Energy-Efficient Offloading in Edge Slicing with Non-Linear Power Functions

We focus on energy-efficient offloading strategies in a slicing-enabled large-scale edge network, or an "edge slicing" system, with different computing/storage components, on which the service capacities are dynamically released and reused by the incoming user requests. The offloading problem is challenged by its large problem size and the heterogeneity of the service components and user requests, leading to the high-dimensional state space of the underlying stochastic process. We formulate the problem in the manner of the restless-bandit-based (RB-based) resource allocation problem and generalize unrealistic previously made assumptions on specific forms of the power functions, such as linearity, convexity, and taking only binary power states. We adapt the RB-based resource allocation technique to the offloading problem. We quantify actions of selecting certain service components to serve requests through marginal rewards, which take consideration of both the history and future effects of the corresponding action. The marginal rewards exist in closed forms when assuming linear power functions, but it remains an open question in the non-linear case. We approximate the marginal rewards by introducing state-dependent coefficients that compensate for the undesirable effects of non-linearity. We propose a scheduling policy that always prioritizes the service components with the highest marginal rewards, which is simple and applicable in the large-scale case. In the special case with linear power functions, the policy becomes asymptotically optimal - it approaches optimality when the number of components tends to infinity. We numerically demonstrate the effectiveness and robustness of the proposed policy in practical situations with respect to energy efficiency.