Optimization of p-cycle protection schemes in optical networks
Network survivability is a very interesting area of technical study and a critical concern in network design. As more and more data are carried over communication networks, a single outage can disrupt millions of users and result in millions of dollars of lost revenue. Survivability techniques involve providing some redundant capacity within the network and automatically rerouting traffic around the failure using this redundant capacity.  This thesis concerns the design of survivable optical networks using p-cycle based schemes, more particularly, path-protecting p-cycles, in link failure scenarios. Our study focuses on the placement of p-cycle protection structures assuming that the working routes for the set of connection requests are defined a priori. Most existing work carried out on p-cycles concerns heuristic algorithms or methods suffering from critical lack of scalability. Thus, the objective of this thesis is twofold: on the one hand, to propose scalable models and solution methods enabling to approach larger problem instances and on the other hand, to produce optimal or near optimal solutions with mathematically proven optimality gaps. For this, we rely on the column generation technique which is suitable to solve large scale linear programming problems. Here, column generation is used as an intelligent way of implicitly enumerating promising cycles to be part of p-cycle designs.  At first, we propose mathematical formulations for the master and the pricing problems as well as the first column generation algorithm for the design of survivable networks based on path-protecting p-cycles. The resulting algorithm obtains better solutions within reasonable running time in comparison with existing methods. Then, a much more compact formulation of the pricing problem is obtained. In addition, we also propose a new hierarchical decomposition method which greatly improves the efficiency of the whole algorithm and allows us to solve larger problem instances. As for integer solutions, two heuristic approaches are proposed to obtain good solutions.  Next, we dedicate our attention to a systematic comparison of p-cycles and classical shared protection schemes. We perform an accurate comparison by using a unified column generation framework to find provably good results. Afterwards, our study concerns an empirical evaluation of directed and undirected link- and path-protecting p-cycles under asymmetric traffic scenarios. We show how much additional protection cost results from employing bidirectional systems in such scenarios.   Finally, we investigate a column generation formulation for the design of p-cycle networks under availability requirements and obtain the first lower bounds for the problem.
Network Design Telecommunications Shared protection Column generation