Module 2: Transportation planning

Lecture 8 Trip distribution

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Doubly constrained growth factor model

When information is available on the growth in the number of trips originating and terminating in each zone, we know that there will be different growth rates for trips in and out of each zone and consequently having two sets of growth factors for each zone. This implies that there are two constraints for that model and such a model is called doubly constrained growth factor model. One of the methods of solving such a model is given by Furness who introduced balancing factors $a_i$ and $b_j$ as follows:

$$T_{ij} = t_{ij}\times a_i\times b_j$$ (1)

In such cases, a set of intermediate correction coefficients are calculated which are then appropriately applied to cell entries in each row or column. After applying these corrections to say each row, totals for each column are calculated and compared with the target values. If the differences are significant, correction coefficients are calculated and applied as necessary. The procedure is given below:

1. Set $b_j$ = 1
2. With $b_j$ solve for $a_i$ to satisfy trip generation constraint.
3. With $a_i$ solve for $b_j$ to satisfy trip attraction constraint.
4. Update matrix and check for errors.
5. Repeat steps 2 and 3 till convergence.

Here the error is calculated as: $E= \Sigma{\vert O_i - O_i^1\vert}+\Sigma{\vert D_j - D_j^1\vert}$ where $O_i$ corresponds to the actual productions from zone $i$ and $O_i^1$ is the calculated productions from that zone. Similarly $D_j$ are the actual attractions from the zone $j$ and $D_j^1$ are the calculated attractions from that zone.