The Traffic Grooming Problem in Optical Networks with Respect to ADMs and OADMs: Complexity and Approximation

Abstract

All-optical networks transmit messages along lightpaths in which the signal is transmitted using the same wavelength in all the relevant links. We consider the problem of switching cost minimization in these networks. Specifically, the input to the problem under consideration is an optical network modeled by a graph G, a set of lightpaths modeled by paths on G, and an integer g termed the grooming factor. One has to assign a wavelength (modeled by a color) to every lightpath, so that every edge of the graph is used by at most g paths of the same color. A lightpath operating at some wavelength λ uses one Add/Drop multiplexer (ADM) at both endpoints and one Optical Add/Drop multiplexer (OADM) at every intermediate node, all operating at a wavelength of λ. Two lightpaths, both operating at the same wavelength λ, share the ADMs and OADMs in their common nodes. Therefore, the total switching cost due to the usage of ADMs and OADMs depends on the wavelength assignment. We consider networks of ring and path topology and a cost function that is a convex combination α·|OADMs|+(1−α)|ADMs| of the number of ADMs and the number of OADMs deployed in the network. We showed that the problem of minimizing this cost function is NP-complete for every convex combination, even in a path topology network with g=2. On the positive side, we present a polynomial-time approximation algorithm for the problem.

Minimizing equipment and energy cost in mixed 10G and 100G/200G filterless horseshoe networks with hierarchical OTN boards

“…In [12], the route of traffic demands is given as input, and the number of ADMs is then decided based on grooming of traffic and established lightpaths. Similarly, network cost minimization through an approximation algorithm is presented in [16]. The cost model accounts for both ADMs and optical components (OADMs) by deploying ADMs at end nodes of a lightpath and an OADM at every intermediate node.…”