{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T04:39:59Z","timestamp":1750307999144,"version":"3.41.0"},"reference-count":35,"publisher":"Association for Computing Machinery (ACM)","issue":"3","license":[{"start":{"date-parts":[[2006,7,1]],"date-time":"2006-07-01T00:00:00Z","timestamp":1151712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Model. Comput. Simul."],"published-print":{"date-parts":[[2006,7]]},"abstract":"<jats:p>We develop a class of techniques for analyzing the output of simulations of a semi-regenerative process. Called the semi-regenerative method, the approach is a generalization of the regenerative method, and it can increase efficiency. We consider the estimation of various performance measures, including steady-state means, expected cumulative reward until hitting a set of states, derivatives of steady-state means, and time-average variance constants. We also discuss importance sampling and a bias-reduction technique. In each case, we develop two estimators: one based on a simulation of a single sample path, and the other a type of stratified estimator in which trajectories are generated in an independent and identically distributed manner. We establish a central limit theorem for each estimator so confidence intervals can be constructed.<\/jats:p>","DOI":"10.1145\/1147224.1147228","type":"journal-article","created":{"date-parts":[[2006,10,18]],"date-time":"2006-10-18T18:11:32Z","timestamp":1161195092000},"page":"280-315","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":6,"title":["The semi-regenerative method of simulation output analysis"],"prefix":"10.1145","volume":"16","author":[{"given":"James M.","family":"Calvin","sequence":"first","affiliation":[{"name":"New Jersey Institute of Technology, Newark, NJ"}]},{"given":"Peter W.","family":"Glynn","sequence":"additional","affiliation":[{"name":"Stanford University"}]},{"given":"Marvin K.","family":"Nakayama","sequence":"additional","affiliation":[{"name":"New Jersey Institute of Technology, Newark, NJ"}]}],"member":"320","published-online":{"date-parts":[[2006,7]]},"reference":[{"volume-title":"Proceedings of the 1998 Winter Simulation Conference, D. J. Medeiros, E. F. Watson, J. S. Carson, and M. S. Manivannan, Eds. IEEE","author":"Alexopoulos C.","key":"e_1_2_1_1_1","unstructured":"Alexopoulos , C. and Shultes , B. C . 1998. The balanced likelihood ratio method for estimating performance measures of highly reliable systems . In Proceedings of the 1998 Winter Simulation Conference, D. J. Medeiros, E. F. Watson, J. S. Carson, and M. S. Manivannan, Eds. IEEE , Los Alamitos, CA. 1479--1486. Alexopoulos, C. and Shultes, B. C. 1998. The balanced likelihood ratio method for estimating performance measures of highly reliable systems. In Proceedings of the 1998 Winter Simulation Conference, D. J. Medeiros, E. F. Watson, J. S. Carson, and M. S. Manivannan, Eds. IEEE, Los Alamitos, CA. 1479--1486."},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","first-page":"497","DOI":"10.1017\/S0269964800004022","article-title":"Accelerated regeneration for Markov chain simulations","volume":"9","author":"Andrad\u00f6ttir S.","year":"1995","unstructured":"Andrad\u00f6ttir , S. , Calvin , J. M. , and Glynn , P. W. 1995 . Accelerated regeneration for Markov chain simulations . Probab. Engin. Informat. Sciences 9 , 497 -- 523 . Andrad\u00f6ttir, S., Calvin, J. M., and Glynn, P. W. 1995. Accelerated regeneration for Markov chain simulations. Probab. Engin. Informat. Sciences 9, 497--523.","journal-title":"Probab. Engin. Informat. Sciences"},{"key":"e_1_2_1_3_1","doi-asserted-by":"crossref","first-page":"12","DOI":"10.1214\/aoms\/1177705136","article-title":"Statistical methods in Markov chains","volume":"32","author":"Billingsley P.","year":"1961","unstructured":"Billingsley , P. 1961 . Statistical methods in Markov chains . Ann. Mathemat. Statis. 