{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T13:02:13Z","timestamp":1770901333547,"version":"3.50.1"},"reference-count":46,"publisher":"Informa UK Limited","issue":"4","content-domain":{"domain":["www.tandfonline.com"],"crossmark-restriction":true},"short-container-title":["Sequential Analysis"],"published-print":{"date-parts":[[2016,10]]},"DOI":"10.1080\/07474946.2016.1238266","type":"journal-article","created":{"date-parts":[[2016,11,17]],"date-time":"2016-11-17T09:57:38Z","timestamp":1479376658000},"page":"536-559","update-policy":"https:\/\/doi.org\/10.1080\/tandf_crossmark_01","source":"Crossref","is-referenced-by-count":4,"title":["On stochastic ordering and control charts for tra\ufb03c intensity"],"prefix":"10.1080","volume":"35","author":[{"given":"Manuel Cabral","family":"Morais","sequence":"first","affiliation":[{"name":",","place":["Portugal"]}]},{"given":"Ant\u00f3nio","family":"Pacheco","sequence":"additional","affiliation":[{"name":",","place":["Portugal"]}]}],"member":"301","published-online":{"date-parts":[[2016,11,17]]},"reference":[{"key":"e_1_3_2_2_1","unstructured":"Adan I. and Resing (2002). Queueing Theory Department of Mathematics and Computing Science Eindhoven University of Technology The Netherlands."},{"key":"e_1_3_2_3_1","unstructured":"Asmussen S. (2003). Applied Probability and Queues New York: Springer-Verlag."},{"key":"e_1_3_2_4_1","first-page":"185","volume":"22","author":"Assaf D.","year":"1985","unstructured":"Assaf, D., Shaked M, ., and Shanthikumar, J. G. (1985). First-Passage Times with PFr Densities, Journal of Applied Probability 22: 185\u2013196.","journal-title":"First-Passage Times with PFr Densities, Journal of Applied Probability"},{"key":"e_1_3_2_5_1","first-page":"939","volume":"36","author":"Bene\u0161 V. E.","year":"1957","unstructured":"Bene\u0161, V. E. (1957). A Su\ufb03cient Set of Statistics for a Simple Telephone Exchange Model, Bell System Technical Journal 36: 939\u2013964.","journal-title":"A Su\ufb03cient Set of Statistics for a Simple Telephone Exchange Model, Bell System Technical Journal"},{"key":"e_1_3_2_6_1","first-page":"94","volume":"44","author":"Bhat U. N.","year":"1971","unstructured":"Bhat, U. N. (1971). A Control Technique for the Parameters of Stochastic Processes, Bulletin de l\u2019Institut International de Statistique 44: 94\u201398.","journal-title":"A Control Technique for the Parameters of Stochastic Processes, Bulletin de l\u2019Institut International de Statistique"},{"key":"e_1_3_2_7_1","first-page":"151","volume":"8","author":"Bhat U. N.","year":"1987","unstructured":"Bhat, U. N. (1987). A Statistical Technique for the Control of Tra\ufb03c Intensity in Markovian Queue, Annals of Operations Research 8: 151\u2013164.","journal-title":"A Statistical Technique for the Control of Tra\ufb03c Intensity in Markovian Queue, Annals of Operations Research"},{"key":"e_1_3_2_8_1","first-page":"955","volume":"20","author":"Bhat U. N. and Rao","year":"1972","unstructured":"Bhat, U. N. and Rao (1972). A Statistical Technique for the Control of Tra\ufb03c Intensity in the Queuing Systems M\/G\/1 and GI\/M\/1, Operations Research 20: 955\u2013966.","journal-title":"A Statistical Technique for the Control of Tra\ufb03c Intensity in the Queuing Systems M\/G\/1 and GI\/M\/1, Operations Research"},{"key":"e_1_3_2_9_1","first-page":"539","volume":"59","author":"Brook D. and Evans","year":"1972","unstructured":"Brook, D. and Evans (1972). An Approach to the Probability Distribution of CUSUM Run Length, Biometrika 59: 539\u2013549.","journal-title":"An Approach to the Probability Distribution of CUSUM Run Length, Biometrika"},{"key":"e_1_3_2_10_1","first-page":"1000","volume":"11","author":"Brown M. and Chaganty","year":"1983","unstructured":"Brown, M. and Chaganty (1983). On the First Passage Time Distribution for a Class of Markov Chains, Annals of Probability 11: 1000\u20131008.","journal-title":"On the First Passage Time Distribution for a Class of Markov Chains, Annals of Probability"},{"key":"e_1_3_2_11_1","first-page":"782","volume":"58","author":"Chen