Have a look at the VoronoiDiagrammer transformer.

That should be able to do something similar.

You might have to create a rectangle for the entire area first.

As @erik_jan says, the VoronoiDiagrammer transformer is a way to create assigned areas based on strict spatial location (so the resulting polygon will be the area that is closest to the original point).

This is a good example.

However, if you want the areas to be based on the actual road network distance (or time) then I think you would need to the use the NetworkCostCalculator transformer. This article here shows one example. That example actually uses firehall zones that were calculated using the VoronoiDiagrammer, so it's a mix of techniques. Anyway, I think this will be a good starting point for you.

You'll also find some help here in previous questions - like this or this.

Thank you for the suggestions. I have created distance isochrones for a single service station, but I am a bit stuck on how to go from there to create catchment areas for the whole data set (about 100 points). Thanks in advance for any further suggestions.

The article you posted from Zimmerman using Grass Gis can be fully emulated using fme.

Snapper, topology builder network calculation and some supporting transformers.

Building a decent network is required.

Maybe post sample data, we can construct sample?