Efficient loss estimation in high speed networks

An efficient approximation for finding loss in high speed networks is proposed. We use an infinite buffer model to derive an upper bound on the performance of finite buffer models. We also use a large buffer approximation and Markov modulated fluid (MMF) models to represent the sources. We approximate loss by the product of an overflow probability and a conditional expectation of the instantaneous input rate minus the channel capacity, when the buffer occupancy exceeds a threshold. The overflow probability can be approximated by using the dominant eigenvalue and a Chernoff bound on the probability that the incoming rate exceeds the channel capacity. The conditional expectation is approximated using the eigenvector corresponding to the dominant eigenvalue. The result is an efficient algorithm. In the numerical studies we have found the algorithm to be conservative. We also conclude that our loss estimate gives a close upper bound on the exact loss when the offered load is relatively large and the peak rate of each source is relatively small compared with the channel capacity