A four-state DMMPP for characterizing multimedia traffic with short-term and long-term correlations

We present a four-state discrete-time Markov-modulated Poisson process (DMMPP) to characterize multimedia traffic which exhibits both short-term and long-term correlation. By taking advantage of the correlation structure of a two-state DMMPP, we can construct a four-state DMMPP by superposing two two-state DMMPPs in which one two-state DMMPP captures the short-term correlation of arrivals and the other two-state DMMPP captures the long-term correlation of arrivals. We have developed a systematic algorithm to match eight parameters of two two-state DMMPPs which can exactly capture the mean and the variance of the measured trace and also closely fit the probability mass function and the autocorrelation function. In addition, we present two experiments of traces, including a computer-generated trace and a measured trace. The results show that under certain time scales this four-state DMMPP model can capture the statistical behavior of the arrival process and predict the queueing performance very well