Comparison of the analytic N-burst model with other approximations to telecommunications traffic

A wide variety of traffic models are presently used to study the performance of telecommunications networks. These are shown to be limiting cases of N-burst/G/1 queues. The analytic N-burst model describes traffic as superposition of N packet streams of ON/OFF type. When using power-tail distributions for the duration of the ON periods, self-similar properties, which are critical for understanding tele-traffic, are observed. For very low intraburst packet rates, the N-burst/G/1 model reduces to an M/G/1 queue. For λ_p → ∞ all packets in a burst arrive simultaneously and the model becomes a bulk arrival, or M^(X)/G/1, queue. In the same limit, the packet-based model can be compared to a model of the burst level, an M/G/1 queue where the individual customers represent complete bursts rather than individual packets. Thus the mean system time describes the mean delay for the last packet in a burst rather than the average over all packets. The continuous flow model is also shown to be a limiting case of the N-burst model by letting the number of packets in a burst, n_p, and the router´s packet service rate, ν, go to infinity while holding their ratio constant. Numerical results are presented comparing the steady-state results for mean packet delay and for buffer overflow probabilities of the different analytic models. They collectively show the critical importance of the burstiness parameter. The N-burst/M/1 model with self-similar properties shows drastically changing steady-state performance for specific values of the burstiness parameter. The limiting models are incapable of describing the detailed structure of the performance in this transition region