Multi-tier data storage using inclusive/exclusive burst buffer caching based on reference counts

Improved multi-tier data storage is provided using inclusive/exclusive burst buffer caching techniques based on reference counts. An exemplary multi-tier storage system comprises at least first and second storage tiers for storing data, wherein at least one of the first and second storage tiers comprises at least one cache, and wherein the data is retained in the at least one cache as a given cached data item based on a reference count indicating a number of expected requests for the given cached data item. The number of expected requests for the given cached data item in a given cache is based, for example, on a number of nodes serviced by the given cache. A burst buffer appliance is also provided for implementing the cache retention policies described herein.