Problem No$.3$

Consider the following transportation network with two routes between an origin $"$O$"$ and a

destination $"$ D $".N_1$ and $N_2$ are the two nodes on the network. $t_1,t_2,t_3,$ and $t_4$ are the link

performance functions that give travel times on each link as a function of traffic volumes $,$

$q_3,$ and $q_4)$ on the links. The demand between $O$ and $D$ is $6$ vehicle trips per day.

a$.$ Assuming that both routes are used, estimate the traffic flows and total system travel time

$($i$.$e$.,$ the total travel time of all travelers between $O$ and $D)$ based on the user equilibrium

principle.

b$.$ To the network above, the government constructs a new road connecting nodes $N_1$ and $N_2$

with an objective to reduce the total travel time in the system. The resulting new network

and the performance function of the new link is shown in the figure below. Would you

expect the total system level travel time to reduce after adding an extra road to the system?

Explain based on the traffic flows you obtain from the user equilibrium principle applied

to the network below.