A PDE-based Stochastic Model for the Amount of Data Transmitted over Multi-State Wireless Channels

Efficient characterization of the behavior of wireless channels is critical to the performance of any time-sensitive wireless application requiring a minimum quality of experience (QoE) such as video streaming applications. Hence, in this study, an analytical expression for the distribution of the total amount of data that can be transmitted over a multi-state wireless channel is derived. This is done by characterizing the channel behavior using a system of partial differential equations (PDEs). The proposed system of PDEs is then used to obtain the distribution of the total amount of data that can be transmitted through the underlying wireless channel. The solution is presented analytically for different situations where the channel could initially be at the steady state or at any arbitrary initial state. Moreover, using Monte-Carlo simulations, a comparative study is carried out to verify the accuracy of the resulting distributions.