Origin-destination matrices

As also already said in Sec. 2.2, 2.2, [[check]] origin-destination (OD) matrices contain the number of trips from $n$ starting points to $n$ destinations; it is therefore an $n \times n$ matrix. As also said, these matrices can refer to arbitrary time periods; these days, one typically uses ``morning peak'' and ``afternoon peak'' periods.

There are many ways to obtain origin-destination matrices. In transportation planning, the typical methods is to anchor them to the land use, and to use behavioral ``rates'' to determine trip frequencies (e.g. (71)). Residential areas ``produce'' so and so many trips per capita; commercial areas ``attract'' so and so many trips per capita. The matching of origins to destinations is done via gravity methods, i.e. the probability of a trip to go to a certain destination is some function of the attraction of this destination and the generalized cost of getting there.

Another method is to derive OD matrices from traffic counts. Here, one collects counts on as many links of the transportation network as possible, and then uses statistical estimators to derive OD matrices from this (e.g. (24)). Statistical estimators are necessary because the problem is under-determined. Sometimes, the two approaches are combined, i.e. the historical OD-matrices are used as starting points, but they are corrected via traffic counts (40).

Figure 21.1: Example of a sequence of activities for a person in Portland/Oregon. From R.J. Beckman.