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UPDATE 1:

@Jendrusk: Thanks for your answer. YES, I am already using indexing. The columns id, source and target have BTREE index, whereas, geom_way column has gist type of index.

The query roughly takes 16ms. If you have any idea to optimize it further, I would be happy to know it. Thanks allot for the help. :)

@Jendrusk: I am already using indexing. The columns id, source and target have BTREE index, whereas, geom_way column has gist type of index.

The query roughly takes 16ms. If you have any idea to optimize it further, I would be happy to know it.

SOLUTION The first problem was with the projections. After solving it the problem was with the boundingbox. It was not big enough. The correct query is as below:

SELECT seq, id1 AS node, id2 AS edge, di.cost, ST_AsText(ST_Transform(geom_way, 4326)) FROM pgr_dijkstra('SELECT id, source, target, st_length(geom_way) as cost FROM hh_2po_4pgr WHERE geom_way && ST_MakeEnvelope(13.754883,45.636547,13.801408,45.647708, 4326)', 21000, 1855, false, false ) as di JOIN hh_2po_4pgr ON di.id2 = hh_2po_4pgr.id 

The query roughly takes 16ms. If you have any idea to optimize it further, I would be happy to know it. Thanks allot for the help. :)

So now the boundingbox subquery is giving back results but the whole query gives back an empty table. I am looking in to JOIN and the outer query at the moment.

So far, I tried the following query:

select * FROM pgr_dijkstra('SELECT id, source, target, st_length(geom_way) as cost FROM hh_2po_4pgr WHERE geom_way && ST_MakeEnvelope(13.794389, 45.636805, 13.775791, 45.638375, 4326)', 21000, 1855, false, false ) as di 

This gives back an empty table and in result of this the whole query gives an emtpy table. Therefore, now the problem is in pgr_dijkstra() function. Without the boundingbox subquery, it gives back results but with the boundingbox query it gives back an empty table.