Open Journal of Optimization, 2015, 4, 1-9 Published Online March 2015 in SciRes. http://www.scirp.org/journal/ojop http://dx.doi.org/10.4236/ojop.2015.41001 How to cite this paper: Kitsuwan, N., Siswanto, D.F. and Oki, E. (2015) Mathematical Model for Dynamic Pump-Wavelength Selection Switch. Open Journal of Optimization, 4, 1-9. http://dx.doi.org/10.4236/ojop.2015.41001 Mathematical Model for Dynamic Pump-Wavelength Selection Switch Nattapong Kitsuwan, Dwina Fitriyandini Siswanto, Eiji Oki Department of Communication Engineering and Informatics, The University of Electro-Communications, Tokyo, Japan Email: kitsuwan@uec.ac.jp Received 13 February 2015; accepted 3 March 2015; published 6 March 2015 Copyright © 2015 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract This paper presents a mathematical model based on dynamic pump-wavelength selection for an optical packet switch (OPS). In the OPS, multiple packets that carry the same wavelength from dif- ferent input ports could be addressed to the same output port at the same time slot. This condition is called wavelength contention. Of those contended packets, only one is forwarded to the output fiber while the others are dropped. Parametric wavelength conversion is used to convert the con- tended wavelengths into available non-contending wavelengths. The OPS based on the dynamic pump-wavelength selection scheme, where the pump-wavelengths are adjusted based on the re- quests in every time slot, uses a heuristic matching algorithm to minimize the number of packet losses. However, there is no guarantee that the heuristic algorithm outputs the optimum result. The mathematical model presented in this paper is used to confirm the performance of the heuris- tic matching algorithm for the DPS-based OPS. A simulation shows that the heuristic matching al- gorithm achieves the same performance as the optimum solution provided by the mathematical model. Keywords Optical Packet Switching, Wavelength Converter, Optimization 1. Introduction Optical packet switched (OPS) networks are emerging as a serious candidate for the evolution of optical tele- communication networks needed to support high-throughput services such as voice over IP (VoIP) and high quality video streaming on demand. In an optical packet network with OPSs interconnected with optical fibers running wavelength division multiplexing (WDM), packets are transmitted from source to destination without