Performance Gradient Estimation for M/G/1 Queueing System Using Nonstandard Analysis

Estimating performance gradient is an important issue in the study of Discrete Event Dynamic Systems(DEDS). Because of discontinuous sample path, it is difficult to estimate performance gradient with respect to probability parameters by traditional perturbation analysis.A new kind of algorithm, which is based on Dirac δ-Function, is established by Nonstandard Analysis for M/G/1 queueing system performance gradient estimation with respect to a kind of probability parameter.Strongly consistency and asymptotically unbiasedness of new estimators are proved by means of integrating finite increment with infinitesimal one. New method uses special spline functions to approximate δ-Function in its implementation. It can estimate simultaneously sojourn time and busy period length gradient w.r.t probability parameter. Numerical results indicate that new estimators have lower relative errors and t-test value of unbiasedness.