Software Defined Networking (SDN) has been preferred over traditional networking due to its dynamic nature in adapting the network structure. This agile nature of SDN imparts non-stationarity in traffic. In this work, we characterize the SDN traffic and study its behavior under dynamic conditions using Augmented Dickey Fuller (ADF) test. Later, we model the SDN under non-stationary conditions using queueing model and solve for average queue length at both controller and switch using Pointwise Stationary Fluid Flow Approximation (PSFFA). The analytical results have been validated through simulations. We develop congestion control algorithm based on (a) Proportional Integral Derivative (PID) control mechanism and (b) Dynamic Random Early Detection (DRED) control mechanism for SDN controller using the fluid flow model. Finally we demonstrate their effectiveness in stabilizing the queue length at the switch and controller under non-stationary conditions. In nut shell our work brings out the importance of the non-stationary behaviour of the traffic in the design and analysis of SDN and its control algorithms. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.