On exponential bounds for the waiting time of TES/GI/1 queues

The TES (Transform-Expand-Sample) technique has emerged as a general methodology for modeling autocorrelated random processes with arbitrary marginal distributions. Because of their generality and practical applicability, TES models can be readily used to accurately characterize bursty traffic streams in ATM networks (e.g., variable-bit-rate compressed video). Although TES models can be easily implemented for simulation studies, the need still exists for analytical results on the performance of queueing systems under TES traffic. Of particular interest are the tail probabilities of waiting time or buffer occupancy in queues driven by bursty traffic. Such probabilities may be difficult to obtain via conventional simulation when they become exceedingly small. In this paper we present a general result concerning exponential bounds for the waiting time under continuous state-space Markov chains. We apply this result to a TES/GI/1 queue, show a numerical example, and compare our bound with simulation results. In order to obtain accurate estimates of extremely low probabilities fast simulation techniques based on importance sampling are used