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

2025-06-16

AI Summary

This work addresses end-to-end latency minimization in arbitrary heterogeneous edge networks by jointly optimizing congestion-aware data/result routing and computational offloading decisions. To capture node capability heterogeneity and nonlinear, congestion-dependent transmission and processing delays, we formulate the first geodesically convex optimization model for this problem. We derive a sufficient global optimality condition based on the Karush–Kuhn–Tucker (KKT) conditions and establish lower semicontinuity of the solution set to ensure robustness against parameter perturbations. Furthermore, we design a fully distributed algorithm with provable convergence to the global optimum. Experiments demonstrate that our approach significantly reduces end-to-end latency compared to multiple baseline methods, while improving resource utilization and system fairness. It also supports utility-driven congestion control and admits natural extensions for fairness enhancement.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Non-convex Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Optimize routing and offloading in heterogeneous edge networks
• Address congestion-dependent nonlinear transmission delays
• Ensure global optimality with distributed algorithm convergence

Innovation

• Joint optimization of routing and computation offloading
• Geodesic-convexity for global optimality
• Distributed algorithm for congestion control