SEQUENTIAL ESTIMATION OF STEADY-STATE QUANTILES : LESSONS LEARNED AND FUTURE DIRECTIONS

We survey recent developments concerning Sequest and Sequem, two simulation-based sequential procedures for estimating steady-state quantiles. These procedures deliver improved point and confidence-interval (CI) estimators of a selected steady-state quantile, where the CI approximately satisfies user-specified requirements on the CI’s coverage probability and its absolute or relative precision. Sequest estimates a nonextreme quantile (i.e., its order is between 0.05 and 0.95) based on the methods of batching and sectioning. Sequem estimates extreme quantiles using a combination of batching, sectioning, and the maximum transformation. Two test problems show both the advantages and the limitations of these procedures. Based on the lessons learned in designing, justifying, implementing, and stress-testing Sequest and Sequem, we discuss future challenges in advancing the theory, algorithmic development, software implementation, performance evaluation, and practical application of improved procedures for steady-state quantile estimation.

[1]  Richard W. Conway,et al.  Some Tactical Problems in Digital Simulation , 1963 .

[2]  Samuel Karlin,et al.  A First Course on Stochastic Processes , 1968 .

[3]  Donald L. Iglehart,et al.  Simulating Stable Stochastic Systems, VI: Quantile Estimation , 1976, JACM.

[4]  Andrew F. Seila,et al.  Estimation of percentiles in discrete event simulation , 1982 .

[5]  Philip Heidelberger,et al.  Quantile Estimation in Dependent Sequences , 1984, Oper. Res..

[6]  Imrich Chlamtac,et al.  The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations , 1985, CACM.

[7]  A. Ya. Kreinin,et al.  Joint distributions in Poissonian tandem queues , 1992, Queueing Syst. Theory Appl..

[8]  John A. Buzacott,et al.  Stochastic models of manufacturing systems , 1993 .

[9]  Athanassios N. Avramidis,et al.  Correlation-induction techniques for estimating quantiles in simulation experiments , 1995, Winter Simulation Conference Proceedings, 1995..

[10]  A. McNeil,et al.  Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach , 2000 .

[11]  Paul Glasserman,et al.  Monte Carlo Methods in Financial Engineering , 2003 .

[12]  Holger Drees,et al.  Extreme quantile estimation for dependent data with applications to finance , 2003 .

[13]  W. David Kelton,et al.  Quantile and tolerance-interval estimation in simulation , 2006, Eur. J. Oper. Res..

[14]  W. David Kelton,et al.  Estimating steady-state distributions via simulation-generated histograms , 2008, Comput. Oper. Res..

[15]  Emily K. Lada,et al.  Skart: A skewness- and autoregression-adjusted batch-means procedure for simulation analysis , 2008, 2008 Winter Simulation Conference.

[16]  Gerald T. Mackulak,et al.  Indirect cycle time quantile estimation using the Cornish–Fisher expansion , 2009 .

[17]  Murat Kulahci,et al.  Simulation-based cycle-time quantile estimation in manufacturing settings employing non-FIFO dispatching policies , 2009, J. Simulation.

[18]  Peter W. Glynn,et al.  On the Marginal Standard Error Rule and the Testing of Initial Transient Deletion Methods , 2016, ACM Trans. Model. Comput. Simul..

[19]  James R. Wilson,et al.  Automated Estimation of Extreme Steady-State Quantiles via the Maximum Transformation , 2017, ACM Trans. Model. Comput. Simul..

[20]  Kai-Wen Tien,et al.  Sequest: A Sequential Procedure for Estimating Quantiles in Steady-State Simulations , 2019, Oper. Res..