M/G/1排队系统性能梯度估计的非标准分析法

如何估计系统性能梯度是离散事件动态系统研究中的一个重要问题.系统性能对于概率参数的梯度无法用传统的摄动分析法来估计,我们从非标准分析的角度提出了一种基于Dirac δ函数的摄动分析算法,分析了相应估计量的强相合性和渐近无偏性.新算法在实现过程中需要用样条函数来近似δ函数,但可以同时估计M/G/1排队系统中顾客期望系统时间和忙期期望长度对概率参数的梯度.数值实验结果表明估计量的相对误差和无偏性检验值都比较小,新算法能够很好地估计M/G/1排队系统的性能梯度.

M/G/1排队系统性能梯度估计的非标准分析法

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.