Calculating driving distances from a number of post codes to a number of services usi

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I am hoping to calculate the driving distance from a large number of post codes to their nearest service.

I have used the RoadGraph plugin but this only calculates the distance and time from one point to another.

I already have my roads shapefile. I have previously used ArcGIS Network Analyst to calculate distances from centroids to the nearest service but unfortunately I don't have access to Network Analyst anymore.

Is there a way to do this in QGIS? Or are there any plans to add this type of tool to QGIS in the near future.

Thanks



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