Hi,
As I understand, you want to reduce the time when upgrading the site collections to SharePoint 2013.
If you want to upgrade to SharePoint 2013, you could use the database-attach method. The upgrade process separates the upgrade of database content schema from the upgrades of site collections. And this method comes with some new enhancements
for performing site collection upgrades.
For more detailed information, you could refer to the articles below.
The article below is about determining strategy for upgrade to SharePoint 2013
https://technet.microsoft.com/en-us/library/cc263447.aspx
The article below is about preparing for a SharePoint 2013 Upgrade: Defining a Strategy Part 3.
http://blogs.askcts.com/2013/03/28/preparing-for-a-sharepoint-2013-upgrade-defining-a-strategy-part-3/
The article below is about SharePoint 2013 Upgrade: Six Job-Saving Features.
http://blog.fpweb.net/sharepoint-2013-upgrade-six-job-saving-features/#.VePpJ3novwo
Best regards,
Sara Fan