Long-Term Evolution (LTE) was implemented to fulfill and satisfy users' needs as well as their demands for an improvised, fast and efficient Quality of service (QoS). A minimal aggregate of waiting time in return would give users a better Quality of experience (QoE). Real-time service packet scheduling is an important process in allocating resources to users. An efficient packet scheduling scheme will be able to cater fairly and efficiently to its users in the LTE network. Hence, studies are performed focusing on real-time traffic which includes video as well as Voice over Internet Protocol (VoIP) transmissions. In this work, the existing exponential rule (EXP rule) is utilized to benchmark our proposed packet scheduling techniques so that we are able to further evaluate the scheduling performance. In response to the increasing likelihood of losing packets in the EXP rule's algorithm and maximizing the throughput rate, several schemes have been experimented with. The proposed schemes include 1) simplified EXP rule (sEXP Rule), 2) modified EXP rule (mEXP Rule), 3) EXP rule with maximum throughput (MT) (EXP_MT Rule), and 4) enhanced EXP rule with MT (E2M). By adding MT as a weight to the EXP rule, the throughput is maximized, thus providing higher throughput rates for real-time and non-real-time traffic. The simulation results show that the sEXP rule has a better performance in throughput, packet loss rate (PLR), and spectral efficiency for video traffic. Aside from this, our proposed E2M rule performs better than the benchmark EXP rule and outperforms the other proposed schemes, as well. It is observed that the E2M rule has better QoS support for real-time transmission in terms of delay, packet loss, throughput and spectral efficiency, within the LTE network. Hence, our proposed E2M rule is an enhancement of the benchmark EXP rule, which is commonly used in LTE packet scheduling.