I did implement an A* routing "offline" routing algorithm based on GTFS data + walking paths (OptiTravel) and built a GTFS server (to easily serve the data, do geospatial queries, ...) a few years ago. Granted that this was a university project, for some cities the calculation was rather intensive (e.g: London). I might be wrong though.
[1]: https://github.com/denysvitali/optitravel
[2]: https://github.com/denysvitali/gtfs-server