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Multi-hop cellular networks (MCNs), which reduce the transmit power, mitigate the inter-cell interference, and improve the system performance, have been widely studied nowadays. The relay selection scheme is a key technique that achieves these advantages, and inappropriate relay selection causes frequent relay switchings, which deteriorates the overall performance. In this study, we analyze the conditions for relay switching in MCNs and obtain the expressions for the relay switching rate and relay activation time. Two mobile-based relay selection schemes are proposed on the basis of this analysis. These schemes select the relay node with the longest relay activation time and minimal relay switching rate through mobility prediction of the mobile node requiring relay and available relay nodes. We compare the system performances via simulation and analyze the impact of various parameters on the system performance. The results show that the two proposed schemes can obtain a lower relay switching rate and longer relay activation time when there is no reduction in the system throughput as compared with the existing schemes.