Metamodels for Estimating Quantiles of Systems with One Controllable Parameter

We investigate the properties and robustness of histogram approximation to construct non-functional-form metamodels for estimating quantiles of systems with one controllable parameter, providing a general trend of quantiles. By non-functional-form metamodel, we mean the metamodel is not described by a single formula. The procedure constructs histograms by tracking sample quantiles at certain grid points. The algorithm dynamically increases the sample size so that the quantile estimates obtained via the histogram satisfy the proportional precision. The non-functional-form metamodel is constructed with a set of carefully selected histograms. Quantiles can then be estimated via the metamodel. An experimental performance evaluation demonstrates the validity of using non-functional-form metamodels to estimate quantiles.

[1]  P. Sen.  On the Bahadur representation of sample quantiles for sequences of φ-mixing random variables , 1972 .

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

[3]  D. McNickle,et al.  ANALYSIS OF THE TIME EVOLUTION OF QUANTILES IN SIMULATION , 2006 .

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

[5]  E. Jack Chen,et al.  Some Procedures of Selecting the Best Designs with Respect to Quantile , 2008, Simul..

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

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

[8]  Kimmo E. E. Raatikainen,et al.  Simultaneous estimation of several percentiles , 1987, Simul..

[9]  Barry L. Nelson,et al.  Estimating Cycle Time Percentile Curves for Manufacturing Systems via Simulation , 2008, INFORMS J. Comput..

[10]  Donald E. Knuth,et al.  The Art of Computer Programming, Volumes 1-3 Boxed Set , 1998 .

[11]  Gerald T. Mackulak,et al.  Indirect Cycle-Time Quantile Estimation for Non-Fifo Dispatching Policies , 2006, Proceedings of the 2006 Winter Simulation Conference.

[12]  Cecil Hastings,et al.  Approximations for digital computers , 1955 .

[13]  Kimmo E. E. Raatikainen,et al.  Sequential procedure for simultaneous estimation of several percentiles , 1990 .

[14]  L. Jeff Hong,et al.  Kernel estimation for quantile sensitivities , 2007, WSC 2007.

[15]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[16]  W. David Kelton,et al.  Determining simulation run length with the runs test , 2003, Simul. Model. Pract. Theory.