Latency-Aware Optimization of Submarine Communication Cable Systems With Trunk-and-Branch Topologies

Abstract

We provide an optimized design solution, called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lagrangian Fast Marching</i> (LAFM), for the most popular submarine cable system topology (trunk-and-branch), on the undersea surface of the earth modeled by a triangulated 2D manifold in a 3D Euclidean space. Design optimization is formulated as a Steiner minimal tree problem, where each Steiner node models a branching unit (BU). Our objective is to minimize the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">total</i> cost of the cable system, including both actual cable laying and BU costs as well as a measure of risk associated with location and topography. We minimize this total cost while imposing latency constraints limiting the length of cable between specified pairs of nodes. As most BUs in practice are Y-shaped, Steiner nodes are assumed to have three branches, in accord with the theory of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Steiner trees</i> in the Euclidean plane. This paper discusses methodological ideas related to the general problem and provides two algorithms, LAFM-I and LAFM-II, to solve the constrained optimization problem. We have proved that LAFM-I finds the optimal solution for cable systems with one latency constraint. We also show that LAFM-II provides a solution with provable bounds for problems with multiple latency constraints. We find optimal solutions (zero gap between the bounds) for examples with two and four latency constraints. We also demonstrate the superiority of our LAFM method over a simulated annealing (SA) based algorithm, and demonstrate the applicability of LAFM-I, LAFM-II and SA to realistic scenarios with real-world data.