Modeling correlated traffic with a generalized IPP ?
Modelers of telecommunication and computer network traffic have been increasingly concerned with the need for good analytical models which allow easy inclusion of correlated traffic in analytical queueing models, or in simulations of such models. This work shows that the generalized interrupted Poisson process (GIPP) and the generalized interrupted Bernoulli process (GIBP) have attractive properties for the modeling of correlated teletraffic, and are susceptible to analytic solution. In particular, they possess an invariance property which allows convenient matching of empirical and hypothetical behavior. Matrix algebraic solutions for stationary marginal distributions, and for covariance structures, of the interdeparture stream are derived for both models using generally distributed on-and off-times. The invariance of the covariance to all but the mean of the off-time marginal distribution is proved and exploited. The model is exercised showing the lag-times and marginals for certain on/off distributions, and demonstrating a practical ability to match empirical data to the parameters of the models.
interrupted poisson process correlated traffic models linear algebraic queueing theory matrix-exponential distribution