Zones in Macro Transport Model described with "optimal" points: part I: Center of Gravity

This post reports on how I attempted to solved zone parameterization problem in transport models. This report consists of three parts:
1) Center of Gravity 
2) Optimal Access Point
3) Second Optimal Center of Gravity

Part I: Center of Gravity

Summary:

I created Visum network with reasonably big “zones” (i.e. counties). For each of the zones I locate centroid precisely in center of gravity and describe connectors with either average, or distribution of travel times from city/village to centroid. Calculations are done in Matlab, while database is accessed from Visum .ver file via COM object (‘Visum.Visum’). This kind of zone description seems more appropriate for modeling.

The next steps of this analysis can be found in those posts:  

Background:

Basic element of Demand Model in transport modeling is zones, elements of analysis area. Common practice is to split area (i.e. City) into number of zones. The zones are defined via boundaries, areas within boundaries, and “centroids” being virtual points representing the zone area. This discretization means that entire area of zone is presented as a single point. Most transport modeling packages (i.e. PTV Visum) model demand basing just on single points, beoing points when demand origins and destines. That is a handy, and computionally efficient  solution, but what does it mean for us when we model?

Transformation:

Let’s me show you how I parameterized areas being regions in one of my models.

I got GIS database consisting of:

·        Location of  place with information about their population (fig.1)

·        Transport network (roads + railway) (fig.2)

·        Administrative division (zones) (fig.1+2) (each zone was about 50k inhabitants, 2k km²)

That was enough to try to define zones more properly. When Zones are aggregated we assume each travel starts at centroid not at real point of departure (city inside region). That means we are losing some of network information. My analysis shows how can we partially overcome this discretization issue.

First I calculated “Center of gravity” for each zone:

Which was good approximation to pecisely locate centroid of area. During calculation I gained data about average distances to centroid and I was able to generate histogram of the distances for area.

So now the zone is defined much more precisely and we can add connector time (with distributions) to overall travel times. Thus we can have much better estimate i.e. for accessibility.

See other posts being continuation of those characteristics (http://wieledrog.blogspot.com/2011/06/optimal-access-point.html)