{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,4]],"date-time":"2025-07-04T13:04:02Z","timestamp":1751634242315,"version":"3.41.0"},"reference-count":19,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2004,10,1]],"date-time":"2004-10-01T00:00:00Z","timestamp":1096588800000},"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":[[2004,10]]},"abstract":"<jats:p>When simulating a stochastic system, simulationists often are interested in estimating various steady-state performance measures. The classical point estimator for such a measure involves simply taking the time average of an appropriate function of the process being simulated. Since the simulation can not be initiated with the (unknown) steady-state distribution, the classical point estimator is generally biased. In the context of regenerative steady-state simulation, a variety of other point estimators have been developed in an attempt to minimize the bias. In this paper, we provide an empirical comparison of these estimators in the context of four different continuous-time Markov chain models. The bias of the point estimators and the coverage probabilities of the associated confidence intervals are reported for the four models. Conclusions are drawn from this experimental work as to which methods are most effective in reducing bias.<\/jats:p>","DOI":"10.1145\/1029174.1029175","type":"journal-article","created":{"date-parts":[[2005,1,26]],"date-time":"2005-01-26T16:35:53Z","timestamp":1106757353000},"page":"325-343","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":7,"title":["Empirical performance of bias-reducing estimators for regenerative steady-state simulations"],"prefix":"10.1145","volume":"14","author":[{"given":"Ming-Hua","family":"Hsieh","sequence":"first","affiliation":[{"name":"National Chengchi University, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Donald L.","family":"Iglehart","sequence":"additional","affiliation":[{"name":"Stanford University, Stanford, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Peter W.","family":"Glynn","sequence":"additional","affiliation":[{"name":"Stanford University, Stanford, CA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2004,10]]},"reference":[{"volume-title":"Proceedings of the 1992 Winter Simulation Conference. IEEE Computer Society, Press, Los Alamitos, Calif., 577--585","author":"Cash C. R.","key":"e_1_2_1_1_1","unstructured":"Cash , C. R. , Dippold , D. , Long , J. , Nelson , B. , and Pollard , W . 1992. Evaluation of tests for initial conditions bias . In Proceedings of the 1992 Winter Simulation Conference. IEEE Computer Society, Press, Los Alamitos, Calif., 577--585 . 10.1145\/167293.167640 Cash, C. R., Dippold, D., Long, J., Nelson, B., and Pollard, W. 1992. Evaluation of tests for initial conditions bias. In Proceedings of the 1992 Winter Simulation Conference. IEEE Computer Society, Press, Los Alamitos, Calif., 577--585. 10.1145\/167293.167640"},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1080\/00949658408810721","article-title":"Some asymptotic formulas for markov chain with applications to simulation","volume":"19","author":"Glynn P. W.","year":"1984","unstructured":"Glynn , P. W. 1984 . Some asymptotic formulas for markov chain with applications to simulation . J. Stat. Comput. Simul. 19 , 97 -- 112 . Glynn, P. W. 1984. Some asymptotic formulas for markov chain with applications to simulation. J. Stat. Comput. Simul. 19, 97--112.","journal-title":"J. Stat. Comput. Simul."},{"key":"e_1_2_1_3_1","volume-title":"Proc. IEEE 77","author":"Glynn P. W.","year":"1989","unstructured":"Glynn , P. W. 1989 . A GSMP formalism for discrete event systems . Proc. IEEE 77 . 14--23. Glynn, P. W. 1989. A GSMP formalism for discrete event systems. Proc. IEEE 77. 14--23."},{"key":"e_1_2_1_4_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 Appl. Math. 34 , 225 -- 236 . Glynn, P. W. 1994. Some topics in regenerative steady-state simulation. Acta Appl. Math. 34, 225--236.","journal-title":"Acta Appl. Math."},{"key":"e_1_2_1_5_1","volume-title":"Proceedings of the 1995 Winter Simulation Conference. IEEE Computer Society Press, Los Alamitos, Calif. (Arlington, Va.). 165--170","author":"Glynn P. W.","year":"1995","unstructured":"Glynn , P. W. 1995 . Some new results on the initial transient problem . In Proceedings of the 1995 Winter Simulation Conference. IEEE Computer Society Press, Los Alamitos, Calif. (Arlington, Va.). 165--170 . 10.1145\/224401.224458 Glynn, P. W. 1995. Some new results on the initial transient problem. In Proceedings of the 1995 Winter Simulation Conference. IEEE Computer Society Press, Los Alamitos, Calif. (Arlington, Va.). 165--170. 10.1145\/224401.224458"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1287\/opre.38.5.801"},{"key":"e_1_2_1_7_1","doi-asserted-by":"crossref","first-page":"437","DOI":"10.1016\/0167-6377(91)90020-P","article-title":"Analysis of initial transient deletion for replicated steady-state simulations","volume":"10","author":"Glynn P. W.","year":"1991","unstructured":"Glynn , P. W. and Heidelberger , P. 1991 a. Analysis of initial transient deletion for replicated steady-state simulations . Oper. Res. Lett. 10 , 437 -- 443 . Glynn, P. W. and Heidelberger, P. 1991a. Analysis of initial transient deletion for replicated steady-state simulations. Oper. Res. Lett. 10, 437--443.","journal-title":"Oper. Res. Lett."