Algorithms for Restoration Planning in a Telecommunications Network

• Authors: S. Cwilich;M. Deng;D. F. Lynch;S. J. Philips;Jeffery Westbrook
• Venue: ALENEX '99 Selected papers from the International Workshop on Algorithm Engineering and Experimentation
• Year: 1999

One of the major tasks of telecommunications network planners is deciding where and how much spare capacity to build so that disrupted traffic may be rerouted in the event of a network failure. This paper presents an experimental study comparing two techniques for restoration capacity planning. The first, linear programming using column generation, produces optimal fractional solutions that can be integerized in practice for little extra cost. This approach is time-consuming, however, and for some networks of interest the linear programs are too large to be practically solvable. The second algorithm is a fast heuristic called LOCAL, which can be practically applied to much larger problem sizes than column generation. A fast linear-programming lower bound is used to measure the efficiency of the solutions. The purpose of the study was threefold: to determine how much benefit is obtained by using column generation, when the problem size is small enough that column generation is practical; to determine the quality of solutions produced by LOCAL on both small and large problems; and to investigate the utility of the lower-bound LP.We find that column generation produces networks whose restoration capacity cost is 10% to 16% less than those produced by LOCAL. Sometimes the total cost of the network is of primary interest, including both the cost of service and restoration capacity, and in this case the difference between column generation and LOCAL is 4% to 6%. Column generation is the method of choice for making final decisions about purchasing spare capacity. When millions are to be spent, running time is not a consideration, unless the computation simply will not complete in the available time. In such cases, the differential between column generation and LOCAL is small enough and consistent enough that LOCAL can safely be used. LOCAL is the method of choice for network design "spreadsheet" applications, where different architectures can be quickly compared, modified, and then compared again, and where a consistent approximation to the optimum is sufficient. The bound produced by the lower-bound LP is consistently extremely close to the true optimum, so the lower-bound LP can be effectively used to monitor the performance of both methods.