Capacity, reliability, and latency are seen as key requirements of new emerging applications, namely Vehicle-to-Everything (V2X) and Machine Type Communication (MTC) in future cellular networks. Device-to-Device (D2D) communication is envisaged to be the enabler to accomplish the requirements for the applications as mentioned earlier. Due to the scarcity of radio resources, a hierarchical radio resource allocation, namely the sub-granting scheme, has been considered for the overlay D2D communication. In this paper, we investigate the assignment of underutilized radio resources from D2D communication to Device-to-Infrastructure (D2I) communication, which are moving in a dynamic environment. The sub-granting assignment problem is cast as a maximization problem of the uplink cell throughput. Firstly, we evaluate the sub-granting signaling overhead due to mobility in a centralized sub-granting resource algorithm, Dedicated Sub-Granting Radio Resource (DSGRR), and then a distributed heuristics algorithm, Open Sub-Granting Radio Resource (OSGRR) is proposed and compared with the DSGRR algorithm and no sub-granting case. Simulation results show improved cell throughput for the OSGRR compared with other algorithms. Besides, it is observed that the overhead incurred by the OSGRR is less than the DSGRR while the achieved cell throughput is yet close to the maximum achievable uplink cell throughput.