Streaming video is becoming the predominant type of traffic over the Internet with reports forecasting the video content to account for 82% of all traffic by 2021. With significant investment on Internet backbone, the main bottleneck remains at the edge servers (e.g., WiFi access points, small cells, etc.). In this paper, we obtain and prove the optimality of a multiuser resource allocation mechanism operating at the edge server that minimizes the probability of stalling of video streams due to buffer under-flows. Our derived policy utilizes media presentation description files of clients that are sent in compliant to dynamic adaptive streaming over HTTP protocol to be cognizant of the deadlines of each of the media file to be displayed by the clients. Our policy allocates the available channel resources to the users, in a time division manner, in the order of their deadlines. After establishing the optimality of this policy to minimize the stalling probability for a network with links associated with fixed loss rates, the utility of the algorithm is verified under realistic network conditions with detailed NS-3 simulations.