For years, organizations have been using On-premises relational database systems as the heart of mission-critical applications. The classic On-premise relational mode as we know might not likely survive in the world of cloud computing.
The first aspect which I like to discuss is fate of database model in cloud: Relational vs. NoSQL. RDBMS requires that data is normalized so that it can provide quality results and prevent duplicates and orphan records. Normalizing the data requires creation of more tables, which require table joins, and thus requiring more indexes and keys. The problem becomes more apparent with highly diverse datasets with lots of unstable indexes on them probably a hundred or so tables, and each table having varying indexes. I/O becomes chaotic when indexes of different tables are stored on different parts of persistence storage devices like HDD or SSD and you have concurrent reads/writes. In case of Cloud, the storage represented to the user may be different disks or different kinds of store; Cloud storage comes with abstraction; as databases start to grow into the terabytes or even petabytes, performance starts to fall off significantly.