Large deviation properties of a correlated arrival process

Abstract

An exact matrix representation of the operator associated with a correlated arrival process is obtained from which an accurate numerical procedure is derived for the computation of the dominant eigenvalue . The peakedness function is studied in order to obtain a useful approximation to and to permit the numerical computation of peakedness. This is important in practice because direct observation of data allows peakedness determination but does not lead directly to the eigenvalue; however, performance measures of queueing models depend directly on Large deviation limit formulae are derived for this correlated arrival process, namely, for the time to the l'th arrival and for the number of arrivals in , which are then used to obtain the decrements (critical exponent coefficients) for the waiting time in a single server queue and for the number in system. A consequence of these formulae is a simple relation between the two decrements. Also, approximations for the distributions of complementary waiting time and number in system are constructed