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When the observations are batched, the method generalizes the method of batch means. One advantage of the method is that it can be used without batching the observations; that is, it can allow for the process variance to be estimated at any time as the simulation runs without waiting for a fixed time horizon to complete. When used in conjunction with batching, the method can improve efficiency (the reciprocal of work times mean-squared error) compared with the standard method of batch means. In numerical experiments, efficiency improvement ranged from a factor of 1.5 (for the waiting time sequence in an M\/M\/1 queueing system with a single integrated path) up to a factor of 14 (for an autoregressive process and 19 integrated paths).<\/jats:p>","DOI":"10.1145\/1243991.1243994","type":"journal-article","created":{"date-parts":[[2007,9,14]],"date-time":"2007-09-14T13:44:55Z","timestamp":1189777495000},"page":"13","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":10,"title":["Simulation output analysis using integrated paths"],"prefix":"10.1145","volume":"17","author":[{"given":"James M.","family":"Calvin","sequence":"first","affiliation":[{"name":"New Jersey Institute of Technology, Newark, NJ"}]}],"member":"320","published-online":{"date-parts":[[2007,7]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1060.0198"},{"key":"e_1_2_1_2_1","doi-asserted-by":"crossref","unstructured":"Billingsley P. 1999. Convergence of Probability Measures second ed. John Wiley & Sons New York New York.  Billingsley P. 1999. Convergence of Probability Measures second ed. John Wiley & Sons New York New York.","DOI":"10.1002\/9780470316962"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.43.9.1288"},{"key":"e_1_2_1_4_1","unstructured":"Knuth D. 1997. The Art of Computer Programming Volume 1: Fundamental Algorithms third ed. Addison-Wesley Reading Massachusetts.   Knuth D. 1997. The Art of Computer Programming Volume 1: Fundamental Algorithms third ed. Addison-Wesley Reading Massachusetts."},{"key":"e_1_2_1_5_1","unstructured":"Meketon M. S. and Schmeiser B. W. 1984. Overlapping batch means: something for nothing&quest; In Proceedings of the 1984 Winter Simulation Conference. Institute of Electrical and Electronics Engineers Piscataway New Jersey 227--230.   Meketon M. S. and Schmeiser B. W. 1984. 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Institute of Electrical and Electronics Engineers","author":"Yeh Y.","key":"e_1_2_1_10_1"}],"container-title":["ACM Transactions on Modeling and Computer Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1243991.1243994","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/1243991.1243994","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T14:47:49Z","timestamp":1750258069000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/1243991.1243994"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,7]]},"references-count":10,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2007,7]]}},"alternative-id":["10.1145\/1243991.1243994"],"URL":"https:\/\/doi.org\/10.1145\/1243991.1243994","relation":{},"ISSN":["1049-3301","1558-1195"],"issn-type":[{"type":"print","value":"1049-3301"},{"type":"electronic","value":"1558-1195"}],"subject":[],"published":{"date-parts":[[2007,7]]},"assertion":[{"value":"2007-07-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}