A Note on Skewness in Regenerative Simulation

Abstract

The purpose of this article is to show, empirically and theoretically, that performance evaluation by means of regenerative simulation often involves random variables with distributions that are heavy tailed and heavily skewed. This, in turn, leads to the variance of estimators being poorly estimated, and confidence intervals having actual coverage quite different from (typically lower than) the nominal one. We illustrate these general ideas by estimating the mean occupancy and tail probabilities in M/G/1 queues, comparing confidence intervals computed from batch means to various intervals computed from regenerative cycles. In addition, we provide theoretical results on skewness to support the empirical findings.

Keywords:

• ABC interval
• Batch means
• Busy cycle
• Busy period
• Coverage probability
• Fieller test
• Jackknife
• M/G/1 queue
• Regenerative process
• Regenerative simulation
• Skewness

Mathematics Subject Classification:

• Primary 00A72, 65C05
• Secondary 68M20, 90B05, 90B22