Video streaming methods have evolved greatly over the years. Today, the most prevalent technique to stream live and video on-demand is the adaptive HTTP streaming and is used by several commercial vendors. In this paper, we present an approximate analytic model for live adaptive streaming over HTTP. Using this model, we propose a new rate control algorithm that makes the rate transitions less frequent and increases the quality of experience for the viewer. Also, the model can be used to characterize the departure packet process at the video server. To the best of our knowledge, this is the first video traffic model for adaptive HTTP streaming to be reported in the literature.