### Abstract

In this paper, a few models for optical router nodes are considered. The stations (ports) of such a node try to transmit packets. Successful transmission of a packet of type j at station i gives a profit γ_{ij}, but there is also a positive probability that such a packet is dropped, causing a penalty θ_{ij}. Consider one fixed cycle (frame), in which each station is assigned some visit time. The goal is to choose the visit times in such a way that the revenue is maximized. In our first model there is only one wavelength, and we take the finiteness of buffers into account. The revenue maximization problem is shown to be separable concave, thus allowing application of a very efficient algorithm. In our second model we allow multiple 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. Finally, some model variants are briefly discussed.

Original language | English |
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Article number | 102108 |

Number of pages | 15 |

Journal | Performance Evaluation |

Volume | 140-141 |

Early online date | 7 May 2020 |

DOIs | |

Publication status | Published - 1 Jul 2020 |

### Keywords

- Finite buffer
- Multiple wavelengths
- Optical node
- Optical routing
- Optimization
- Revenue

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## Cite this

*Performance Evaluation*,

*140-141*, [102108]. https://doi.org/10.1016/j.peva.2020.102108