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Seminar “Dynamic Traffic Models in Transportation Science” at Schloss Dagstuhl
by [Han, Friesz, Yao 2013], [Cominetti, Correa, Larré, 2015].
(1) Compute a finite dominating walk set $\Wc'$
(2) Choose any initial flow $h^0 \in C$, $k \leftarrow 0$
(3) Repeat
(4) .. Calculate network loading for $h^k$ and costs $c$
(5) .. Find functions $v_i: [0,T] \to \IR$ s.th. f.a. $i \in I, \theta \in [0,T]$:
(0) .. .. $\sum_{(i,W) \in \Wc'} \left[h^k_{i,W}(\theta) - \alpha c_{i,W}(\theta) + v_i(\theta)\right]_+ = u_i(\theta)$
(6) .. Set $h^{k+1}_{i,W} \leftarrow \left[h^k_{i,W}(\theta) - \alpha c_{i,W}(\theta) + v_i(\theta)\right]_+$ and increment $k$
(7) Until $\frac{\norm{h^k-h^{k-1}}}{h^k} \leq \varepsilon$
for all unsaturated alternative walks $W'$ $\in D_{i,W}(h^*,\theta)$.
where $H_{i,W \to W'}(h,\theta,\varepsilon,\delta) \coloneqq (h'_{j,Q})$ with