This will depend on a number of factors like quality of arrangement or composition, the medium you have arranged or composed for and the saleable quality of the music ie: will it be cost effect for publication to take place.
One of the points that we make clear to arrangers and composers is that your title may take time for customers to purchase it. You will not sell hundreds of copies with the first week or month. It takes time to get your name known in the music field.
We tend to look for compositions and arrangements that have not been done before or have very few versions available. This makes your work stand out more.
The length of time taken to get a piece in print depends on the type of work and if it needs typesetting or not. If you send pieces that are already in Sibelius then this makes the process a lot shorter as we can set out your piece for publication much quicker. If we have to engrave music, type your music into Sibelius, then this process will take much longer as we have to have it proofread and looked many times before we will allow it to go into print.