Attempting to predict these assignments are nearly impossible and that is especially true for the bullpens. Any number of pitchers could end up in the bullpens but I am going to take some guesses.
AAA: Jared Hughes, Daniel Moskos, Justin Wilson, Bryan Morris, Jo-Jo Reyes, Aaron Poreda, Ryota Igarashi
Any number of pitchers could end up here. Basically there are three types of pitchers who make up a AAA bullpen. One is major league depth which in the case is Hughes and Moskos, another are prospects in the case that is Wilson and Morris. Finally their are organizational depth pitchers and that is who will round out the bullpen. My guess is it will be Reyes, Poreda and Igarashi filling these roles but Slaten, Kensing, Alderson, Crotta, Wood, Johnson, Colla, McSwain and others are also possibilities.
AA: Matt McSwain, Jose Diaz, Diego Moreno, Tim Alderson, Duke Welker, Brian Leach, Tyler Waldron
A+: Zac Fuesser, Victor Black, Jhonathan Ramos, Quinton Miller, Porfirio Lopez, Casey Sadler, Jason Townsend
A: Matt Benedict, Kevin Decker, Emmanuel De Leon, Orlando Castro, Vincent Payne, Rinku Singh, Kevin Kleis
To be honest I have no clue about any of the bullpens below AAA. There are so many arms that are possibilities that anything I post would just be a wild guess. So basically all I did was try and pick 7 pitchers I see pitching at that particular level this season.