How to calculate Network Service Areas in QGIS?

A Solution can be found via:

"Using GIS for Decision Support in Emergency Medical Services" Example

Programs required:

QGIS (with GRASS)
OpenOffice
R 

"To conduct an analysis of ambulance service areas, Geographic Resources Analysis Support System (GRASS) was used within Quantum GIS (QGIS). GRASS is included with the QGIS download. One of the benefits of GRASS is that the .dbf files which contain the attribute data are stored in their own file folder. This is helpful when accessing the statistical data. Open source options available to do this are OpenOffice or R. "

Full Tutorial and Conclusion: http://gracilis.carleton.ca/CUOSGwiki/index.php/Using_GIS_for_Decision_Support_in_Emergency_Medical_Services

You can include the buffering (rather than polygon based) to your own data.

This answer reflects the 2012 situation. Check my newer answer below for a QGIS-only solution.

I've described how to calculate service areas aka catchment zones in Catchment Areas with pgRouting driving_distance() and related posts. All of them use QGIS and pgRouting - a routing extension for PostGIS databases.

QGIS-only answer

QGIS 3 provides out-of-the-box network analysis tools in its Processing toolbox. There are two service area tools: one to compute service areas around a single point and one to compute service areas for a whole layer of points:

---

Old answer

If you are comfortable with some Python scripting, have a look at the QGIS Network analysis library. The PyQGIS Cookbook contains a snippet on Areas of availability which can serve as a starting point.

Basically, you check the shortest path tree to find all vertices which are reachable with a certain maximum cost.

You can use the free Geoapify API Playground app to generate network service areas in GeoJSON format. GeoJSON is natively supported by QGIS and virtually any other GIS system.

Please check detailed instructions here

Disclaimer: I work for Geoapify