},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1145\/102810.102811"},{"key":"e_1_2_1_9_1","doi-asserted-by":"publisher","DOI":"10.1137\/0913054"},{"key":"e_1_2_1_10_1","doi-asserted-by":"crossref","first-page":"226","DOI":"10.1287\/ijoc.4.3.226","article-title":"Jackknifing under a budget constraint","volume":"4","author":"Glynn P. W.","year":"1992","unstructured":"Glynn , P. W. and Heidelberger , P. 1992 b. Jackknifing under a budget constraint . ORSA J. Comput. 4 , 226 -- 234 . Glynn, P. W. and Heidelberger, P. 1992b. Jackknifing under a budget constraint. ORSA J. Comput. 4, 226--234.","journal-title":"ORSA J. Comput."},{"key":"e_1_2_1_11_1","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1002\/1520-6750(199403)41:2<171::AID-NAV3220410204>3.0.CO;2-N","article-title":"Tests for transient means in simulated time series","volume":"41","author":"Goldsman D.","year":"1994","unstructured":"Goldsman , D. , Schruben , L. , and Swain ., J. 1994 . Tests for transient means in simulated time series . Naval Res. Logist. Quart. 41 , 171 -- 187 . Goldsman, D., Schruben, L., and Swain., J. 1994. Tests for transient means in simulated time series. Naval Res. Logist. Quart. 41, 171--187.","journal-title":"Naval Res. Logist. Quart."},{"key":"e_1_2_1_12_1","doi-asserted-by":"publisher","DOI":"10.1145\/508366.508367"},{"key":"e_1_2_1_13_1","doi-asserted-by":"crossref","first-page":"553","DOI":"10.1002\/nav.3800220311","article-title":"Simulating stable stochastic systems, V: Comparison of ratio estimators","volume":"22","author":"Iglehart D. L.","year":"1975","unstructured":"Iglehart , D. L. 1975 . Simulating stable stochastic systems, V: Comparison of ratio estimators . Naval Res. Logist. Quart. 22 , 553 -- 565 . Iglehart, D. L. 1975. Simulating stable stochastic systems, V: Comparison of ratio estimators. Naval Res. Logist. Quart. 22, 553--565.","journal-title":"Naval Res. Logist. Quart."},{"key":"e_1_2_1_14_1","first-page":"173","article-title":"A renewal theoretic approach to bias reduction in regenerative simulations. Manage","volume":"26","author":"Meketon M.","year":"1982","unstructured":"Meketon , M. and Heidelberger , P. 1982 . A renewal theoretic approach to bias reduction in regenerative simulations. Manage . Sci. 26 , 173 -- 181 . Meketon, M. and Heidelberger, P. 1982. A renewal theoretic approach to bias reduction in regenerative simulations. Manage. Sci. 26, 173--181.","journal-title":"Sci."},{"volume-title":"Handbook of Industrial Engineering, 2 ed.","author":"Nelson B.","key":"e_1_2_1_15_1","unstructured":"Nelson , B. 1992. Initial-condition bias . In Handbook of Industrial Engineering, 2 ed. , G. Salvendy, Ed. Wiley, New York. Nelson, B. 1992. Initial-condition bias. In Handbook of Industrial Engineering, 2 ed., G. Salvendy, Ed. Wiley, New York."},{"key":"e_1_2_1_16_1","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1287\/opre.30.3.569","article-title":"Detecting initialization bias in simulation output","volume":"30","author":"Schruben L.","year":"1982","unstructured":"Schruben , L. 1982 . Detecting initialization bias in simulation output . Oper. Res. 30 , 3, 151 -- 153 . Schruben, L. 1982. Detecting initialization bias in simulation output. Oper. Res. 30, 3, 151--153.","journal-title":"Oper. Res."},{"key":"e_1_2_1_17_1","doi-asserted-by":"crossref","first-page":"1167","DOI":"10.1287\/opre.31.6.1167","article-title":"Optimal tests for initialization bias in simulation output","volume":"31","author":"Schruben L.","year":"1983","unstructured":"Schruben , L. , Singh , H. , and Tierney , L. 1983 . Optimal tests for initialization bias in simulation output . Oper. Res. 31 , 6, 1167 -- 1178 . Schruben, L., Singh, H., and Tierney, L. 1983. Optimal tests for initialization bias in simulation output. Oper. Res. 31, 6, 1167--1178.","journal-title":"Oper. Res."},{"key":"e_1_2_1_18_1","doi-asserted-by":"publisher","DOI":"10.1177\/003754979706900601"},{"volume-title":"Proceedings of the 2000 Winter Simulation Conference. IEEE Computer Society Press, Loss Alamitos, Calif., 755--760","author":"White K. P., J.","key":"e_1_2_1_19_1","unstructured":"White , K. P., J. , Cobb , M. J. , and Spratt , S. C . 2000. A comparison of five steady-state truncation heuristics for simulation . In Proceedings of the 2000 Winter Simulation Conference. IEEE Computer Society Press, Loss Alamitos, Calif., 755--760 . White, K. P., J., Cobb, M. J., and Spratt, S. C. 2000. A comparison of five steady-state truncation heuristics for simulation. In Proceedings of the 2000 Winter Simulation Conference. IEEE Computer Society Press, Loss Alamitos, Calif., 755--760."}],"container-title":["ACM Transactions on Modeling and Computer Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1029174.1029175","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1029174.1029175","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T16:31:07Z","timestamp":1750264267000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1029174.1029175"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10]]},"references-count":19,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2004,10]]}},"alternative-id":["10.1145\/1029174.1029175"],"URL":"https:\/\/doi.org\/10.1145\/1029174.1029175","relation":{},"ISSN":["1049-3301","1558-1195"],"issn-type":[{"type":"print","value":"1049-3301"},{"type":"electronic","value":"1558-1195"}],"subject":[],"published":{"date-parts":[[2004,10]]},"assertion":[{"value":"2004-10-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}