Abstract: How to collaboratively offload tasks between user devices, edge networks (ENs), and cloud data centers is an 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 delay-sensitive 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 as the system model. By using the 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 these 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.

Key words: Edge computing; Offloading scheme; Cloud-edge-device collaboration; Markov chain; Cost function

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