  In their 2004 seminal paper, Glynn and Juneja formally and precisely
established the rate-optimal, probability-of-incorrect-selection, replication
allocation scheme for selecting the best of k simulated systems. In the case of
independent, normally distributed outputs this allocation has a simple form
that depends in an intuitively appealing way on the true means and variances.
Of course the means and (typically) variances are unknown, but the rate-optimal
allocation provides a target for implementable, dynamic, data-driven policies
to achieve. In this paper we compare the empirical behavior of four related
replication-allocation policies: mCEI from Chen and Rzyhov and our new gCEI
policy that both converge to the Glynn and Juneja allocation; AOMAP from Peng
and Fu that converges to the OCBA optimal allocation; and TTTS from Russo that
targets the rate of convergence of the posterior probability of incorrect
selection. We find that these policies have distinctly different behavior in
some settings.
