A PDE-based approach for the evaluation of probability of starvation in video streaming

Characterizing the dynamics of wireless channels is of crucial importance to the performance of application requiring quality of experience (QoE) guarantees like wireless-based time-sensitive video streaming applications. Therefore, in this study, we employ a novel approach to model the distribution of the total amount of data that can be transmitted over a wireless channel that is modeled by a multi-state Markov chain with an arbitrary number of states while permitting transitions to non-adjacent states. This is done by deriving a system of partial differential equations (PDEs) that characterizes the channel behavior. Then, the proposed system of PDEs is used to obtain the distribution of the total amount of data that can be transmitted through the wireless channel and evaluate the probability of starvation at the playback buffer in video streaming applications. The solution is presented analytically for a 2-state wireless channel with alternating good and bad intervals, and numerically for the general case of an n state channel. Moreover, the resulting distributions are verified for their accuracy by comparison with the results obtained using Monte-Carlo simulations. Finally, the cumulative distribution function (CDF) of the distribution is then used to evaluate the probability of starvation, based on which a rate control algorithm is proposed.