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

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.