A study of upper and lower bounds for minimum congestion routing in lightwave networks

This paper considers the combined problem of finding allocation of wavelengths to the stations (configuration) and finding the associated routing of the traffic to minimize congestion (the amount of maximum flow on any link). This work presents efficient algorithms for computing both upper and lower bounds on the congestion. The upper bounds-to obtain approximate solutions of this problem-are based modification of two heuristics (i) variable depth local search, and (ii) simulated annealing. A more significant contribution is a lower bound computation based on building flow trees to find a lower bound on the total flow, and then distributing the total flow over the links provide a lower bound on the congestion. This technique yields a tool which can be used in evaluating the quality of heuristic algorithms, and determining a termination criteria during minimization. This technique can be applied to other problems with flow-based objectives. Performance of the heuristics is analysed, and compared via simulation studies. It is shown that the heuristics perform on the average, within 20% of the computed lower bound, and 15% better than the previous methods to solve this problem