Microsoft has released the Hybrid Free Busy Troubleshooter. A Hybrid Deployment consists of an on-premises Exchange server environment that has at least one Exchange 2010 or Exchange 2013 server. In this environment there is also a DirSync (Directory Synchronization) server, and in many cases, a deployment of ADFS (Active Directory Federation Services) to provide single sign-on capabilities to the users. The idea of the hybrid environment is to allow two separate organizations (Exchange Online and Exchange On-Premises) to feel like one organization.
Free Busy is the most commonly used “feature set” in a hybrid deployment. According to Microsoft, if you were to resolve issues with Free Busy lookups, many of the other potential issues you have with your hybrid deployment would be resolved as well.
The Free Busy Troubleshooter can be found at http://aka.ms/hybridfreebusy.