A vehicular network with Road Side Units (RSUs) provides an efficient way to connect vehicles even on the move. However, due to high deployment and maintenance cost of RSUs, it is necessary to use fewer RSUs, such that the total cost is minimized. It is suggested that cellular networks, such as Long-Term Evolution (LTE), are capable of fulfilling the demands posed in vehicular network scenarios. Availability of high bandwidth, large coverage area, and low latency are some of the advantages of cellular networks, which help in overcoming the challenges of high-speed vehicular communication. In this paper, we propose a maiden approach to analyze the performance of a vehicular network with cellular infrastructure as a backbone. For this, we use mobile Femto Access Points (FAPs) as relays in place of RSUs. We model the network using M/M/m queue and compare the delay and throughput performance with traditional IEEE 802.11p vehicular networks. We also formulate an optimization problem and propose a subchannel power control algorithm to handle increased co-channel interference, which emerges due to high mobility of vehicles in the network. Our suggested approach shows improvement in terms of delay, throughput, and energy efficiency. The results are verified using extensive simulations.