Cycle modulated sources and their correlation structure

The cell generation process resulting from variable bit rate (VBR) video traffic in an ATM environment is known to exhibit a statistical behavior which is not accurately captured by the standard Markovian models. In such an environment, one may identify different cycles where in each cycle, the cell rate and the cell activity process may change significantly. We introduce a new class of discrete time Markovian arrival processes referred to as cycle modulated sources (CMS) where we extend and further generalize the model for general on-off sources to allow different cycles and dependency among them. Each cycle is identified by its on and off period and its cell spacing parameter. Some results on the correlational structure of CMS is provided, where by means of examples we show that for large (but not too large) lags "heavy" correlation can be easily obtained by simple CMS which, is a known property of VBR video traffic. We also examine the queue response to such sources. We find that the distribution, of cells in a queueing environment driven by such sources exhibits a very heavy tail which is not usually observed by traditional models.