Transient Behaviour of a Network Router

The broader use of Software Defined Network (SDN) controllers creates periodic changes in topology and traffic rates at routers that adapt the network to changes in network conditions. 
Thus the transient behaviour of network components, and in particular routers, is becoming of great interest.
Since standard queueing models are difficult to analyze under time-varying conditions, we propose a tractable diffusion approximation for both the transient and steady-state behaviour of a network router. In particular, the analysis provides the steady-state and transient delay and packet loss probability as a function of traffic load and other characteristics. Using these results, we show that when SDN routers change the paths of flows frequently, the network's behaviour may often be far from its steady-state behaviour. Therefore any network optimization conducted with the help of SDN should not be based on steady-state behaviour, but rather on some metric reated to the network time dependent behaviour.