Data compression (DC) has the potential to significantly improve the computation offloading performance in hierarchical fog-cloud systems. However, it remains unknown how to optimally determine the compression ratio jointly with the computation offloading decisions and the resource allocation. This optimization problem is studied in this paper where we aim to minimize the maximum weighted energy and service delay cost (WEDC) of all users. First, we consider a scenario where DC is performed only at the mobile users. We prove that the optimal offloading decisions have a threshold structure. Moreover, a novel three-step approach employing convexification techniques is developed to optimize the compression ratios and the resource allocation. Then, we address the more general design where DC is performed at both the mobile users and the fog server. We propose three algorithms to overcome the strong coupling between the offloading decisions and the resource allocation. Numerical results show that the proposed optimal algorithm for DC at only the mobile users can reduce the WEDC by up to 65% compared to computation offloading strategies that do not leverage DC or use sub-optimal optimization approaches. The proposed algorithms with additional DC at the fog server lead to a further reduction of the WEDC.

中文翻译：

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分层雾云系统中的联合数据压缩和计算卸载

数据压缩 (DC) 有可能显着提高分层雾云系统中的计算卸载性能。然而，如何结合计算卸载决策和资源分配来最佳地确定压缩比仍然未知。本文研究了这个优化问题，我们的目标是最小化所有用户的最大加权能量和服务延迟成本 (WEDC)。首先，我们考虑仅在移动用户处执行 DC 的场景。我们证明了最佳卸载决策具有阈值结构。此外，开发了一种采用凸化技术的新型三步法来优化压缩比和资源分配。然后，我们讨论更通用的设计，其中 DC 在移动用户和雾服务器上执行。我们提出了三种算法来克服卸载决策和资源分配之间的强耦合。数值结果表明，与不利用 DC 或使用次优优化方法的计算卸载策略相比，所提出的仅针对移动用户的 DC 最优算法可以将 WEDC 减少多达 65%。在雾服务器上具有额外 DC 的建议算法导致 WEDC 的进一步减少。