Joint Data Compression and Computation Offloading in Hierarchical Fog-Cloud Systems

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.