Module 2: Transportation planning

Lecture 9 Modal split

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Binary logit model

Binary logit model is the simplest form of mode choice, where the travel choice between two modes is made. The traveler will associate some value for the utility of each mode. if the utility of one mode is higher than the other, then that mode is chosen. But in transportation, we have disutility also. The disutility here is the travel cost. This can be represented as

$$c_{ij}=a_1t^{v}_{ij}+a_2t^{w}_{ij}+a_3t^{t}_{ij}+a_4t_{nij}+a_5F_{ij}+a_6\phi_j+\delta$$ (1)

where $t^v_{ij}$ is the in-vehicle travel time between $i$ and $j$, $t^w_{ij}$ is the walking time to and from stops, $t^t_{ij}$ is the waiting time at stops, $F_{ij}$ is the fare charged to travel between $i$ and $j$, $\phi_j$ is the parking cost, and $\delta$ is a parameter representing comfort and convenience. If the travel cost is low, then that mode has more probability of being chosen. Let there be two modes (m=1,2) then the proportion of trips by mode 1 from zone $i$ to zone $j$ is($P_{ij}^1$) Let $c_{ij}^1$ be the cost of traveling from zone $i$ to zone$j$ using the mode 1, and $c_{ij}^2$ be the cost of traveling from zone$i$ to zone $j$ by mode 2,there are three cases:

1. if $c_{ij}^2$ - $c_{ij}^1$ is positive, then mode 1 is chosen.
2. if $c_{ij}^2$ - $c_{ij}^1$ is negative, then mode 2 is chosen.
3. if $c_{ij}^2$ - $c_{ij}^1$ = 0 , then both modes have equal probability.