Traffic Grooming in Bidirectional WDM Ring Networks

TL;DR

This paper investigates minimizing the number of Add-Drop Multiplexers in bidirectional WDM ring networks by formulating the problem through graph decompositions, providing bounds, optimal constructions, and comparisons with unidirectional rings.

Contribution

It introduces a graph-theoretic formulation for ADM minimization, derives bounds, and constructs optimal solutions for specific grooming factors and ring sizes.

Findings

Established lower bounds for ADM minimization.

Provided optimal constructions for C=1, 2, 3, and specific cases of C>3.

Compared cost functions between unidirectional and bidirectional rings.

Abstract

We study the minimization of ADMs (Add-Drop Multiplexers) in optical WDM bidirectional rings considering symmetric shortest path routing and all-to-all unitary requests. We precisely formulate the problem in terms of graph decompositions, and state a general lower bound for all the values of the grooming factor $C$ and $N$, the size of the ring. We first study exhaustively the cases C=1, $C = 2$, and C=3, providing improved lower bounds, optimal constructions for several infinite families, as well as asymptotically optimal constructions and approximations. We then study the case $C>3$, focusing specifically on the case $C = k(k+1)/2$ for some $k \geq 1$. We give optimal decompositions for several congruence classes of $N$ using the existence of some combinatorial designs. We conclude with a comparison of the cost functions in unidirectional and bidirectional WDM rings.