Delay-optimal Congestion-aware Routing and Computation Offloading in Arbitrary Network

TL;DR

This paper presents a novel framework for delay-optimal routing and computation offloading in heterogeneous edge networks, achieving global optimality through a geodesic-convex formulation and distributed algorithms.

Contribution

It introduces a globally optimal solution for delay-aware routing and offloading in arbitrary networks with nonlinear delays, extending to utility-based congestion control.

Findings

Significant delay reductions compared to baseline algorithms.

Global optimality achieved via geodesic-convex problem formulation.

Distributed algorithm converges to the global optimum.

Abstract

Emerging edge computing paradigms enable heterogeneous devices to collaborate on complex computation applications. However, for arbitrary heterogeneous edge networks, delay-optimal forwarding and computation offloading remains an open problem. In this paper, we jointly optimize data/result routing and computation placement in arbitrary networks with heterogeneous node capabilities, and congestion-dependent nonlinear transmission and processing delay. Despite the non-convexity of the formulated problem, based on analyzing the KKT condition, we provide a set of sufficient optimality conditions that solve the problem globally. To provide the insights for such global optimality, we show that the proposed non-convex problem is geodesic-convex with mild assumptions. We also show that the proposed sufficient optimality condition leads to a lower hemicontinuous solution set, providing stability against user-input perturbation. We then extend the framework to incorporate utility-based congestion control and fairness. A fully distributed algorithm is developed to converge to the global optimum. Numerical results demonstrate significant improvements over multiple baselines algorithms.