  We consider flows over time within the deterministic queueing model and study
the solution concept of instantaneous dynamic equilibrium (IDE) in which flow
particles select at every decision point a currently shortest path. The length
of such a path is measured by the physical travel time plus the time spent in
queues. Although IDE have been studied since the eighties, the efficiency of
the solution concept is not well understood. We study the price of anarchy for
this model and show an upper bound of order $\mathcal{O}(U\cdot \tau)$ for
single-sink instances, where $U$ denotes the total inflow volume and $\tau$ the
sum of edge travel times. We complement this upper bound with a family of quite
complex instances proving a lower bound of order $\Omega(U\cdot\log\tau)$.
