With the development of Internet of Things (IoT) technology,its application scenarios have exploded recently,and such applications are generally delay-sensitive and resource-constrained.It is a focused issue in the way of offloading the real-time tasks under the condition of limited resource.Besides,it is a NP-hard combinatorial optimization problem to allocate limited computational resources for the real-time tasks.To solve this problem,this paper proposes a real-time resource management algorithm based on Lyapunov optimization,aiming at stabilizing the virtual queues while optimizing the total power consumption and total utility.Firstly,the optimization model for the total power consumption and weighted total utility is proposed under the constraint of computation and communication resources.This model contains of two virtual buffer queues,and tasks are unloaded in a device-to-device (D2D) scheduling model.Then,an optimization algorithm is proposed based on Lyapunov optimization to decompose the joint long-term average sum energy consumption and sum utility optimization problem into a series of real-time optimization problems.To solve these problems,a greedy-based matching algorithm is proposed.Experimental results demonstrate that the performance of the proposed algorithm is 8.6% better than the best result of random method and can approximate the exhaustive attack method under different connection degrees.