In my previous company (O/B Operation was 40 FTE) we used Divine (formally eShare, formally Melita).
However other notable names would be:
Avaya Mosaix, Concerto (formally Davox), RoyalBlue/Rostrvm, and Genesys.
All solutions can be configured to initiate calls when an agent is available. However the more you start to limit the calls/agent ratio the more you move away from your predictive element - Finding the right balance for you is the game!
In the UK we have recommendations from the DMA (Closest thing to a O/B regulatory body) which advise all it's members to send a CLI, and make the CLI link to either a recorded message or live agent, and limit Nuisance Calls to 5%.