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The current travel time at time \(\theta\) on edge \(e\) is: \[c_e(\theta) := \tau_e + q_e(\theta)/\nu_e\]
A flow is in Instantaneous Dynamic Equilibrium (IDE) if the following holds:
Whenever positive flow enters an edge, this edge must lie on a currently shortest path towards the respective sink (w.r.t. \(c\)).
(we call such an edge \(vw\) active)
Goal of this Talk: Answer 24 questions about IDE flows:
Then: \(g \in K\) is IDE extension \(\iff \langle g, \mathcal{A}(g)\rangle = 0\) \(\iff \langle \mathcal{A}(g),g'g\rangle \geq 0\) f.a. \(g' \in K\)
Model  SingleSink Networks  MultiSink Networks  
Physical  Behavioral  Existence:  Termination:  Existence:  Termination: 
\(s_i\)
\(t_i\)
\(f_{i,e}^+(\theta)\)
\(q_{e}(\theta)\)
\((\tau_e, \nu_e)\)

IDEFlows only use currently shortest paths (active edges) 