Estimation Methods for Delays in Non-regenerative Discrete-Event Systems

REFERENCES

• Shedler , G.S. 1993 . Regenerative Stochastic Simulation New York : Academic Press .
   Google Scholar
• Haas , P.J. 2002 . Stochastic Petri Nets: Modelling, Stability, Simulation New York : Springer-Verlag .
   Google Scholar
• Haas , P.J. and Shedler , G.S. “ One-dependent cycles and passage times in stochastic Petri nets ” . In Proc. Sixth Intl. Workshop Petri Nets Performance Models 191 – 202 . IEEE Computer Society Press, Los Alamitos, California, 1995 .
   Google Scholar
• Haas , P.J. and Shedler , G.S. 1996 . Estimation methods for passage times using one-dependent cycles . Discrete Event Dynam. Syst. Theory Appl. , 6 : 43 – 72 .
   Google Scholar
• Haas , P.J. and Shedler , G.S. 1993 . Passage times in colored stochastic Petri nets . Commun. Stat. Stochastic Models , 9 : 31 – 79 .
   Google Scholar
• Prisgrove , L.A. and Shedler , G.S. 1986 . Symmetric stochastic Petri nets . IBM J. Res. Dev. , 30 : 278 – 293 .
   Google Scholar
• Glynn , P.W. and Iglehart , D.L. 1990 . Simulation output analysis using standardized time series . Math. Oper. Res. , 15 : 1 – 16 .
   Web of Science ®Google Scholar
• Schruben , L.W. 1983 . Confidence interval estimation using standardized time series . Oper. Res. , 31 : 1090 – 1108 .
   Web of Science ®Google Scholar
• Conway , R.W. 1963 . Some tactical problems in digital simulation . Manag. Sci. , 10 : 47 – 61 .
   Web of Science ®Google Scholar
• Brillinger , D.R. 1973 . Estimation of the mean of a stationary time series by sampling . J. Appl. Prob. , 10 : 419 – 431 .
   Web of Science ®Google Scholar
• Fox , B.L. , Goldsman , D. and Swain , J.J. 1991 . Spaced batch means . Oper. Res. Lett. , 10 : 255 – 263 .
   Web of Science ®Google Scholar
• Goldsman , D. , Meketon , M.S. and Schruben , L.W. 1990 . Properties of standardized time series weighted area variance estimators . Manag. Sci. , 36 : 602 – 612 .
   Web of Science ®Google Scholar
• Durrett , R. 1991 . Probability: Theory and Examples Pacific Grove, CA : Wadsworth and Brooks/Cole .
   Google Scholar
• Haas , P.J. 1999 . Estimation methods for non-regenerative stochastic Petri nets . IEEE Trans. Software Eng. , 25 : 218 – 236 .
   Google Scholar
• Haas , P.J. 1999 . On simulation output analysis for generalized semi-Markov processes . Commun. Stat. Stochastic Models , 15 : 53 – 80 .
   Google Scholar
• Glynn , P.W. “ Simulation output analysis for general state space Markov chains. ” . Stanford, CA : Department of Operations Research, Stanford University .
   Google Scholar
• Sigman , K. 1990 . One-dependent regenerative processes and queues in continuous time . Math. Oper. Res. , 15 : 175 – 189 .
   Web of Science ®Google Scholar
• Muñoz , D.F. and Glynn , P.W. 1997 . A batch means methodology for estimation of a nonlinear function of a steady-state mean . Manag. Sci. , 43 : 1121 – 1135 .
   Google Scholar
• Meyn , S.P. and Tweedie , R.L. 1993 . Markov Chains and Stochastic Stability London : Springer-Verlag .
   Google Scholar
• Haas , P.J. “ Recurrence and regeneration in non-Markovian simulations ” . Stanford, CA : Department of Operations Research, Stanford University .
   Google Scholar
• Asmussen , S. 1987 . Applied Probability and Queues New York : Wiley .
   Google Scholar
• Billingsley , P. 1968 . Convergence of Probability Measures New York : Wiley .
   Google Scholar
• Haas , P.J. and Glynn , P.W. 2002 . On the validity of long-run estimation methods for discrete-event systems . Performance Eval. Rev. , 30 : 35–37
   Google Scholar
• Schmeiser , B. 1982 . Batch size effects in the analysis of simulation output . Oper. Res. , 30 : 556 – 568 .
   Web of Science ®Google Scholar
• Muñoz , D.F. and Glynn , P.W. 2001 . Multivariate standardized time series for steady-state simulation output analysis . Oper. Res. , 49 : 413 – 422 .
   Google Scholar
• Glynn , P.W. and Whitt , W. 1986 . A central-limit-theorem version of L=λW . Queueing Syst. Theory Appl. , 2 : 191 – 215 .
   Google Scholar
• Glynn , P.W. and Meyn , S.P. 1996 . A Lyapunov bound for solutions of Poisson's equation . Ann. Prob. , 24 : 916 – 931 .
   Web of Science ®Google Scholar
• Roberts , G.O. and Tweedie , R.L. 1999 . Bounds on regeneration times and convergence rates for Markov chains . Stochastic Process. Appl. , 80 : 211 – 229 .
   Web of Science ®Google Scholar
• Glynn , P.W. and L'Ecuyer , P. 1995 . Likelihood ratio gradient estimation for stochastic recursions . Adv. Appl. Prob. , 27 : 1019 – 1053 .
   Web of Science ®Google Scholar
• Gut , A. 1988 . Stopped Random Walks: Limit Theorems and Applications New York : Springer-Verlag .
   Google Scholar
• Loéve , M. 1977 . Probability Theory , 4th Ed. New York : Springer-Verlag .
   Google Scholar