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A useful starting model treats a road network as a directed flow network and travelers as a divisible population in a nonatomic congestion game: an individual traveler has negligible effect on link congestion. For each source-sink pair $k$, fix a demand $d_k$ and a finite set ${\mathcal{P}}_k$ of allowed routes. Let $f_p\ge 0$ be the flow on route $p$, with ${\sum }_{p\in {\mathcal{P}}_k}{f}_p=d_k$. The link-route incidence matrix $A$ gives link loads $v=Af$. If link $e$ has delay ${\ell }_e(v_e)$, the route travel time isA Wardrop equilibrium is a feasible route-flow vector for which every used route has minimum travel time among the routes serving the same source-sink pair. Equivalently, there are numbers ${\lambda }_k$ such thatThe condition says that a traveler cannot lower their own delay by changing route. It does not assert that their choice minimizes the total delay experienced by all travelers. At a Wardrop equilibrium, unused routes may have exactly the same delay as used ones.

This static flow network model requires delay to depend on present link load, with each source-sink demand fixed. Models from queueing theory instead describe vehicles or packets as discrete customers whose delay depends on random arrivals, service and accumulated queues; a time-dependent model must also track changes of flow and travel-time propagation. Those models answer different questions from a static Wardrop equilibrium. The static model is nevertheless valuable because its route-choice condition has a precise convex optimization formulation, as developed next.