N.","year":"2011","unstructured":"Chen, N., Yuan, Y., and Zhou, S. (2011). Performance Analysis of Queue Length Monitoring of M\/G\/1 Systems, Naval Research Logistics 58: 782\u2013794.","journal-title":"Performance Analysis of Queue Length Monitoring of M\/G\/1 Systems, Naval Research Logistics"},{"key":"e_1_3_2_12_1","first-page":"245","volume":"57","author":"Chen N. and Zhou","year":"2015","unstructured":"Chen, N. and Zhou (2015). CUSUM Statistical Monitoring of M\/M\/1 Queues and Extensions, Technometrics 57: 245\u2013256.","journal-title":"CUSUM Statistical Monitoring of M\/M\/1 Queues and Extensions, Technometrics"},{"key":"e_1_3_2_13_1","first-page":"1036","volume":"28","author":"Clarke A. B.","year":"1957","unstructured":"Clarke, A. B. (1957). Maximum Likelihood Estimates in a Simple Queue, Annals of Mathematical Statistics 28: 1036\u20131040.","journal-title":"Maximum Likelihood Estimates in a Simple Queue, Annals of Mathematical Statistics"},{"key":"e_1_3_2_14_1","unstructured":"Feller W. (1971). An Introduction to Probability Theory and Its Applications 2nd ed. New York: Wiley."},{"key":"e_1_3_2_15_1","first-page":"153","volume":"21","author":"Greenberg I.","year":"1997","unstructured":"Greenberg, I. (1997). Markov Chain Approximation Methods in a Class of Level-Crossing Problems, Operations Research Letters 21: 153\u2013158.","journal-title":"Markov Chain Approximation Methods in a Class of Level-Crossing Problems, Operations Research Letters"},{"key":"e_1_3_2_16_1","doi-asserted-by":"crossref","unstructured":"Gross D. Shortle J. F. Thompson J. M. and Harris C. M. (2008). Fundamentals of Queueing Theory 4th ed. Hoboken: Wiley.","DOI":"10.1002\/9781118625651"},{"key":"e_1_3_2_17_1","first-page":"200","volume":"30","author":"Hung Y.-C.","year":"2012","unstructured":"Hung, Y.-C., Michailidis, G., and Chuang, S.-C. (2012). Estimation and Monitoring of Tra\ufb03c Intensities with Application to Control of Stochastic Systems, Applied Stochastic Models in Business and Industry 30: 200\u2013217.","journal-title":"Estimation and Monitoring of Tra\ufb03c Intensities with Application to Control of Stochastic Systems, Applied Stochastic Models in Business and Industry"},{"key":"e_1_3_2_18_1","doi-asserted-by":"publisher","DOI":"10.1016\/0026-2714(95)00047-6"},{"key":"e_1_3_2_19_1","first-page":"131","volume":"58","author":"Jain S.","year":"2000","unstructured":"Jain, S. (2000). An Autoregressive Process and Its Application to Queueing Model, Metron 58: 131\u2013138.","journal-title":"An Autoregressive Process and Its Application to Queueing Model, Metron"},{"key":"e_1_3_2_20_1","doi-asserted-by":"publisher","DOI":"10.1080\/07474948908836173"},{"key":"e_1_3_2_21_1","first-page":"899","volume":"5","author":"Kamae T.","year":"1977","unstructured":"Kamae, T., Krengel, U., and O\u2019Brien, G .L. (1977). Stochastic Inequalities on Partially Ordered Spaces, Annals of Probability 5: 899\u2013912.","journal-title":"Stochastic Inequalities on Partially Ordered Spaces, Annals of Probability"},{"key":"e_1_3_2_22_1","first-page":"827","volume":"27","author":"Karasu I. and \u00d6zekici","year":"1989","unstructured":"Karasu, I. and \u00d6zekici (1989). NBUE and NWUE Properties of Increasing Markov Processes, Journal of Applied Probability 27: 827\u2013834.","journal-title":"NBUE and NWUE Properties of Increasing Markov Processes, Journal of Applied Probability"},{"key":"e_1_3_2_23_1","first-page":"33","volume":"11","author":"Karlin S.","year":"1964","unstructured":"Karlin, S. (1964). Total Positivity, Absorption Probabilities and Applications, Transactions of American Mathematical Society 11: 33\u2013107.","journal-title":"Total Positivity, Absorption Probabilities and Applications, Transactions of American Mathematical Society"},{"key":"e_1_3_2_24_1","first-page":"151","volume":"13","author":"Kendall D. G.","year":"1951","unstructured":"Kendall, D. G. (1951). Some Problems in the Theory of Queues, Journal of Royal Statistical Society, Series B 13: 151\u2013185.","journal-title":"Some Problems in the Theory of Queues, Journal of Royal