Arthur Sale, Professor of Computing Research at the University of Tasmania (Australia), has researched how authors upload their papers in universities with mandatory deposit policies.
Amongst the significant findings is that by six months after publication date, more than 80% of authors have already deposited. Also it seems to take 2-3 years for a university mandatory policy to become fully institutionalized, though the process is almost instant with departmental mandates. The data is drawn from three sources:  University of Tasmania,  Queensland University of Technology in Australia, and  the University of Southampton in the UK.
The preprint of this paper is available in the UTas ePrints repository:
The acquisition of open access research articles (2006)
(originally found on SERIALST-L)