Question $7[15$ marks$]$

Consider the following road network with one $OD$ pair from $A$ to $B_2$ and there are five links connecting A and B $.$ The link performance functions of the five links are shown in the following figure. Travel demand from A to B is $q=1000.$

What is the All$-$or$-$nothing assignment $($AON$)$ result on the above network? What is the total travel time under the AON assignment? $[3$ marks$]$

What is the Deterministic User Equilibrium $($UE$)$ assignment resul$]$ on the above network? What is the total travel time under the UE assignment? $[5$ marks$]$

What is the objective function for System Optimal $($SO$)$ assignment n the above network? $($You do not need to solve it$.)[2$ marks$]$

What is the objective function for Stochastic User Equilibrium $($SUE$)$ assignment on the above network? $($You do not need to solve it$.)$

If we can design a toll on each link, how we set the toll such that UE equals SO$?[3$ marks$]$