great savings

PHYSICAL TOPOLOGY DESIGN AND ROUTING ALGORITHMS FOR DEGREE-CONSTRAINED FSO MESH NETWORKS

Free-space optical (FSO) mesh networks are emerging as broadband communication networks because of their high bandwidth (up to Gbps), low cost, and easy installation. However, there are two existing problems in the deployment of FSO networks: the physical topology design problem, and the routing problem. This dissertation presents an algorithm for the physical topology design of FSO mesh networks in order to enhance network reliability under defined degree constraint of each FSO node. The methodology presented enlarges the minimum angle between adjacent links at each node. Simulation results show that, compared to other methods, the proposed algorithm not only provides higher connectivity and lower delay for FSO networks, but also makes the FSO networks so constructed more tolerant in a dynamically changing environment. Further, this algorithm is enhanced to include the 3-dimensional (3-D) space, where the heights of the FSO nodes are not identical. This enhancement will apply to FSO nodes in difficult terrains where it is not feasible or desirable to have the FSO transceivers on a plane.This dissertation also addresses the routing problem in degree-constrained free-space optical (FSO) mesh networks. To solve the routing problem, four different routing algorithms are proposed. Their performances are evaluated through extensive simulations for a number of FSO mesh networks with different topologies and nodal degrees. The performance parameter against which these algorithms are evaluated is the mean end-to-end delay. The proposed least cost path (LCP) routing algorithm, which is based on minimizing the end-to-end delay, is considered as the bench mark. The performance of each of the other three algorithms is evaluated against the bench mark. The proposed minimum hop count with load-balancing (MHLB) routing algorithm is based on the number of hops between the source and the destination node to route the traffic. Simulation shows that the MHLB routing algorithm performs best in most cases compared with the other two. It results in minimum average delay and least blocked traffic

Compilation of thesis abstracts, June 2007

NPS Class of June 2007This quarter’s Compilation of Abstracts summarizes cutting-edge, security-related research conducted by NPS students and presented as theses, dissertations, and capstone reports. Each expands knowledge in its field.http://archive.org/details/compilationofsis109452750

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