DASH is new ISO/IEC MPEG and 3GPP standard for HTTP multimedia streaming that begins to be widely accepted in the industry. DASH is design to be flexible and support various multimedia formats. DASH unify the proprietary adaptive streaming solutions and suggests differing between them by using different behavioral approaches, each one best suited for the specific streaming application. Each behavior is determined by Adaptation Logic (AL), which decides according to the estimation of the network conditions and buffer state what is the best suitable segment to be requested from the streaming server. This work presents the drawback of current DASH standard and its vulnerability to variable bit rate stream encoding. We have found that the advertised bit rate for each quality layer that was dictated by the Media Presentation Description (MPD) isn't accurate for VBR streaming. Moreover, we suggest an Adaptive Buffer Moving Median (ABMM) buffer sensitive adaptation logic that will support its bandwidth estimation decisions based on the client buffer redundancy. The new method was found to be suitable for mobile network traffic which is characterized with large fluctuations with network bandwidth. Our proposed solution showed more than 20 percent better average PSNR improvement compared to the original VLC plug-in rate adaptation logic.