Multi-access edge computing (MEC) has been an important and promising paradigm for offering computing services to mobile users with computation-intensive and latency-critical tasks. In this paper, we study a D2D collaboration based MEC system, where the service platform purchases resources from resource-rich collaborative D2D devices when the task arrival rate exceeds the platform’s capability for providing satisfactory QoS. The design objective is to maximize the platform profit while maximally satisfying the delay requirements of tasks. We define delay based utility functions for different participants and accordingly formulate the platform profit maximization problem as a Mixed Integer Non-Linear Programming (MINLP) problem. For the online case where future task arrivals are unknown in advance, we propose a reverse auction based task assignment and urgency-value based transmission scheduling algorithm (RAGM). We present the detailed algorithm design and deduce its computation complexity. We prove that RAGM satisfies individual rationality of all participants. We conduct extensive simulations and the results show the high performance of RAGM as compared with benchmark algorithms.