Replication Method for Steady-State Simulations

• If initialization bias in the point estimator has been reduced to a negligible level, the method of independent replications can be used to estimate point-estimator variability and to construct a confidence interval.

• If significant bias remains in the point estimator and a large number of replications are used to reduce point estimator variability, the result confidence interval can be misleading.
  • The bias is not affected by the number of replications R, but by deleting more data (i.e. increasing $T_0$) or extending the length of each run (i.e. increasing $T_E$.
  • Increasing the number of replications R may produce shorter confidence intervals around a ``wrong point'' $\theta + b$, rather than $\theta$

• If d is the number of observations to delete from a total of n observations, a rough rule is n-d should be at least 10d, or $T_E$ should be at least $10 T_0$.

• Given the run length, the number of replications should be as many as possible. Kelton in 1986 established that there is little value to run more than 25 replications. So if time is available, make the simulation longer, instead of making more replications.

• See Example 12.14 on page 460 and Example 12.15 on page 461, where Example 12.15 demonstrate the cases where few obsevations were deleted.

  A couple of notes as fewer observations were deleted (d is smaller):

  1. The confidence interval shifts downward, reflecting the greater downward bias in $\overline{Y}_{..} (15,d)$ as d decreases. This can be attributed as the result of a ``cold start''.
  2. The standard error of $\overline{Y}_{..} (15,d)$, namely $S/\sqrt{R}$ decreases as d decreases. As d decreases, the number of samples included in the statistics increases, reducing the error range.