Diffusion approximation modeling for Markov modulated bursty traffic and its applications to bandwidth allocation in ATM networks

We consider a statistical multiplexer model, in which each of K sources is a Markov modulated rate process (MMRP). This formulation allows a more general source model than the well studied “on–off” source model in characterizing variable bit rate (VBR) sources such as compressed video. 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 nodes. By extending our earlier results [17] we introduce an M dimensional diffusion process to approximate the aggregate 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 queueing behavior of buffer content is analyzed by applying a diffusion process approximation to the aggregate arrival process. We show some numerical examples which illustrate typical sample paths, and autocorrelation functions of the aggregate traffic and its diffusion process representation. Simulation results validate our proposed approximation model, showing good fits for distributions and autocorrelation functions of the aggregate rate process and the asymptotic queueing behaviors. We also discuss how the analytical formulas derived from the diffusion approximation can be applied to compute equivalent bandwidth for real-time call admission controls, and how the model can be modified to characterize traffic sources with long-range dependence.