THE ASYMPTOTIC-BEHAVIOR OF QUEUING-SYSTEMS - LARGE DEVIATIONS THEORY AND DOMINANT POLE APPROXIMATION

This paper presents the exact asymptotics of the steady state behavior of a broad class of single-node queueing systems. First we show that the asymptotic probability functions derived using large deviations th eory are consistent (in a certain sense) with the result using dominan t pole approximations. Then we present an exact asymptotic formula for the cumulative probability function of the queue occupancy and relate it to the ''cell loss ratio'', an important performance measure for s ervice systems such as ATM networks. The analysis relies on a new gene ralization of the Taylor coefficients of a complex function which we c all ''characteristic coefficients''. Finally we apply our framework to obtain new results for the M/D/1 system and for a more intricate mult iclass M/D/n system.