Database based solution for TDSP (Fastest)

I have tried pgRouting in PostGres for finding shortest path

select d.*, bs.starttime, bs.endtime, bs.trip_id from pgr_dijkstra(
    'select id, source, target, traveltime as cost from my_table',
    19,
    21,
    directed := true
) d JOIN my_table bs on d.edge = bs.id;

The above doesn’t consider time as parameter. Before selecting the next edge, I want to check the time of the transport as well.

Eg:

A ---- > B (03.00PM) (travel time 5)

B ---- > C (3.30PM) (travel time 15)

B ---- > C (11:00AM) (travel time 10)

Current algorithm consider the path with travel time 10 (Without considering the time).

Is there a standard solution for this. I have seen lot of implementations like A* algorithm. I’m talking about half million edges.

Or is there any way to get a hook on previous node or next node while computing pgr algorithms ?