32 , 12 -- 40 . Billingsley, P. 1961. Statistical methods in Markov chains. Ann. Mathemat. Statis. 32, 12--40.","journal-title":"Ann. Mathemat. Statis."},{"key":"e_1_2_1_4_1","volume-title":"Probability and Measure","author":"Billingsley P.","unstructured":"Billingsley , P. 1995. Probability and Measure 3 rd Ed. John Wiley & Sons , New York, NY . Billingsley, P. 1995. Probability and Measure 3rd Ed. John Wiley & Sons, New York, NY.","edition":"3"},{"volume-title":"Convergence of Probability Measures","author":"Billingsley P.","key":"e_1_2_1_5_1","unstructured":"Billingsley , P. 1999. Convergence of Probability Measures , Second ed. John Wiley & Sons , New York . Billingsley, P. 1999. Convergence of Probability Measures, Second ed. John Wiley & Sons, New York."},{"volume-title":"Proceedings of the 2001 Winter Simulation Conference, B. A. Peters, J. S. Smith, D. J. Medeiros, and M. W. Rohrer, Eds. IEEE","author":"Calvin J. M.","key":"e_1_2_1_6_1","unstructured":"Calvin , J. M. , Glynn , P. W. , and Nakayama , M. K . 2001. Importance sampling using the semi-regenerative method . In Proceedings of the 2001 Winter Simulation Conference, B. A. Peters, J. S. Smith, D. J. Medeiros, and M. W. Rohrer, Eds. IEEE , Los Alamitos, CA. 441--450. Calvin, J. M., Glynn, P. W., and Nakayama, M. K. 2001. Importance sampling using the semi-regenerative method. In Proceedings of the 2001 Winter Simulation Conference, B. A. Peters, J. S. Smith, D. J. Medeiros, and M. W. Rohrer, Eds. IEEE, Los Alamitos, CA. 441--450."},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1145\/280265.280273"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.48.5.776.12409"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0269964800142056"},{"volume-title":"Proceedings of the 2002 Winter Simulation Conference, E. Y\u00fccesan, C.-H. Chen, J. L. Snowdon, and J. M. Charnes, Eds. IEEE","author":"Calvin J. M.","key":"e_1_2_1_10_1","unstructured":"Calvin , J. M. and Nakayama , M. K . 2002. A comparison of output-analysis methods for simulations of processes with multiple regeneration sequences . In Proceedings of the 2002 Winter Simulation Conference, E. Y\u00fccesan, C.-H. Chen, J. L. Snowdon, and J. M. Charnes, Eds. IEEE , Los Alamitos, CA. 328--335. Calvin, J. M. and Nakayama, M. K. 2002. A comparison of output-analysis methods for simulations of processes with multiple regeneration sequences. In Proceedings of the 2002 Winter Simulation Conference, E. Y\u00fccesan, C.-H. Chen, J. L. Snowdon, and J. M. Charnes, Eds. IEEE, Los Alamitos, CA. 328--335."},{"volume-title":"Introduction to Stochastic Processes","author":"\u00c7inlar E.","key":"e_1_2_1_11_1","unstructured":"\u00c7inlar , E. 1975. Introduction to Stochastic Processes . Prentice Hall , Englewood Cliffs, NJ . \u00c7inlar, E. 1975. Introduction to Stochastic Processes. Prentice Hall, Englewood Cliffs, NJ."},{"volume-title":"Markov Chains with Stationary Transition Probabilities","author":"Chung K. L.","key":"e_1_2_1_12_1","unstructured":"Chung , K. L. 1967. Markov Chains with Stationary Transition Probabilities . Springer-Verlag , Berlin, Germany . Chung, K. L. 1967. Markov Chains with Stationary Transition Probabilities. Springer-Verlag, Berlin, Germany."},{"key":"e_1_2_1_13_1","volume-title":"Sampling Techniques","author":"Cochran W. G.","unstructured":"Cochran , W. G. 1977. Sampling Techniques 3 rd Ed. Wiley , New York, NY . Cochran, W. G. 1977. Sampling Techniques 3rd Ed. Wiley, New York, NY.","edition":"3"},{"key":"e_1_2_1_14_1","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1287\/opre.23.1.33","article-title":"Simulating stable stochastic systems, III: Regenerative processes and discrete-event simulations","volume":"23","author":"Crane M.","year":"1975","unstructured":"Crane , M. and Iglehart , D. L. 1975 . Simulating stable stochastic systems, III: Regenerative processes and discrete-event simulations . Operat. Resear. 