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Simul."],"published-print":{"date-parts":[[2017,7,31]]},"abstract":"<jats:p>In both cyclic and finite-horizon contexts, piecewise-constant rate functions are commonly encountered in models with nonhomogeneous Poisson processes. We develop an algorithm, with no user-specified parameters, that returns a smoother rate function that maintains the expected number of arrivals. The algorithm proceeds in two steps: PQRS (Piecewise-Quadratic Rate Smoothing) returns a continuous and differentiable piecewise-quadratic function without regard to negativity. If negative rates occur, then MNO (Max Nonnegativity Ordering) returns the maximum of zero and another piecewise-quadratic function. MNO maintains continuity of rates and first derivatives, but with some exceptions. Our analysis allows fitting the MNO--PQRS function to require storage complexity of the order of the number of intervals and computational complexity of the order of the number of intervals squared. MNO--PQRS can be used as a stand-alone routine, or as an endgame for the authors\u2019 earlier algorithm, I-SMOOTH.<\/jats:p>","DOI":"10.1145\/3067663","type":"journal-article","created":{"date-parts":[[2017,8,2]],"date-time":"2017-08-02T19:36:12Z","timestamp":1501702572000},"page":"1-19","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":9,"title":["MNO--PQRS"],"prefix":"10.1145","volume":"27","author":[{"given":"Huifen","family":"Chen","sequence":"first","affiliation":[{"name":"Chung-Yuan University, Taiwan"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bruce W.","family":"Schmeiser","sequence":"additional","affiliation":[{"name":"Purdue University, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2017,8,2]]},"reference":[{"key":"e_1_2_2_1_1","volume-title":"Stegun","author":"Abramowitz Milton","year":"1972","unstructured":"Milton Abramowitz and Irene A . Stegun . 1972 . Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (AMS55). Dover Publications , Inc, New York. Milton Abramowitz and Irene A. Stegun. 1972. Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables (AMS55). Dover Publications, Inc, New York."},{"key":"e_1_2_2_2_1","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.46.7.989.12037"},{"key":"e_1_2_2_3_1","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.1040.0236"},{"key":"e_1_2_2_4_1","doi-asserted-by":"publisher","DOI":"10.1109\/WSC.2011.6147776"},{"key":"e_1_2_2_5_1","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.1120.0512"},{"key":"e_1_2_2_6_1","doi-asserted-by":"publisher","DOI":"10.1109\/WSC.2014.7019914"},{"key":"e_1_2_2_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/WSC.2015.7408197"},{"key":"e_1_2_2_8_1","volume-title":"Conte and Carl de Boor","author":"Samuel","year":"1980","unstructured":"Samuel D. Conte and Carl de Boor . 1980 . Elementary Numerical Analysis: An Algorithmic Approach. McGraw-Hill , Inc, New York. Samuel D. Conte and Carl de Boor. 1980. Elementary Numerical Analysis: An Algorithmic Approach. McGraw-Hill, Inc, New York."},{"key":"e_1_2_2_9_1","volume-title":"Matrices with Applications in Statistics","author":"Graybill Franklin A.","unstructured":"Franklin A. Graybill . 1983. Matrices with Applications in Statistics ( 2 nd ed.). Wadsworth, Inc. , Belmont, California . Franklin A. Graybill. 