Maximizing the utility of large-scale Internet of Things (IoT) is an important issue in practice. In this paper, we attempt to improve the performance of IoT edge computing system (IoT ECS) from a perspective of task value, which decays with execution time. We consider such an IoT ECS which is composed of multiple mobile equipments (MEs) and edge nodes (ENs). Each ME holds a task with a certain task value decay curve (TVDC) that decides whether to execute locally or at the edge nodes. Further more, we use a system utility function to describe the overall performance of the network by trading-off task value, calculation cost, and network risk factor. We convert the IoT ECS utility maximization problem into a multi-knapsack and multi-dimensional knapsack problem and prove it's NP-hard. Then, we adopt the piecewise linearization method to conquer the non-linear, even non-convex challenge of the objective function, and develop a distributed task offloading scheme based on Lagrange relaxation framework (TOS-LRPLM). Finally, numerical experiments prove the effectiveness of our proposed strategies and its superiority to others.
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