Module 2: Transportation planning

Lecture 9 Modal split

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This relationship is normally expressed by a logit curve as shown in figure  1 Therefore the proportion of trips by mode 1 is given by

$$P_{ij}^1 = T_{ij}^1/T_{ij} = \frac{e^{-\beta{c_{ij}^1}}}{{e^{-\beta{c_{ij}^1}}+e^{-\beta{c_{ij}^2}}}}$$ (1)

This functional form is called logit, where $c_{ij}$ is called the generalized cost and $\beta$ is the parameter for calibration. The graph in figure 1 shows the proportion of trips by mode 1 ( $T_{ij}^1/T_{ij}$) against cost difference.

Figure 1: logit function