## Abstract

Using a graph-theoretic formulation, a grooming in a SONET ring network may be interpreted as a decomposition of an undirected simple graph G=(V,E), where V corresponds to the n nodes in the ring, and each edge {i,j}∈E represents the traffic requirements for the primitive ring {i,j}. In G={G _{1},...,G_{s}}, the decomposition of G, each subgraph Gi specifies a set of primitive rings assigned to the same wavelength. If the maximum size set is c then G is a c-grooming. In this paper, bounding the maximum throughput tp̄(c,n,ℓ) of a c-grooming G is addressed, subject to each node being equipped with a limited number ℓ of adddrop multiplexers (ADMs). Naturally, restricting the number of ADMs limits the achievable throughput. For all ℓ, precise determinations of maximum throughput for grooming ratios c=2, 3, and 4 are given. These underlie substantially improved bounds for larger grooming ratios.

Original language | English (US) |
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Pages (from-to) | 10-16 |

Number of pages | 7 |

Journal | Journal of Optical Communications and Networking |

Volume | 3 |

Issue number | 1 |

DOIs | |

State | Published - Jan 1 2011 |

## Keywords

- Graph decompositions
- SONET ring
- Throughput maximization
- Traffic grooming

## ASJC Scopus subject areas

- Computer Networks and Communications