It is widely known that deep neural networks (DNNs) can perform well in many applications, and can sometimes exceed human ability. However, their cost limits their impact in a variety of realworld applications, such as IoT and mobile computing. Recently, many DNN compression and acceleration methods have been employed to overcome this problem. Most methods succeed in reducing the number of parameters and FLOPs, but only a few can speed up expected inference times because of either the overhead generated from using such methods or DNN framework deficiencies. Edge-cloud computing has recently emerged and presents an opportunity for new model acceleration and compression techniques. To address the aforementioned problem, we propose a novel technique to speed up expected inference times by using several networks that perform the exact same task with different strengths. Although our method is based on edge-cloud computing, it is suitable for any other hierarchical computing paradigm. Using a simple yet strong enough estimator, the system predicts whether the data should be passed to a larger network or not. Extensive experimental results demonstrate that the proposed technique can speed up expected inference times and beat almost all state-of-the-art compression techniques, including pruning, low-rank approximation, knowledge distillation, and branchy-type networks, on both CPUs and GPUs. INDEX TERMS Edge computing, mobile computing, network compression and acceleration.