Problem $1$

i$.$ What is a node? Discuss two examples in which a node would be required in the coding of an urban area's road transport network.

ii$.$ What is a centroid? How is a centroid connected to the road network in a graph representation of an urban area's network.

iii. What is a link? State two types of links and describe under what conditions you would use each.

iv$.$ Briefly discuss three considerations in the definition of zone boundaries.

v$.$ Three routes connect an origin zone i to a destination zone j$.$ the respective performance functions for these routes are

$t_1=15+1\mathrm{.}5x_1$

and

$t_2=15+1\mathrm{.}4x_2$

and $t_3=20+0\mathrm{.}8x_3$

where the x$\text{'}$s are in thousands of vehicles per hour. During the peak$-$period, a total of $10,000$ vehicles from zone i to zone $j.$ An incremental assignment is to be performed with the total flow being divided into five equal parts. Perform the assignment and determine the flow and travel$-$time on each route