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Asymptotic performance of a buffer model in a data sharing environment

The performance of a transaction processing system is very sensitive to the buffer hit probability. In a data sharing environment where multiple computing nodes are coupled together with direct access to shared data on disks, buffer coherency needs to be maintained such that if a data granule is updated by a node, the old copies of this granule present in the buffer of other nodes must be invalidated. The buffer invalidation phenomenon reduces the buffer hit probability in a multi-node environment. After the buffer reaches a certain size, the buffer hit probability will remain constant regardless of further increase in buffer size due to the buffer invalidation effect. This puts an upper limit on the achievable buffer hit probability. Thus the selection of appropriate buffer size is one of the critical issues in a data sharing environment. In this paper, we develop an asymptotic analysis of the Markov model for a buffer in the data sharing environment. Important relations between buffer size, number of nodes, write-probability and the size of the database to the buffer hit probability had been found in all range of system parameters. A simple expression is obtained for the maximum achievable buffer hit probability and also for the maximum usable buffer size. Various properties of the maximum achievable buffer hit probability and usable buffer size are derived for a skewed access workload. The accuracy of the asymptotic method is validated by numerous case studies.