Statistical Society, Series B"},{"key":"e_1_3_2_25_1","first-page":"338","volume":"24","author":"Kendall D. G.","year":"1953","unstructured":"Kendall, D. G. (1953). Stochastic Processes Occurring in the Theory of Queues and Their Analysis by the Method of the Imbedded Markov Chain, Annals of Mathematical Statistics 24: 338\u2013354.","journal-title":"Stochastic Processes Occurring in the Theory of Queues and Their Analysis by the Method of the Imbedded Markov Chain, Annals of Mathematical Statistics"},{"key":"e_1_3_2_26_1","doi-asserted-by":"crossref","unstructured":"Kijima M. (1997). Markov Processes for Stochastic Modeling London: Chapman & Hall.","DOI":"10.1007\/978-1-4899-3132-0"},{"key":"e_1_3_2_27_1","first-page":"317","volume":"39","author":"Kim S.-H.","year":"2007","unstructured":"Kim, S.-H., Alexopoulos, C., Tsui, K.-L., and Wilson, J. R. (2007). A Distribution-Free Tabular CUSUM Chart for Autocorrelated Data, IIE Transactions 39: 317\u2013330.","journal-title":"A Distribution-Free Tabular CUSUM Chart for Autocorrelated Data, IIE Transactions"},{"key":"e_1_3_2_28_1","doi-asserted-by":"publisher","DOI":"10.1016\/0304-4149(95)00020-8"},{"key":"e_1_3_2_29_1","first-page":"1","volume":"34","author":"Li H. and Shaked","year":"1997","unstructured":"Li, H. and Shaked (1997). Aging First-Passage Times of Markov Processes: A Matrix Approach, Journal of Applied Probability 34: 1\u201313.","journal-title":"Aging First-Passage Times of Markov Processes: A Matrix Approach, Journal of Applied Probability"},{"key":"e_1_3_2_30_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0305004100027638"},{"key":"e_1_3_2_31_1","unstructured":"Marshall A. W. and Olkin (2007). Life Distributions: Structure of Nonparametric Semiparametric and Parametric Families New York: Springer."},{"key":"e_1_3_2_32_1","unstructured":"Morais M. C. (2002). Stochastic Ordering in the Performance Analysis of Quality Control Schemes Ph.D. diss. Instituto Superior T\u00e9cnico Universidade T\u00e9cnica de Lisboa."},{"key":"e_1_3_2_33_1","volume-title":"On ARL-unbiased Charts to Monitor the Tra\ufb03c Intensity of a Single Server Queue, in Proceedings XIIth International Workshop on Intelligent Statistical Quality Control","author":"Morais M. C. and Knoth","year":"2016","unstructured":"Morais, M. C. and Knoth (2016). On ARL-unbiased Charts to Monitor the Tra\ufb03c Intensity of a Single Server Queue, in Proceedings XIIth International Workshop on Intelligent Statistical Quality Control, August 16\u201319, Hamburg, Germany."},{"key":"e_1_3_2_34_1","first-page":"405","volume":"25","author":"Morais M. C. and Pacheco","year":"2006","unstructured":"Morais, M. C. and Pacheco (2006). Assessing the Impact of Head Starts in the Performance of One-Sided Markov-Type Control Schemes, Sequential Analysis 25: 405\u2013420.","journal-title":"Assessing the Impact of Head Starts in the Performance of One-Sided Markov-Type Control Schemes, Sequential Analysis"},{"key":"e_1_3_2_35_1","first-page":"88","volume":"31","author":"Morais M. C. and Pacheco","year":"2012","unstructured":"Morais, M. C. and Pacheco (2012). A Note on the Aging Properties of the Run Length of Markov-Type Control Charts, Sequential Analysis 31: 88\u201398.","journal-title":"A Note on the Aging Properties of the Run Length of Markov-Type Control Charts, Sequential Analysis"},{"key":"e_1_3_2_36_1","first-page":"161","volume":"7","author":"Nadarajah S. and Kotz","year":"2005","unstructured":"Nadarajah, S. and Kotz (2005). On the Linear Combination of Exponential and Gamma Random Variables, Entropy 7: 161\u2013171.","journal-title":"On the Linear Combination of Exponential and Gamma Random Variables, Entropy"},{"key":"e_1_3_2_37_1","volume-title":"Queueing theory, in Encyclopedia of Statistical Sciences, vol. 7, S. Kotz and N. L. Johnson, eds., pp. 483\u2013489","author":"Pakes A. G.","year":"1986","unstructured":"Pakes, A. G. (1986). Queueing theory, in Encyclopedia of Statistical Sciences, vol. 7, S. Kotz and N. L. Johnson, eds., pp. 483\u2013489, New York: Wiley."