Streaming videos over wireless networks suffers from low video quality due to network ability limitations. The quality of the channel and the characteristics of source play the major role in transmitting video stream over mobile environments. On failure of wireless video transmission, retransmission method was employed to improve the reliability of wireless link. However, retransmission of video leads to significant impact on energy consumption and bounded average waiting time is also increased. The longer waiting time on retransmission results in buffer starvation. Therefore, it is desirable to reduce the variable bit rate of transmitted video signal and increase the stability level when buffer starvation is occurs. In order to overcome such limitation, a technique named Response based Stabilization Analysis (RSA) using Distributed Optimality Bit Rate Allocation (RSA-DOBRA) is proposed in this paper. Initially, video stream is segregated into frames of different classes (i.e., size). Each frame is transmitted based on the variable bit rate response using Optimal Quantization process. Secondly, Linear Lyapunov Functions is employed with RSA to prove the stability of different bit rates on wireless video streaming. The application of Linear Lyapunov Function maintains the stability level of bit rate on different class of frame transmission on wireless link. Finally, Distributed Optimality Bit Rate Allocation uses the time slicing procedure to reduce the bounded average waiting time. RSA performs the time slicing based on multiplexed wireless video transmission on variable bit rate to avoid buffer starvation. RSA at the final stage reduces the energy consumption by improving the reliability of wireless link. Experiment is conducted on factors such as buffered starvation rate, waiting time on video frame transmission, and energy consumption rate.