1983. Matrices with Applications in Statistics (2nd ed.). Wadsworth, Inc., Belmont, California.","edition":"2"},{"key":"e_1_2_2_10_1","doi-asserted-by":"publisher","DOI":"10.1177\/003754978404300406"},{"key":"e_1_2_2_11_1","doi-asserted-by":"publisher","DOI":"10.1080\/00949650008812036"},{"key":"e_1_2_2_12_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0377-2217(00)00203-4"},{"key":"e_1_2_2_13_1","doi-asserted-by":"publisher","DOI":"10.5555\/3217859.3217868"},{"key":"e_1_2_2_14_1","doi-asserted-by":"publisher","DOI":"10.1080\/07408170490507693"},{"key":"e_1_2_2_16_1","doi-asserted-by":"publisher","DOI":"10.1109\/TAP.1983.1143132"},{"key":"e_1_2_2_17_1","doi-asserted-by":"publisher","DOI":"10.2307\/2690437"},{"key":"e_1_2_2_18_1","doi-asserted-by":"publisher","DOI":"10.1109\/WSC.2014.7019915"},{"key":"e_1_2_2_19_1","volume-title":"Leemis","author":"Nicol David M.","year":"2016","unstructured":"David M. Nicol and Lawrence M . Leemis . 2016 . Continuous Piecewise-Linear Intensity Function Estimation for Nonhomogeneous Poisson Process Count Data. Technical Report, Department of Mathematics, The College of William 8 Mary. David M. Nicol and Lawrence M. Leemis. 2016. Continuous Piecewise-Linear Intensity Function Estimation for Nonhomogeneous Poisson Process Count Data. Technical Report, Department of Mathematics, The College of William 8 Mary."},{"key":"e_1_2_2_20_1","doi-asserted-by":"publisher","DOI":"10.1145\/2331140.2331143"},{"key":"e_1_2_2_21_1","volume-title":"Proceedings of the 1980 Winter Simulation Conference, T. I. Oren, C. M. Shub, and P. F. Roth (Eds.). Institute of Electrical and Electronics Engineers","author":"Schmeiser Bruce W.","year":"1980","unstructured":"Bruce W. Schmeiser . 1980 . Random Variate Generation: A Survey . In Proceedings of the 1980 Winter Simulation Conference, T. I. Oren, C. M. Shub, and P. F. Roth (Eds.). Institute of Electrical and Electronics Engineers , Piscataway, New Jersey, 79--104. Bruce W. Schmeiser. 1980. Random Variate Generation: A Survey. In Proceedings of the 1980 Winter Simulation Conference, T. I. Oren, C. M. Shub, and P. F. Roth (Eds.). Institute of Electrical and Electronics Engineers, Piscataway, New Jersey, 79--104."},{"key":"e_1_2_2_22_1","volume-title":"Proceedings of the Industrial Engineering Research Conference. Institute of Industrial Engineers, 6","author":"Schmeiser Bruce W.","year":"2003","unstructured":"Bruce W. Schmeiser , Rishab M. Rao , and Nyoman Kumala . 2003 . Smoothing piecewise-constant rate functions . In Proceedings of the Industrial Engineering Research Conference. Institute of Industrial Engineers, 6 pages (cd only). Bruce W. Schmeiser, Rishab M. Rao, and Nyoman Kumala. 2003. Smoothing piecewise-constant rate functions. In Proceedings of the Industrial Engineering Research Conference. Institute of Industrial Engineers, 6 pages (cd only)."},{"key":"e_1_2_2_23_1","doi-asserted-by":"publisher","DOI":"10.1109\/WSC.2014.7019913"}],"container-title":["ACM Transactions on Modeling and Computer Simulation"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3067663","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3067663","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,18]],"date-time":"2025-06-18T03:30:18Z","timestamp":1750217418000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3067663"}},"subtitle":["Max Nonnegativity Ordering\u2014Piecewise-Quadratic Rate Smoothing"],"short-title":[],"issued":{"date-parts":[[2017,7,31]]},"references-count":22,"journal-issue":{"issue":"3","published-print":{"date-parts":[[2017,7,31]]}},"alternative-id":["10.1145\/3067663"],"URL":"https:\/\/doi.org\/10.1145\/3067663","relation":{},"ISSN":["1049-3301","1558-1195"],"issn-type":[{"type":"print","value":"1049-3301"},{"type":"electronic","value":"1558-1195"}],"subject":[],"published":{"date-parts":[[2017,7,31]]},"assertion":[{"value":"2015-12-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-03-01","order":1,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2017-08-02","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}