Peter W. Glynn, Philip Heidelberger
ACM Transactions on Modeling and Computer Simulation (TOMACS)
The semi-Markov process (SMP) has long been used as a model for the underlying process of a discrete-event stochastic system. Important refinements of this model include the continuous-time Markov chain (CTMC) and important extensions include the generalized semi-Markov process (GSMP). Functional central limit theorems (FCLTS) give basic conditions under which these various processes exhibit stable long-run behavior, as well as providing approximations for cumulative-reward distributions and confidence intervals for statistical estimators. We give FCLTS for finite-state CTMCS, SMPS, and GSMPS under minimal conditions that involve irreducibility and finite second moments on the "holding time" distributions. We consider both continuous and lump-sum rewards; our emphasis is on the use of martingale theory and on the explicit computation, when possible, of the variance constant in the FCLT.
Peter W. Glynn, Philip Heidelberger
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Peter J. Haas, Joseph M. Hellerstein
SIGMOD 2001
Ihab Ilyas, Volker Markl, et al.
ICAC 2004
Cathy H. Xia, George Michailidis, et al.
Probab. Eng. Inf. Sci.