Trip Distribution Analysis

a$.$ What is the primary purpose in calibrating the gravity distribution model and how

is the calibration process pursued in practice?

b$.$ You have been hired as a transportation planning consultant to carry out a

transportation planning study of a small town. The town has been divided into $3$

land use zones. The trip generation analysis has resulted in the target year zonal

trip productions and relative attractiveness as shown in the following table.

In order to perform the trip distribution analysis, a Gravity Model was calibrated

based on the base year data and resulted in the relationship between the friction

factor $F$ and the travel time $W,$ which is $F=\frac{1}{W}.$ Given the target year

predicted zonal travel time $W$ and socioeconomic adjustment factor $K,$ as follows,

apply the gravity model to calculate all interchange trip ends between all zones.

NOTE: The gravity model formula is given by the following:

$T_{ij}=P_i(\frac{A_j{F}_{ij}{K}_{ij}}{{\displaystyle \underset{x}{\overset{?}{}}}{A}_x{F}_{ix}{K}_{ix}})$

Where: $,T_{ij}$ is the trips between zone ${?}_{\text{I}}$ and zone $j$;

$P_i$ is the trip productions for zone I;

$A_j$ is the trip attractions for zone $j$;

$F_{ij}$ is the friction factor, given by $\frac{1}{W}ij$; and

$K_{ij}$ is the socioeconomic adjustment factor.