Regenerative steady-state simulation of discrete-event systems

The regenerative method possesses certain asymptotic properties that dominate those of other steady-state simulation output analysis methods, such as batch means. Therefore, applying the regenerative method to steady-state discrete-event system simulations is of great interest. In this paper, we survey the state of the art in this area. The main difficulty in applying the regenerative method in our context is perhaps in identifying regenerative cycle boundaries. We examine this issue through the use of the "smoothness index." Regenerative cycles are easily identified in systems with unit smoothness index, but this is typically not the case for systems with nonunit smoothness index. We show that "most" (in a certain precise sense) discrete-event simulations will have nonunit smoothness index, and extend the asymptotic theory of regenerative simulation estimators to this context.

[1]  Sلأren Asmussen,et al.  Applied Probability and Queues , 1989 .

[2]  P. Glynn,et al.  Likelihood ratio gradient estimation for stochastic recursions , 1995, Advances in Applied Probability.

[3]  A. W. Kemp,et al.  Applied Probability and Queues , 1989 .

[4]  P. Haas.  On simulation output analysis for generalized semi-markov processes , 1999 .

[5]  Peter W. Glynn,et al.  Can the regenerative method be applied to discrete-event simulation? , 1999, WSC '99.

[6]  Gerald S. Shedler.  Regenerative Stochastic Simulation , 1992 .

[7]  D. Iglehart.  Simulating stable stochastic systems, V: Comparison of ratio estimators , 1975 .

[8]  P. Haas,et al.  Regenerative generalized semi-markov processes , 1987 .

[9]  Paul Bratley,et al.  A guide to simulation (2nd ed.) , 1986 .

[10]  Upendra Dave,et al.  Applied Probability and Queues , 1987 .

[11]  Ronald W. Wolff,et al.  Stochastic Modeling and the Theory of Queues , 1989 .

[12]  G. S. Shedler,et al.  Regeneration and Networks of Queues , 1986 .

[13]  Peter W. Glynn,et al.  Likelihood ratio gradient estimation for stochastic systems , 1990, CACM.

[14]  Averill M. Law,et al.  Simulation Modeling and Analysis , 1982 .

[15]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[16]  Paul Bratley,et al.  A guide to simulation , 1983 .

[17]  W GlynnPeter,et al.  Regenerative steady-state simulation of discrete-event systems , 2001 .

[18]  U. Grenander,et al.  Statistical analysis of stationary time series , 1957 .

[19]  P. Glynn,et al.  Simulation output analysis for general state space Markov chains , 1982 .

[20]  P. Glynn,et al.  Accelerated regeneration for markov chain simulations , 1995 .

[21]  H. Robbins,et al.  Moments of Randomly Stopped Sums , 1965 .

[22]  B. Schmeiser,et al.  Optimal mean-squared-error batch sizes , 1995 .

[23]  Dénes König,et al.  Verallgemeinerungen der Erlangschen und Engsetschen Formeln : Eine Methode in der Bedienungstheorie , 1967 .

[24]  W.,et al.  Conditions for the Applicability of the Regenerative Method* , 1993 .

[25]  Svante Janson,et al.  Renewal Theory for $M$-Dependent Variables , 1983 .

[26]  P. Glynn,et al.  A joint central limit theorem for the sample mean and regenerative variance estimator , 1987 .

[27]  Ward Whitt,et al.  Continuity of Generalized Semi-Markov Processes , 1980, Math. Oper. Res..

[28]  L. D. Fossett.  Simulating generalized semi-Markov processes , 1979 .

[29]  Peter W. Glynn,et al.  Derandomizing Variance Estimators , 1999, Oper. Res..

[30]  Philip Heidelberger,et al.  Bias Properties of Budget Constrained Simulations , 1990, Oper. Res..

[31]  D. Burman.  Insensitivity in queueing systems , 1980, Advances in Applied Probability.

[32]  U. Grenander,et al.  Statistical analysis of stationary time series , 1958 .

[33]  E. Nummelin.  General irreducible Markov chains and non-negative operators: List of symbols and notation , 1984 .

[34]  P. Glynn,et al.  Notes: Conditions for the Applicability of the Regenerative Method , 1993 .

[35]  P. Glynn.  A GSMP formalism for discrete event systems , 1989, Proc. IEEE.

[36]  P. Glynn.  Some topics in regenerative steady-state simulation , 1994 .

[37]  P. Heidelberger,et al.  A Renewal Theoretic Approach to Bias Reduction in Regenerative Simulations , 1982 .