The P2 algorithm for dynamic calculation of quantiles and histograms without storing observations
Communications of the ACM
Proceedings of the 35th conference on Winter simulation: driving innovation
Indirect cycle-time quantile estimation for non-FIFO dispatching policies
Proceedings of the 38th conference on Winter simulation
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The cycle-time distribution of manufacturing systems employing dispatching rules other than FIFO can be both highly skewed and have heavy tails. Previous cycle-time quantile estimation work has suggested that the Cornish-Fisher expansion can be used in conjunction with discrete-event simulation to provide cycle-time quantile estimates for a variety of systems operating under FIFO dispatching without requiring excess data storage. However, when the cycle-time distribution exhibits heavy skewness and kurtosis, the accuracy of quantile estimates obtained using the Cornish-Fisher expansion may degrade, sometimes severely. This paper demonstrates the degradation and motivates the need for a modification to the Cornish-Fisher expansion for estimating quantiles under non-FIFO dispatching rules. A solution approach combining a data transformation, the maximum (minimum)-transformation, with the Cornish-Fisher expansion is presented. Results show that this provides significant improvements in accuracy over using the Cornish-Fisher expansion alone while still retaining the advantage of requiring minimal data storage.