Editing Route assignment (section)

===Example===
An example from Eash, Janson, and Boyce (1979) will illustrate the solution to the nonlinear program problem. There are two links from node 1 to node 2, and there is a resistance function for each link (see Figure 1).  Areas under the curves in Figure 2 correspond to the integration from 0 to ''a'' in equation 1, they sum to 220,674.  Note that the function for link ''b'' is plotted in the reverse direction.

<math>
S_a  = 15\left( {1 + 0.15\left( {\frac{{v_a }}{{1000}}} \right)^4 } \right) 
</math>

<math> 
S_b  = 20\left( {1 + 0.15\left( {\frac{{v_b }}{{3000}}} \right)^4 } \right)
</math>

<math>
v_a  + v_b  = 8000
</math>

Figure 1: Two Route Network
[[Image:TwoRouteNetwork.png|center|500px|Figure 1 - Two Route Network]]

Figure 2: Graphical Solution to the Equilibrium Assignment Problem
[[Image:EquilibriumAssignment2.png|center|500px|Figure 2 - Graphical Solution to the Equilibrium Assignment Problem]]

Figure 3: Allocation of Vehicles not Satisfying the Equilibrium Condition
[[Image:EquilibriumAssignment3.png|center|500px|Figure 3 - Allocation of Vehicles not Satisfying the Equilibrium Condition]]

At equilibrium there are 2,152 vehicles on link ''a'' and 5847 on link ''b''.  Travel time is the same on each route: about 63.

Figure 3 illustrates an allocation of vehicles that is not consistent with the equilibrium solution.  The curves are unchanged.  But with the new allocation of vehicles to routes the shaded area has to be included in the solution, so the Figure 3 solution is larger than the solution in Figure 2 by the area of the shaded area.