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Lower bound on number of ADMs in WDM rings with nonuniform traffic demands

Introduction: In traffic grooming, the lower bounds on the numbers of ADMs and wavelengths are important parameters in evaluating the grooming results. Although much work has been done on the grooming of traffic in WDM ring networks and the lower and upper bounds on the number of wavelengths and the upper bound on that of ADMs are relatively easy to derive, the lower bound on the number of ADMs has only been derived for uniform traffic demands [1–3] or in some special cases for nonuniform ones, in which the traffic demand was assumed to be a unit, i.e. either 0 or 1 [1, 2]. We have derived a lower bound on the number of ADMs with arbitrary nonuniform traffic demands [4]. However, that lower bound is not tight enough as to effectively evaluate the grooming results. In this Letter, a much tighter lower bound with nonuniform traffic demands is derived. In some cases, this new lower bound reaches the infimum.