In this paper, we propose a model of discrete time dynamic congestion games with atomic players. This approach allows to give a precise description of the dynamics induced by the individual strategies of players and to study how the steady state is reached, either when players act selfishly, or when the traffic is controlled by a planner. We model also seasonalities by assuming that departure flows fluctuate periodically with time. We focus mostly on simple networks and give closed form formulas for the long-run equilibrium and optimal latencies, as functions of the seasonality. We then derive computations and bounds on the price of anarchy. We also characterize optimal and equilibrium flows and show that, although they produce different costs, they coincide from some time onwards. 