Generalized variance-based Markovian fitting for self-similar traffic modelling

Most of the proposed self-similar traffic models are asymptotic in nature. Hence, they are less effective in queueing-based performance evaluation when the buffer sizes are small. In this paper, we propose a short range dependent (SRD) process modelling by a generalized variance-based Markovian fitting to provide effective queueing-based performance measures when buffer sizes are small. The proposed method is to match the variance of the exact second-order self-similar processes. The fitting procedure determines the related parameters in an exact and straightforward way. The resultant traffic model essentially consists of a superposition of several two-state Markov-modulated Poisson processes (MMPPs) with distinct modulating parameters. We present how well the resultant MMPP could emulate the variance of original self-similar traffic in the range of the specified time scale, and could provide more accurate bounds for the queueing-based performance measures, namely tail probability, mean waiting time and loss probability. Numerical results show that both the second-order statistics and queueing-based performance measures when buffer capacity is small are more accurate than that of the variance-based fitting where the modulating parameters of each superposed two-state MMPP are equal. We then investigate the relationship between time scale and the number of superposed two-state MMPPs. We found that when the performance measures pertaining to larger time scales are not better than that of smaller ones, we need to increase the number of superposed two-state MMPPs to maintain the accurate and reliable queueing-based performance measures. We then conclude from the extensive numerical examples that an exact second-order self-similar traffic can be well represented by the proposed model.