  We consider a dynamic model of traffic that has received a lot of attention
in the past few years. Users control infinitesimal flow particles aiming to
travel from an origin to a destination as quickly as possible. Flow patterns
vary over time, and congestion effects are modeled via queues, which form
whenever the inflow into a link exceeds its capacity. Despite lots of interest,
some very basic questions remain open in this model. We resolve a number of
them:
  - We show uniqueness of journey times in equilibria.
  - We show continuity of equilibria: small perturbations to the instance or to
the traffic situation at some moment cannot lead to wildly different
equilibrium evolutions.
  - We demonstrate that, assuming constant inflow into the network at the
source, equilibria always settle down into a "steady state" in which the
behavior extends forever in a linear fashion.
  One of our main conceptual contributions is to show that the answer to the
first two questions, on uniqueness and continuity, are intimately connected to
the third. To resolve the third question, we substantially extend the approach
of Cominetti et al., who show a steady-state result in the regime where the
input flow rate is smaller than the network capacity.
