Study on estimating probabilities of buffer overflow in high-speed communication networks

The paper recommends new methods to estimate effectively the probabilities of buffer overflow in high-speed communication networks. The probability of buffer overflow in queuing system is very small; therefore the overflow is defined as a rare event and can be estimated using rare event simulation with continuous-time Markov chains. First, a two-node queuing system is considered and the buffer overflow at the second node is studied. Two efficient rare event simulation algorithms, based on the Importance sampling and Cross-entropy methods, are developed and applied to accelerate the buffer overflow simulation with Markov chain modeling. Then, the buffer overflow in self-similar queuing system is studied and simulations with long-range dependent self-similar traffic source models are conducted. A new efficient simulation algorithm, based on the RESTART method with limited relative error technique, is developed and applied to accelerate the buffer overflow simulation with SSM/M/1/B modeling using different parameters of arrival processes and different buffer sizes. Numerical examples and simulation results are provided for all methods to estimate the probabilities of buffer overflow, proposed in this paper.