Already most of north bound trains from Bengaluru / Mysuru are running via these routes:
1) Hassan, Arsikere / Tumakuru, Davangere, Hubballi, Belagavi, Miraj
2) Dharmavaram, Guntakal, Raichur, Kalburgi (Gulbarga), Solapur
3) Dharmavaram, Gooty, Kurnool, Kacheguda
So...
more... these two routes also should be given preference for north bound trains:
1) Hassan, Arsikere / Tumakuru, Chikjajur, Chitradurga, Ballari, Hosapete, Koppal, Gadag, Bagalkot, Vijayapura, Solapur
2) Dharmavaram, Guntakal, Ballari, Hosapete, Koppal, Gadag, Bagalkot, Vijayapura, Solapur