On synchronous properties of periodically generated data sequences

We address the problem of choosing synchronous data combinations from periodically generated data sequences (PGDAs). In real time systems, PGDAs play a major role. When integrating PGDAs generated from various information sources, we face the problem of choosing which data combinations to use, since different PGDAs, in general, have different data generation intervals. A data combination is defined as a set of data each obtained from distinct PGDAs. As a criterion for choosing a data combination, we propose a novel notion of synchronousness of data combinations. We present two theorems for calculating upper bounds of the synchronousness of data combinations, given a set of PGDAs: one for PGDAs with the same periodic interval and the other for PGDAs with different periodic intervals. These theorems give the synchronousness upper bounds that guarantee to find the data combinations at the constant interval that is the same as the maximum periodic interval of all the PGDAs