  We propose a model of discrete time dynamic congestion games with atomic
players and a single source-destination pair. The latencies of edges are
composed by free-flow transit times and possible queuing time due to capacity
constraints. We give a precise description of the dynamics induced by the
individual strategies of players and of the corresponding costs, either when
the traffic is controlled by a planner, or when players act selfishly. In
parallel networks, optimal and equilibrium behavior eventually coincides, but
the selfish behavior of the first players has consequences that cannot be
undone and are paid by all future generations. In more general topologies, our
main contributions are three-fold.
  First, we show that equilibria are usually not unique. In particular, we
prove that there exists a sequence of networks such that the price of anarchy
is equal to $n-1$, where $n$ is the number of vertices, and the price of
stability is equal to 1.
  Second, we illustrate a new dynamic version of Braess's paradox: the presence
of initial queues in a network may decrease the long-run costs in equilibrium.
This paradox may arise even in networks for which no Braess's paradox was
previously known.
  Third, we propose an extension to model seasonalities by assuming that
departure flows fluctuate periodically over time. We introduce a measure that
captures the queues induced by periodicity of inflows. This measure is the
increase in costs compared to uniform departures for optimal and equilibrium
flows in parallel networks.
