Mobile networks have to cope with an ever increasing demand for video streaming, an application that imposes high quality requirements for user satisfaction. In this paper, we present an analytical model to calculate two important quality measures for streaming traffic, namely the video startup delay distribution and the buffer starvation probability. The queuing-theoretic model differs from related work by incorporating data flow dynamics of the considered cell, as well as the dynamics of fluctuating interference from neighboring cells, with the goal of accurately representing a multi-cellular environment. In this regard, we propose a finite-volume method to approximate the solution of the involved system of partial differential equations, where other approaches from comparable work were faced with numerical problems. We also evaluate two simplified versions of the model, where only the interference dynamics or all coupling terms are omitted, respectively. The model allows us to study the impact of different parameters on buffered video streaming performance. Additionally, we propose a user-centric metric to measure quality of experience (QoE). To the best of our knowledge, our approach is novel and has not been covered by comparable work. The presented results can help to design future cellular networks with enhanced video streaming experience.