We present a model of a Software Defined Network (SDN) where frequent changes in routing and traffic rates at routers are needed to respond to the security, quality of service (QoS), and energy savings requirements of applications such as the Internet of Things.
Such frequent path and traffic changes introduce time-dependent network behaviours, and standard queueing models are not well adapted to analyse the transient regime, we propose a tractable diffusion approximation for both the transient and steady-state behaviour.
Our model can represent any network topology transmitting time-dependent flows with routing changes, and computes queue length and delay distributions at each network node and along complete paths between senders and receivers. 
Using realistic router parameters, we show that transients occupy a significant fraction of system time, so that the optimisation conducted with SDN controllers needs to include the effect of time-dependent behaviours.