Relaxed Schroedinger bridges and robust network routing

TL;DR

This paper introduces a relaxed Schroedinger bridge approach for robust network routing under random link failures, providing a fast-converging iterative algorithm based on a generalized Schroedinger system.

Contribution

It formulates a new relaxed transport problem for network routing with a novel Schroedinger system solution and an efficient iterative algorithm.

Findings

Unique solution obtained via generalized Schroedinger system

Fast convergence of the iterative algorithm

Effective handling of link failures in network routing

Abstract

We consider network routing under random link failures with a desired final distribution. We provide a mathematical formulation of a relaxed transport problem where the final distribution only needs to be close to the desired one. The problem is a maximum entropy problem for path distributions with an extra terminal cost. We show that the unique solution may be obtained solving a generalized Schroedinger system. An iterative algorithm to compute the solution is provided. It contracts the Hilbert metric with contraction ratio less than 1/2 leading to extremely fast convergence.