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Abstract: Task offloading, which refers to processing (computation-intensive) data at facilitating servers, is an exemplary service that greatly benefits from the fog computing paradigm, which brings computation resources to the edge network for reduced application latency. However, the resource-consuming nature of task execution, as well as the sheer scale of IoT systems, raises an open and challenging question: whether fog is a remedy or a resource drain, considering frequent and massive offloading operations? This question is nontrivial, because participants of offloading processes, i.e., fog nodes, may have diversified technical specifications, while task generators, i.e., task nodes, may employ a variety of criteria to select offloading targets, resulting in an unmanageable space for performance evaluation. To overcome these challenges of heterogeneity, we propose a gravity model that characterizes offloading criteria with various gravity functions, in which individual/system resource consumption can be examined by the device/network effort metrics, respectively. Simulation results show that the proposed gravity model can flexibly describe different offloading schemes in terms of application and node-level behavior. We find that the expected lifetime and device effort of individual tasks decrease as O(1/N) over the network size N , while the network effort decreases much slower, even remain O(1) when load balancing measures are employed, indicating a possible resource drain in the edge network.