We want to determine the User Equilibrium $($UE$)$ flow patterns and the equilibrium travel time for the network illustrated below.

Consider City A as the origin and City C as the destination, with City B situated between them, where all the routes pass through it$.$

Given that $150$ individuals seek to travel from City A to City C:

A$)$

Determine the number of possible routes available for this journey. Also, enumerate all routes and specify the links utilized within each route.

B$)$

Assume that at the equilibrium, all the links are being used to travel from City A to City C$.$ Use the provided cost functions below, network diagram, and principles of User Equilibrium $($UE$)$ to:

I.

Find the traffic flow patterns for each link and route at equilibrium.

II$.$

Calculate the equilibrium travel time for each link and route.