On Describing the Routing Capacity Regions of Networks

TL;DR

This paper refines the characterization of routing capacity regions in networks with multiple unicast sessions, providing a finite description based on network parameters and analyzing complexity for specific network types.

Contribution

It offers a finite description of the routing capacity region using properties of boundary solutions, improving upon the infinite linear inequalities characterization.

Findings

Finite description of routing capacity regions derived

Complexity results for undirected ring networks provided

Enhanced understanding of boundary solutions in capacity regions

Abstract

The routing capacity region of networks with multiple unicast sessions can be characterized using Farkas' lemma as an infinite set of linear inequalities. In this paper this result is sharpened by exploiting properties of the solution satisfied by each rate-tuple on the boundary of the capacity region, and a finite description of the routing capacity region which depends on network parameters is offered. For the special case of undirected ring networks additional results on the complexity of the description are provided.