The poor capacity at cell boundaries is not enough to meet the growing demand and stringent design which required high capacity and throughput irrespective of user's location in the cellular network. In this paper, we propose new schemes for an optimum fixed relay node (RN) placement in LTE-A cellular network to enhance throughput and coverage extension at cell edge region. The proposed approach mitigates interferences between all nodes and ensures optimum utilization with the optimization of transmitted power. Moreover, we proposed a new algorithm to balance the transmitted power of moving relay node (MR) over cell size and providing required SNR and throughput at the users inside vehicle along with reducing the transmitted power consumption by MR. The numerical analysis along with the simulation results indicates that an improvement in capacity for users is 40% increment at downlink transmission from cell capacity. Furthermore, the results revealed that there is saving nearly 75% from transmitted power in MR after using proposed balancing algorithm. ATDI simulator was used to verify the numerical results, which deals with real digital cartographic and standard formats for terrain.