},{"key":"e_1_3_2_38_1","doi-asserted-by":"crossref","unstructured":"Prabhu N. U. (1997). Foundations of Queueing Theory Boston: Kluwer.","DOI":"10.1007\/978-1-4615-6205-4"},{"key":"e_1_3_2_39_1","doi-asserted-by":"publisher","DOI":"10.1080\/01621459.1958.10501474"},{"key":"e_1_3_2_40_1","first-page":"63","volume":"21","author":"Rao S. S.","year":"1984","unstructured":"Rao, S. S., Bhat, U. N., and Harishchandra, K. (1984). Control of Tra\ufb03c Intensity in a Queue\u2014A Method Based on SPRT, Opsearch 21: 63\u201380.","journal-title":"Control of Tra\ufb03c Intensity in a Queue\u2014A Method Based on SPRT, Opsearch"},{"key":"e_1_3_2_41_1","unstructured":"Santos M. D. M. (2016). On Control Charts and the Detection of Increases in the Tra\ufb03c Intensity of Queueing Systems M.Sc. thesis Instituto Superior T\u00e9cnico Universidade de Lisboa."},{"key":"e_1_3_2_42_1","volume-title":"Aging First-Passage Times, In Encyclopedia of Statistical Sciences: Update, vol. 1, S. Kotz, C. B. Read, and D. L. Banks, eds., pp. 11\u201320","author":"Shaked M. and Li","year":"1997","unstructured":"Shaked, M. and Li (1997). Aging First-Passage Times, In Encyclopedia of Statistical Sciences: Update, vol. 1, S. Kotz, C. B. Read, and D. L. Banks, eds., pp. 11\u201320, New York: Wiley."},{"key":"e_1_3_2_43_1","unstructured":"Shaked M. and Shanthikumar (1994). Stochastic Orders and Their Applications London: Academic Press."},{"key":"e_1_3_2_44_1","first-page":"1149","volume":"32","author":"Shore H.","year":"2000","unstructured":"Shore, H. (2000). General Control Charts for Attributes, IIE Transactions 32: 1149\u20131160.","journal-title":"General Control Charts for Attributes, IIE Transactions"},{"key":"e_1_3_2_45_1","first-page":"1117","volume":"38","author":"Shore H.","year":"2006","unstructured":"Shore, H. (2006). Control Charts for the Queue Length in a G\/G\/s System, IIE Transactions 38: 1117\u20131130.","journal-title":"Control Charts for the Queue Length in a G\/G\/s System, IIE Transactions"},{"key":"e_1_3_2_46_1","doi-asserted-by":"publisher","DOI":"10.1017\/S0001867800035874"},{"key":"e_1_3_2_47_1","volume-title":"Control of Tra\ufb03c Intensity in Hyperexponential and Mixed Erlang Queueing Systems with a Method Based on SPRT, Mathematical Problems in Engineering","author":"Zobu M. and Sa\u01e7lam","year":"2013","unstructured":"Zobu, M. and Sa\u01e7lam (2013). Control of Tra\ufb03c Intensity in Hyperexponential and Mixed Erlang Queueing Systems with a Method Based on SPRT, Mathematical Problems in Engineering 2013, article ID 241241. doi: http:\/\/dx.doi.org\/10.1155\/2013\/241241"}],"container-title":["Sequential Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.tandfonline.com\/doi\/pdf\/10.1080\/07474946.2016.1238266","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,12]],"date-time":"2026-02-12T12:01:55Z","timestamp":1770897715000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.tandfonline.com\/doi\/full\/10.1080\/07474946.2016.1238266"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,10]]},"references-count":46,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,10]]}},"alternative-id":["10.1080\/07474946.2016.1238266"],"URL":"https:\/\/doi.org\/10.1080\/07474946.2016.1238266","relation":{},"ISSN":["0747-4946","1532-4176"],"issn-type":[{"value":"0747-4946","type":"print"},{"value":"1532-4176","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,10]]},"assertion":[{"value":"The publishing and review policy for this title is described in its Aims & Scope.","order":1,"name":"peerreview_statement","label":"Peer Review Statement"},{"value":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=lsqa20","URL":"http:\/\/www.tandfonline.com\/action\/journalInformation?show=aimsScope&journalCode=lsqa20","order":2,"name":"aims_and_scope_url","label":"Aim & Scope"},{"value":"2015-11-13","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-08-21","order":1,"name":"revised","label":"Revised","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-09-03","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-11-17","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}