Drop cost and wavelength optimal two-period grooming with ratio 4

TL;DR

This paper determines the minimum drop cost and wavelength requirements for a two-period optical network grooming problem with ratio 4, using graph decomposition techniques to optimize resource allocation.

Contribution

It provides exact solutions for the minimum drop cost and wavelength count in two-period grooming with ratio 4, a novel extension of traffic grooming models.

Findings

Minimum drop cost for C=4 and C' in {1,2,3} is established.

Optimal wavelength requirements are determined for the specified parameters.

Graph decomposition methods are effectively applied to solve the grooming problem.

Abstract

We study grooming for two-period optical networks, a variation of the traffic grooming problem for WDM ring networks introduced by Colbourn, Quattrocchi, and Syrotiuk. In the two-period grooming problem, during the first period of time, there is all-to-all uniform traffic among $n$ nodes, each request using $1/C$ of the bandwidth; and during the second period, there is all-to-all uniform traffic only among a subset $V$ of $v$ nodes, each request now being allowed to use $1/C'$ of the bandwidth, where $C' < C$. We determine the minimum drop cost (minimum number of ADMs) for any $n,v$ and C=4 and $C' \in \{1,2,3\}$. To do this, we use tools of graph decompositions. Indeed the two-period grooming problem corresponds to minimizing the total number of vertices in a partition of the edges of the complete graph $K_n$ into subgraphs, where each subgraph has at most $C$ edges and where furthermore it contains at most $C'$ edges of the complete graph on $v$ specified vertices. Subject to the condition that the two-period grooming has the least drop cost, the minimum number of wavelengths required is also determined in each case.