This paper proposes a performance model for mobile networks carrying adaptive streaming traffic. The proposed model takes into account the flow dynamics in addition to the main parameters influencing the performance of adaptive streaming, such as the playout buffer and the video bit rates. We show how to compute several performance metrics like the average video bit rate, the deficit rate, defined as the probability of having an instantaneous throughput lower than the chosen video bit rate, and the average buffer surplus, related to the amount of data accumulated in the buffer. Considering the coexistence of multiple services and heterogeneous radio conditions that make the exact solution intractable, we propose a simple yet accurate approximation that is easy to integrate in the operator's dimensioning tools. Our numerical results investigate the performance trade-offs between the different parameters of the adaptive streaming service.