23 , 33 -- 45 . Crane, M. and Iglehart, D. L. 1975. Simulating stable stochastic systems, III: Regenerative processes and discrete-event simulations. Operat. Resear. 23, 33--45.","journal-title":"Operat. Resear."},{"key":"e_1_2_1_15_1","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1016\/0167-6377(86)90076-3","article-title":"Discrete time conversion for simulating semi-Markov processes","volume":"5","author":"Fox B. L.","year":"1986","unstructured":"Fox , B. L. and Glynn , P. W. 1986 . Discrete time conversion for simulating semi-Markov processes . Oper. Res. Lett. 5 , 191 -- 196 . Fox, B. L. and Glynn, P. W. 1986. Discrete time conversion for simulating semi-Markov processes. Oper. Res. Lett. 5, 191--196.","journal-title":"Oper. Res. Lett."},{"key":"e_1_2_1_16_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.38.5.801"},{"key":"e_1_2_1_17_1","volume-title":"Proceedings of the 4th Army Conference on Applied Mathematics and Computing. 917--932","author":"Glynn P. W.","year":"1986","unstructured":"Glynn , P. W. 1986 . Sensitivity analysis for stationary probabilities of a Markov chain . In Proceedings of the 4th Army Conference on Applied Mathematics and Computing. 917--932 . Glynn, P. W. 1986. Sensitivity analysis for stationary probabilities of a Markov chain. In Proceedings of the 4th Army Conference on Applied Mathematics and Computing. 917--932."},{"key":"e_1_2_1_18_1","volume-title":"Proceedings of the 1987 Winter Simulation Conference, A. Thesen, H. Grant, and W. D. Kelton, Eds. IEEE","author":"Glynn P. W.","year":"1987","unstructured":"Glynn , P. W. 1987 . Likelihood ratio derivative estimation: An overview . In Proceedings of the 1987 Winter Simulation Conference, A. Thesen, H. Grant, and W. D. Kelton, Eds. IEEE , Los Alamitos, CA. 366--375. 10.1145\/3 18371.318612 Glynn, P. W. 1987. Likelihood ratio derivative estimation: An overview. In Proceedings of the 1987 Winter Simulation Conference, A. Thesen, H. Grant, and W. D. Kelton, Eds. IEEE, Los Alamitos, CA. 366--375. 10.1145\/318371.318612"},{"key":"e_1_2_1_19_1","doi-asserted-by":"publisher","DOI":"10.1145\/84537.84552"},{"key":"e_1_2_1_20_1","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1007\/BF00994267","article-title":"Some topics in regenerative steady-state simulation","volume":"34","author":"Glynn P. W.","year":"1994","unstructured":"Glynn , P. W. 1994 . Some topics in regenerative steady-state simulation . Acta Applicandae Mathematicae 34 , 225 -- 236 . Glynn, P. W. 1994. Some topics in regenerative steady-state simulation. Acta Applicandae Mathematicae 34, 225--236.","journal-title":"Acta Applicandae Mathematicae"},{"key":"e_1_2_1_21_1","doi-asserted-by":"crossref","first-page":"701","DOI":"10.1080\/15326349408807318","article-title":"Importance sampling for Markov chains: Asymptotics for the variance","volume":"10","author":"Glynn P. W.","year":"1995","unstructured":"Glynn , P. W. 1995 . Importance sampling for Markov chains: Asymptotics for the variance . Stochastic Models 10 , 701 -- 717 . Glynn, P. W. 1995. Importance sampling for Markov chains: Asymptotics for the variance. Stochastic Models 10, 701--717.","journal-title":"Stochastic Models"},{"key":"e_1_2_1_22_1","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.35.11.1367"},{"key":"e_1_2_1_23_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.40.3.505"},{"key":"e_1_2_1_24_1","doi-asserted-by":"publisher","DOI":"10.1109\/12.123381"},{"key":"e_1_2_1_25_1","doi-asserted-by":"crossref","first-page":"375","DOI":"10.1287\/opre.28.2.375","article-title":"The almost regenerative method","volume":"28","author":"Gunther F. L.","year":"1980","unstructured":"Gunther , F. L. and Wolff , R. W. 1980 . The almost regenerative method . Operat. Resear. 28 , 375 -- 387 . Gunther, F. L. and Wolff, R. W. 1980. The almost regenerative method. Operat. Resear. 