  We study dynamic network flows and introduce a notion of instantaneous
dynamic equilibrium (IDE) requiring that for any positive inflow into an edge,
this edge must lie on a currently shortest path towards the respective sink. We
measure current shortest path length by current waiting times in queues plus
physical travel times. As our main results, we show: 1. existence and
constructive computation of IDE flows for single-source single-sink networks
assuming constant network inflow rates, 2. finite termination of IDE flows for
multi-source single-sink networks assuming bounded and finitely lasting inflow
rates, 3. the existence of IDE flows for multi-source multi-sink instances
assuming general measurable network inflow rates, 4. the existence of a complex
single-source multi-sink instance in which any IDE flow is caught in cycles and
flow remains forever in the network.
