Diffusion process approximations of a statistical multiplexer with Markov modulated bursty traffic sources

We consider a statistical multiplexer model, in which each of N sources is a Markov modulated rate process (MMRP). This formulation allows a more realistic source model than the well studied but simple “on-off” source model in characterizing variable bit rate (VBR) sources such as compressed video, which is of increasing importance to ATM networks. In our model we allow an arbitrary distribution for the duration of each of M states (or levels) that the source can take on. We formulate Markov modulated sources as a closed queueing network with M infinite-server stations. By extending our earlier results we introduce an M-dimensional diffusion process to approximate the aggregated traffic of such Markov modulated sources. Under a set of reasonable assumptions we then show that this diffusion process can be expressed as an M-dimensional Ornstein-Uhlenbeck (O-U) process. The behavior of buffer content is also approximated by a diffusion process, which is characterized by the aggregated traffic process and the output process. We show some numerical examples which illustrate typical sample paths and auto-correlations of the aggregated traffic from the Markov modulated sources and its diffusion process representation. Simulation results are provided to compare with our diffusion model for queueing analysis