Software-Defined Networks (SDN) dynamically modify the paths of Internet flows in response to the quality of service or security needs, and hence frequently modify traffic levels at network routers. Thus network routers often operate in the transient regime, rather than at steady-state, with significant impact on packet loss probabilities and delay. We, therefore, investigate the time-dependent performance of a small network of routers, modelled as G/G/1/N queueing stations.  A diffusion approximation is developed to predict the quality of service of the routers in the transient regime. Numerical examples show that the results in the transient regime can differ very significantly from the steady-state results, and therefore that the transient analysis must be taken into account in evaluating the performance of routers in a SDN network.