Indirect Estimation Via L = λW
Indirect Estimation Via L = λW
复制标题
通过 L = λW 间接估计
DOI：
10.1287/opre.37.1.82
复制
发表时间：
1989
期刊：
影响因子：
--
通讯作者：
W. Whitt
中科院分区：
文献类型：
--
作者：
P. Glynn;W. Whitt
For a large class of queueing systems, Little's law ( L = λ W ) helps provide a variety of statistical estimators for the long-run time-average queue length L and the long-run customer-average waiting time W . We apply central limit theorem versions of Little's law to investigate the asymptotic efficiency of these estimators. We show that an indirect estimator for L using the natural estimator for W plus the known arrival rate λ is more efficient than a direct estimator for L , provided that the interarrival and waiting times are negatively correlated, thus extending a variance-reduction principle for the GI/G/s model due to A. M. Law and J. S. Carson. We also introduce a general framework for indirect estimation which can be applied to other problems besides L = λ W . We show that the issue of indirect-versus-direct estimation is related to estimation using nonlinear control variables. We also show, under mild regularity conditions, that any nonlinear control-variable scheme is equivalent to a linear control-variable scheme from the point of view of asymptotic efficiency. Finally, we show that asymptotic bias is typically asymptotically negligible compared to asymptotic efficiency.
