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.

Link Link Travel Time Function Variable Description

$11=0\mathrm{.}21+31$: Link $1$ travel time; $1$: Link $1$ traffic flow

$22=2+62$: Link $2$ travel time; $2$: Link $2$ traffic flow

$33=0\mathrm{.}13+13$: Link $3$ travel time; $3$: Link $3$ traffic flow

$44=0\mathrm{.}34+24$: Link $4$ travel time; $4$: Link $4$ traffic flow