28, 375--387.","journal-title":"Operat. Resear."},{"key":"e_1_2_1_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/203091.203094"},{"key":"e_1_2_1_27_1","doi-asserted-by":"publisher","DOI":"10.1145\/508366.508367"},{"key":"e_1_2_1_28_1","doi-asserted-by":"crossref","first-page":"772","DOI":"10.2307\/1425933","article-title":"Discrete-time methods for simulating continuous-time Markov chains","volume":"8","author":"Hordijk A.","year":"1976","unstructured":"Hordijk , A. , Iglehart , D. L. , and Schassberger , R. 1976 . Discrete-time methods for simulating continuous-time Markov chains . Adv. Appl. Probab. 8 , 772 -- 788 . Hordijk, A., Iglehart, D. L., and Schassberger, R. 1976. Discrete-time methods for simulating continuous-time Markov chains. Adv. Appl. Probab. 8, 772--788.","journal-title":"Adv. Appl. Probab."},{"key":"e_1_2_1_29_1","unstructured":"Kemeny J. G. and Snell J. L. 1960. Finite Markov Chains. Van Nostrand Princeton NJ.  Kemeny J. G. and Snell J. L. 1960. Finite Markov Chains. Van Nostrand Princeton NJ."},{"key":"e_1_2_1_30_1","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1287\/mnsc.28.2.173","article-title":"A renewal theoretic approach to bias reduction in regenerative simulations","volume":"24","author":"Meketon M. S.","year":"1982","unstructured":"Meketon , M. S. and Heidelberger , P. 1982 . A renewal theoretic approach to bias reduction in regenerative simulations . Manag. Science 24 , 173 -- 181 . Meketon, M. S. and Heidelberger, P. 1982. A renewal theoretic approach to bias reduction in regenerative simulations. Manag. Science 24, 173--181.","journal-title":"Manag. Science"},{"key":"e_1_2_1_31_1","doi-asserted-by":"crossref","first-page":"830","DOI":"10.1287\/opre.37.5.830","article-title":"Sensitivity analysis for simulations via likelihood ratios","volume":"37","author":"Reiman M. I.","year":"1989","unstructured":"Reiman , M. I. and Weiss , A. 1989 . Sensitivity analysis for simulations via likelihood ratios . Operat. Resear. 37 , 830 -- 844 . Reiman, M. I. and Weiss, A. 1989. Sensitivity analysis for simulations via likelihood ratios. Operat. Resear. 37, 830--844.","journal-title":"Operat. Resear."},{"key":"e_1_2_1_32_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.37.1.72"},{"volume-title":"Approximation Theorems of Mathematical Statistics","author":"Serfling R. J.","key":"e_1_2_1_33_1","unstructured":"Serfling , R. J. 1980. Approximation Theorems of Mathematical Statistics . John Wiley & Sons , New York, NY . Serfling, R. J. 1980. Approximation Theorems of Mathematical Statistics. John Wiley & Sons, New York, NY."},{"volume-title":"Regenerative Stochastic Simulation","author":"Shedler G. S.","key":"e_1_2_1_34_1","unstructured":"Shedler , G. S. 1993. Regenerative Stochastic Simulation . Academic Press , San Diego, CA . Shedler, G. S. 1993. Regenerative Stochastic Simulation. Academic Press, San Diego, CA."},{"key":"e_1_2_1_35_1","doi-asserted-by":"publisher","DOI":"10.1016\/0166-5316(92)90033-D"}],"container-title":["ACM Transactions on Modeling and Computer Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1147224.1147228","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1147224.1147228","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T15:06:23Z","timestamp":1750259183000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1147224.1147228"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,7]]},"references-count":35,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2006,7]]}},"alternative-id":["10.1145\/1147224.1147228"],"URL":"https:\/\/doi.org\/10.1145\/1147224.1147228","relation":{},"ISSN":["1049-3301","1558-1195"],"issn-type":[{"type":"print","value":"1049-3301"},{"type":"electronic","value":"1558-1195"}],"subject":[],"published":{"date-parts":[[2006,7]]},"assertion":[{"value":"2006-07-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}