Travel Demand Model

Homework #$2$

Due by ${11}^{th}$ Feb $11$:$59$ PM

The population of Town A is $14,000.$ Residents in Town A are desirous of participating in a number of daily activities. They have two choices

of where to access these activities:

locally, in their own town $($Town A$),$ or

in a neighboring, more cosmopolitan$,$ town $($Town B$).$

Towns A and B are connected by two roadways, Route #$1$ and Route #$2,$ as shown below.

Traffic on routes #$1$ and #$2$ is governed by the Greenshield's Fundamental Diagram of Traffic Flow, that relates the speed of travel to the

density of traffic on the roadway. The basic form of Greenshield's relationship is:

$S=S_o(1-\frac{D}{D_j})$;$V=S*D.$

The detailed parameter settings of each route are shown in Table $1.$

The travel distance between Town A and Town B by either Route #$1$ or Route #$2$ is $5$ miles. Residents of Town A can travel to activity

locations in Town A mostly by local streets. The average travel time to activities at locations in Town A for the residents of Town A is $3$

minutes, which is given in Table $1.$

The utility that each resident of Town A get from performing activities at each of the two locations, Town A and Town B$,$ is given by:

$U(x)=U_0(1-e^{-x})$

The values of $U_0$ and $$ for Town A and B are shown in Table $1.$

Problems:

Develop an appropriate supply curve for travel from Town A to Town B$,$ assuming travelers always select the shortest $($least time$)$ route.

Develop iso$-$utility curves for the demand for participation in activities at locations in Town A and Town B$,$ assuming that total utility is

equal to the sum of the utilities of participation in activities located in Town A and in Town B$.($Draw curves with

$U=8,9,10,12,15,20).$

Assuming all travel occurs during the period $10$:$00$am$-4$:$00$pm$,$ what will be the hourly volume of traffic on Route #$1$ during the period

$10$:$00$ am $-4$:$00$pm$?$ What will be the hourly volume of traffic on Route #$2$ during the period $10$:$00$ am $-4$:$00$pm$?$ In this problem, we assume

that the total travel time budget is $T_B,$ which is given in Table $1$ below.

Note: Please use the following parameters with your name to complete the problems. You can use the example in Lecture $2$ as the instruction.

Table $1$: Parameter Settings