Experimental Evaluation of Variance Reduction Techniques for Queueing Simulation Using Generalized Concomitant Variables

Article Abstract:

In a companion paper we developed a unified scheme for using poststratified sampling and control variables to improve the efficiency of regenerative queueing simulations. We adapted these variance reduction techniques to the estimation methods of replication analysis and regenerative analysis by exploiting the asymptotic joint normality of certain standardized concomitant variables that are defined on each input process sampled during a queueing simulation. In this paper we present an experimental evaluation of the reductions in point-estimator variance and confidence-interval width that can be achieved with each procedure in several closed and mixed machine-repair systems. For the analytically tractable model, nominal and actual confidence-interval coverage probabilities are also compared. Poststratification generally produced variance reductions ranging from 10 percent to 40 percent and confidence-interval reductions between 1 percent and 20 percent. The control-variates schemes yielded variance reductions ranging from 20 percent to 90 percent and confidence-interval reductions between 10 percent and 70 percent. In some instances where small sample sizes were used, the poststratification schemes produced confidence-interval width increases between 1 percent and 10 percent. With a small number of regenerative cycles, some loss of confidence-interval coverage was observed with both poststratified and controlled regenerative analysis. When larger sample sizes were used, all of the estimation schemes yielded fairly consistent efficiency gains. (Reprinted by Permission of Publisher.)

Management science, Mathematical models, Regression analysis, Performance improvement (Computers), Simulation, Statistical Analysis, Performance Improvement, Queuing Theory, Queuing Networks

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Experimental evaluation of variance reduction techniques for queueing simulation using generalized concomitant variables

Article Abstract:

The use of poststratified control and sampling variables, which increase the effectiveness of regenerative queueing simulations, are examined. The variance reduction methods are used with the projection techniques of replication analysis and regenerative analysis through the optimization of asymptotic joint normality of some standardized concomitant variables that are distinguished with each input process tested during the queueing simulation. The cuts in point-estimator variance and confidence-interval width that can be generated with each technique are evaluated in various closed and mixed machine-repair systems.

Usage, Statistical sampling, Sampling (Statistics), Analysis of variance, Time-series analysis, Time series analysis

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A note on stochastic shop models in which jobs have the same processing requirements on each machine

Article Abstract:

A mathematical model for work processed by job shops, flow shops and open shops is developed. The model is applicable to shop networks that process work on any of several machines with identical capabilities but varying operating speeds. The model and its analysis indicate that in a job shop network where the machine speeds gradually increase from first machine to last machine, the total time required to complete jobs entering the queue is minimized when the jobs are reordered upon entrance to the queue such that the simplest jobs are completed prior to the more complex jobs.

Network analysis (Planning), Machine shops

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