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Abstract: How to collaboratively offload tasks between user devices (UDs), edge networks (ENs) and cloud data centers (CDCs) is a very interesting and challenging research topic. In this paper, we investigate the offloading decision, analytical modeling and system parameter optimization problem in a collaborative cloud–;edge–;device environment, aiming to trade off different performance measures. According to the differentiated delay requirements of tasks, we classify the tasks into delay-sensitive and delay-tolerant tasks. To meet the delay requirements of delaysensitive tasks and process as many delay-tolerant tasks as possible, we propose a cloud–;edge–;device collaborative task offloading scheme, in which delay-sensitive and delay-tolerant tasks follow the access threshold policy and the loss policy, respectively. We establish a four-dimensional continuous-time markov chain (CTMC) as the system model. By using Gauss-Seidel method, we derive the stationary probability distribution of the system model. Accordingly, we present the blocking rate of delay-sensitive tasks and the average delay of the two types of tasks. Numerical experiments are conducted and analyzed to evaluate the system performance, and, numerical simulations are presented to evaluate and validate the effectiveness of the proposed task offloading scheme. Finally, we optimize the access threshold in the EN buffer to obtain the minimum system cost with different proportions of delay-sensitive tasks.