Dev:MPMusicPlayerController

Described by apple, the MPMusicPlayerController class is, "An object used to play audio media items from the device's Music app library." 

Using the systemMusicPlayer property, you can control and access several things, including but not limited to, play, pause, shuffle, adding items, and getting the current playing item, all of these are documented here.

Private Methods
An undocumented property of the systemMusicPlayer is the requestController, using this object, you can control the queue shown in the music app.

Then to get the queue, iterate though the queue with the total number of songs.

To remove an item in the queue, Apple uses a system of commands and requests.

It is also possible to reorder songs in the queue.