Performance of variance updating ranking and selection procedures

Kim and Nelson (2005) developed two indifference-zone procedures for steady-state simulation where the goal is to find the system with the largest or smallest expected steady-state performance measure. One of the procedures, called KN++, updates a variance estimate as more observations become available and is proven to be asymptotically valid when there is no dependence across systems (for example, there is no use of common random numbers). Their procedure exhibits significant improvement over other existing procedures for use in steady-state simulation. In this paper, we first present a modification of KN++ that is asymptotically valid with the use of common random numbers. Then, we study how well KN++ works when data within a system are independent and identically distributed, but data between systems may be positively correlated. Specific applications include the finding-the-best problem when (i) the data are normal, and (ii) the data are Bernoulli.