Diffusion approximation modeling for Markov modulated bursty traffic and its applications to bandwidth allocation in ATM networks. - Qiang Ren
We consider a statistical multiplexer model, in which each of the 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 the 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 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 the 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 behavior. We also discuss how the analytical formulas derived from the diffusion approximation can be applied to compute the equivalent bandwidth for real-time call admission control, and how the model can be modified to characterize traffic sources with long-range dependence
Keywords: ATM networks; B-ISDN.; MMRP; Markov modulated bursty traffic; Markov modulated rate process; Markov modulated sources; Ornstein-Uhlenbeck process; VBR sources; Aggregate arrival process; Aggregate traffic approximation; Analytical formulas; Asymptotic queueing behavior; Autocorrelation functions; Bandwidth allocation; Buffer content; Closed queueing network; Compressed video; Diffusion approximation modeling; Duration distribution; Equivalent bandwidth; Fast packet switching; General source model; Infinite-server nodes; Long-range dependence; Real-time call admission control; Simulation results; Statistical multiplexer model; Traffic sources; Variable bit rate