Analysis of buffer behavior with asynchronous arrival and output processes

Abstract

A semi-Markov process is used to represent a statistical sampling program functioning as a recipient of observation data or as a generator of population data. In the recipient case, the program receives data through a buffer storage that is filled by a fixed-rate arrival process. In the generator case, the program supplies data to a buffer storage that is emptied at fixed intervals. In both cases, a data miss occurs when an arrival encounters a full buffer. The paper develops methods to evaluate the sampling success rate for both the recipient and the generator cases. In practice, these methods can be used to optimize the design of the sampling process by choosing buffer lengths that meet specified minimum success rates. The analysis allows any subset of the states of the semi-Markov process to be associated with the sampling activity. This problem has practical applications in statistical and scientific database systems and many other environments.