10.4. User equilibrium assignment (UE)

Try these first

1. 1.

   Define User Equilibrium in your own words.

   Hint

   Think about the concept of minimizing costs.

2. 2.

   What principle is User Equilibrium based upon?

   Hint

   Recall the key figure in transportation theory.

3. 3.

   What does User Equilibrium ensure?

   • No driver can reduce their travel costs by changing routes
   • All drivers take the same route
   • There are no congestions in the model

   Hint

   Focus on the definition of the principle at hand.

4. 4.

   Wardrop's principle states that:

   • True
   • False

   Hint

   Try to recall who proposed the principle.

5. 5.

   In a simplified urban scenario, you have two parallel routes from A to B with respective flow functions. Apply UE principles to model the flows and calculate the optimal route allocations between the two paths.

   Hint

   Remember to apply the flow conservation and the conditions of User Equilibrium.

6. 6.

   Given a network where you know the travel time functions for several routes, use a nonlinear programming approach similar to Frank-Wolfe to confirm User Equilibrium for these paths. Report final route costs.

   Hint

   Review the initial steps of the optimization process we discussed.