In an edge-cloud system, mobile devices can offload their computation intensive tasks to an edge or cloud server to guarantee the quality of service or satisfy task deadline requirements. However, it is challenging to determine where tasks should be offloaded and processed, and how much network and computation resources should be allocated to them, such that a system with limited resources can obtain a maximum profit while meeting the deadlines. A key challenge in this problem is that the network and computation resources could be allocated on different servers, since the server to which a task is offloaded (e.g., a server with an access point) may be different from the server on which the task is eventually processed. To address this challenge, we first formulate the task mapping and resource allocation problem as a non-convex Mixed-Integer Nonlinear Programming (MINLP) problem, known as NP-hard. We then propose a zero-slack based greedy algorithm (ZSG) and a linear discretization method (LDM) to solve this MINLP problem. Experiment results with various synthetic tasksets show that ZSG has an average of $2.98\%$ worse performance than LDM with a minimum unit of 5 but has an average of $6.88\%$ better performance than LDM with a minimum unit of 15.

翻译：在边缘-云系统中，移动设备可将计算密集型任务卸载至边缘或云服务器，以保证服务质量或满足任务截止时间要求。然而，如何确定任务的卸载处理位置，以及如何为其分配网络与计算资源，使得有限资源的系统能在满足截止时间的同时获得最大收益，具有挑战性。该问题的关键难点在于：网络与计算资源可能分配在不同服务器上，因为任务卸载的目标服务器（例如带有接入点的服务器）与最终处理该任务的服务器可能不同。为解决这一挑战，我们首先将任务映射与资源分配问题形式化为一个非凸混合整数非线性规划（MINLP）问题（NP-难）。随后提出一种基于零松弛的贪心算法（ZSG）和一种线性离散化方法（LDM）来求解该MINLP问题。在多种合成任务集上的实验结果表明，与最小单位为5的LDM相比，ZSG平均性能仅低2.98%；而与最小单位为15的LDM相比，ZSG平均性能提升6.88%。