{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,7,2]],"date-time":"2024-07-02T12:40:01Z","timestamp":1719924001695},"reference-count":72,"publisher":"Walter de Gruyter GmbH","issue":"1","funder":[{"DOI":"10.13039\/501100001871","name":"Funda\u00e7\u00e3o para a Ci\u00eancia e a Tecnologia","doi-asserted-by":"publisher","award":["UID\/Multi\/04621\/2013"],"award-info":[{"award-number":["UID\/Multi\/04621\/2013"]}],"id":[{"id":"10.13039\/501100001871","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2018,6,1]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>This paper describes the application of simple quality control charts to monitor the traffic intensity of single server queues, a still uncommon use of what is arguably the most successful statistical process control tool. These charts play a vital role in the detection of increases in the traffic intensity of single server queueing systems such as the<jats:inline-formula id=\"j_eqc-2017-0030_ineq_9999\"><jats:alternatives><jats:inline-graphic xlink:href=\"graphic\/j_eqc-2017-0030_eq_0125.png\"\/><jats:tex-math>{M\/G\/1}<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>,<jats:inline-formula id=\"j_eqc-2017-0030_ineq_9998\"><jats:alternatives><jats:inline-graphic xlink:href=\"graphic\/j_eqc-2017-0030_eq_0117.png\"\/><jats:tex-math>{GI\/M\/1}<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>and<jats:inline-formula id=\"j_eqc-2017-0030_ineq_9997\"><jats:alternatives><jats:inline-graphic xlink:href=\"graphic\/j_eqc-2017-0030_eq_0115.png\"\/><jats:tex-math>{GI\/G\/1}<\/jats:tex-math><\/jats:alternatives><\/jats:inline-formula>queues. The corresponding control statistics refer solely to a customer-arrival\/departure epoch as opposed to several such epochs, thus they are termed short-memory charts. We compare the RL performance of those charts under three out-of-control scenarios referring to increases in the traffic intensity due to: a decrease in the service rate while the arrival rate remains unchanged; an increase in the arrival rate while the service rate is constant; an increase in the arrival rate accompanied by a proportional decrease in the service rate. These comparisons refer to a broad set of interarrival and service time distributions, namely exponential, Erlang, hyper-exponential, and hypo-exponential. Extensive results and striking illustrations are provided to give the quality control practitioner an idea of how these charts perform in practice.<\/jats:p>","DOI":"10.1515\/eqc-2017-0030","type":"journal-article","created":{"date-parts":[[2018,3,28]],"date-time":"2018-03-28T22:16:22Z","timestamp":1522275382000},"page":"1-21","source":"Crossref","is-referenced-by-count":1,"title":["Comparing Short-Memory Charts to Monitor the Traffic Intensity of Single Server Queues"],"prefix":"10.1515","volume":"33","author":[{"given":"Marta","family":"Santos","sequence":"first","affiliation":[]},{"given":"Manuel Cabral","family":"Morais","sequence":"additional","affiliation":[]},{"given":"Ant\u00f3nio","family":"Pacheco","sequence":"additional","affiliation":[]}],"member":"374","reference":[{"key":"ref601","first-page":"217","article-title":"On ARL-unbiased charts to monitor the traffic intensity of a single server queue","year":"2016","journal-title":"Proceedings of the 12th. 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Soc."},{"key":"ref381","doi-asserted-by":"crossref","first-page":"151","DOI":"10.1007\/BF02187088","article-title":"A statistical technique for the control of traffic intensity in Markovian queue","volume":"8","year":"1987","journal-title":"Ann. Oper. Res."},{"key":"ref281","first-page":"320","article-title":"The performance of control charts for monitoring process dispersion","year":"1995","journal-title":"4th Industrial Engineering Research Conference Proceedings"},{"key":"ref591","year":"2002","journal-title":"Stochastic ordering in the performance analysis of quality control schemes"},{"key":"ref101","volume-title":"An Introduction to Probability Theory And its Applications. 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Res."},{"key":"ref301","year":"2016","journal-title":"On control charts and the detection of increases in the traffic intensity of queueing systems"},{"key":"ref41","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1093\/biomet\/59.3.539","article-title":"An approach to the probability distribution of cusum run length","volume":"59","year":"1972","journal-title":"Biometrika"},{"key":"ref61","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1080\/00401706.2014.923787","article-title":"CUSUM statistical monitoring of M\/M\/1 queues and extensions","volume":"57","year":"2015","journal-title":"Technometrics"},{"key":"ref51","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1002\/nav.20483","article-title":"Performance analysis of queue length monitoring of M\/G\/1 systems","volume":"58","year":"2011","journal-title":"Naval Res. Logist."},{"key":"ref291","volume-title":"Introduction to Probability Models","year":"2006"},{"key":"ref571","volume-title":"Introduction to Modeling and Analysis of Stochastic Systems","year":"2011"},{"key":"ref401","doi-asserted-by":"crossref","first-page":"539","DOI":"10.1093\/biomet\/59.3.539","article-title":"An approach to the probability distribution of cusum run length","volume":"59","year":"1972","journal-title":"Biometrika"},{"key":"ref561","volume-title":"Queueing Systems. 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