Module 2: Transportation planning

Lecture 8 Trip distribution

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Definitions and notations

Trip matrix

The trip pattern in a study area can be represented by means of a trip matrix or origin-destination (O-D)matrix. This is a two dimensional array of cells where rows and columns represent each of the zones in the study area. The notation of the trip matrix is given in figure 1.

Figure 1: Notation of a trip matrix

The cells of each row $i$ contain the trips originating in that zone which have as destinations the zones in the corresponding columns. $T_{ij}$ is the number of trips between origin $i$ and destination $j$. $O_i$ is the total number of trips between originating in zone $i$ and $D_j$ is the total number of trips attracted to zone $j$. The sum of the trips in a row should be equal to the total number of trips emanating from that zone. The sum of the trips in a column is the number of trips attracted to that zone. These two constraints can be represented as: $\Sigma_j{T_{ij}} = O_i$ $\Sigma_i{T_{ij}} = D_j$ If reliable information is available to estimate both $O_i$ and $D_j$, the model is said to be doubly constrained. In some cases, there will be information about only one of these constraints, the model is called singly constrained.