Revenue maximization in an optical router node using multiple wavelengths

In this paper, an optical router node with multiple wavelengths is considered. It is assumed that successful transmission of a packet of type j at station (= port) i of the router node gives a profit γij, but that there is also a positive probability that such a packet is dropped, causing a penalty θ _ij . This brings us to the formulation of a revenue optimization problem. Consider one fixed cycle, in which each station is assigned some visit time at one of the wavelengths. We aim to maximize the revenue by optimally assigning stations to wavelengths and, for each wavelength, by optimally choosing the visit times of the allocated stations within the cycle. This gives rise to a mixed integer linear programming problem (MILP) which is NP-hard. To solve this problem fast and efficiently we provide a three-step heuristic. It consists of (i) solving a separable concave optimization problem, then (ii) allocating the stations to wavelengths using a simple bin packing algorithm, and finally (iii) solving another set of separable concave optimization problems. We present numerical results to investigate the effectiveness of the heuristic and the advantages of having multiple wavelengths.