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Is there any way in QGIS to apply service area buffers e.g if I have a point on a map I wish to show the service coverage of 1 mile, 2 mile, 3 mile, breaks using the road network?

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Have a look at Alternatives to pgRouting question for network analysis tools. – radek Dec 17 '12 at 15:01
    
I found two interesting gists: gist.github.com/laurensversluis/137d903cd547f2f980f8 and gist.github.com/laurensversluis/344c8326e11a952e5fd8. perhaps they can be useful for answering this question – Thomas B Feb 6 at 22:16

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.

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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.

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QGIS-only 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.

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