Regression-adjusted estimates for regenerative simulations, with graphics

Abstract

Dist secial ABSTRACTJs IThe independent block structure of regenerative processes and t vergence rates of the means of ratio estimators are exploited to produce bias-free regression-adjusted estimates (AAfe's) for regenerative simulations. Direct assessments of the variances of the estimates are obtained, as well as indications--both formal and graphical--of normality and symmetry, or lack of it, in the distribution of the estimates.

Disk arm movement in anticipation of future requests

“…Heidelberger and Lewis in [15] warn of a high, positive correlation between an estimate produced during a run, and the width of the confidence interval around that estimate produced by that same run. A sequential-stopping-rule sort of termination is therefore avoided in these simulations.…”

Average regression-adjusted controlled regenerative estimates

“…Given that one can calculate a regression-adjusted regenerative estimate from a simulation of N busy periods, the fi- An immediate concern with forming average regression-adjusted regenerative estimates is determining appropriate values for the various parameters such as M, N, p, the nk and d. Heidelberger and Lewis (1981) describe a graphical protocol which can assist the analyst in selecting some of these values. For the remainder of this chapter, assume that the total number of busy periods in the simulation, namely M x N, has been set at 200,000.…”

“…An alternative method for estimating the variance of the regenerative estimates is to use multiple replications, or equivalently, section one long replication of N cycles into m smaller "replications" of n cycles each. While sectioning eliminates the correlation between the regenerative estimate and the estimate of its variance, one must de-921 termine the sectioning parameters, m and n. Heidelberger and Lewis (1981) developed a method incorporating regression-adjusted and graphical techniques to assist the experimenter in choosing these parameters. Their method produces a reduced-bias regenerative estimate along with a stable estimate of its variance.…”

“…Section 3.3. l briefly describes their average regression-adjusted regenerative estimate. Section 3.3.2 shows how one can use the regressionadjusted technique of Heidelberger and Lewis (1981) with the controlled regenerative estimates of Iglehart and Lewis (1979). This combination of techniques allows one to obtain estimates of the stationary waiting time for the nth customer with much lower estimated mean square error than by using either technique alone.…”