The ALICE experiment at CERN LHC is using a PROOF-enabled cluster for fast physics analysis, detector calibration and reconstruction of small data samples. The current system (CAF - CERN Analysis Facility) consists of some 120 CPU cores and about 45 TB of disk space distributed across the CAF hosts. One of the most important aspects of the data analysis on the CAF is the speed with which it can be carried out. The system is particularly aimed at the prototyping phase of analyses that need a high number of iterations and thus require a short response time. Quasi-online quality assurance of data can be obtained. The paper describes the design principles of the PROOF frame work and presents the current setup, performance tests and usage statistics. Subsets of selected data can be automatically staged in CAF from the Grid storage systems, therefore data distribution and staging techniques are described in depth. A fairshare algorithm to adjust the priorities of concurrently running sessions is also examined. Further more, the adaptation of PROOF to the AliEn/gLite Grid middleware is described. This approach enables a dynamic startup of PROOF nodes worldwide with the purpose to process much larger physics datasets.