This work addresses the modeling of traffic generated by a video source operating in the context of adaptive streaming services. Traffic modeling is a key in several network design issues, such as dimensioning of core and access network resources, developing pricing procedures, carrying out cost-revenue studies. The actual traffic generated during a video streaming session depends on both the video source and the bandwidth variations imposed by lower communication layers. We propose a new traffic model that jointly encompasses these two effects. Specifically, we consider the modeling of the sequence of frame sizes generated by a video streaming source that dynamically adapts its rate to the available communication channel bandwidth using bitstream switching techniques. In order to represent the source rate adaptation to the random network bandwidth variations on the communication channel, we resort to a framework based on Hidden Markov Processes (HMPs). Our HMP model represents the first joint source and sending rate model in adaptive streaming literature. Thanks to effective modeling assumptions on the frame size probability density function (pdf), the HMP parameters can be estimated by means of the Expectation Maximization algorithm. The traffic model is validated by numerical simulations of a mobile adaptive video streaming scenario. We study the model's ability to predict several traffic statistics, including the traffic load of a video streaming source in different network points. Besides, we evaluate the model accuracy in characterizing aggregate video traffic resulting from multiplexing various video sources. In all experiments, we show that the proposed model is able to accurately capture the traffic characteristics. (c) 2013 Elsevier B.V. All rights reserved.