Shortest path from points in one layer to points in another layer via roads in QGIS

I'm looking for a way to calculate the shortest path from addresses to subway stations via a network of roads.

I have the Road Graph plugin, however, the addresses and subway stations are point layers that do not overlap with vertices in the roads layer.

In QGIS, is there a way to calculate the shortest distance from the address/subway station points to the roads, create vertices at those locations, then calculate the shortest distance via the roads network?

• black squares - addresses


• white circles - subway stops


• gray lines - roads