{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,31]],"date-time":"2025-12-31T10:30:43Z","timestamp":1767177043196,"version":"build-2238731810"},"reference-count":14,"publisher":"Cambridge University Press (CUP)","issue":"1","license":[{"start":{"date-parts":[[2016,7,1]],"date-time":"2016-07-01T00:00:00Z","timestamp":1467331200000},"content-version":"unspecified","delay-in-days":3775,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Advances in Applied Probability"],"published-print":{"date-parts":[[2006,3]]},"abstract":"<jats:p>\n                    In this paper, motivated by the problem of the coexistence on transmission links of telecommunications networks of elastic and unresponsive traffic, we study the impact on the busy period of an M\/M\/1 queue of a small perturbation in the service rate. The perturbation depends upon an independent stationary process (\n                    <jats:italic>X<\/jats:italic>\n                    (\n                    <jats:italic>t<\/jats:italic>\n                    )) and is quantified by means of a parameter \u03b5 \u226a 1. We specifically compute the two first terms of the power series expansion in \u03b5 of the mean value of the busy period duration. This allows us to study the validity of the reduced service rate approximation, which consists in comparing the perturbed M\/M\/1 queue with the M\/M\/1 queue whose service rate is constant and equal to the mean value of the perturbation. For the first term of the expansion, the two systems are equivalent. For the second term, the situation is more complex and it is shown that the correlations of the environment process (\n                    <jats:italic>X<\/jats:italic>\n                    (\n                    <jats:italic>t<\/jats:italic>\n                    )) play a key role.\n                  <\/jats:p>","DOI":"10.1239\/aap\/1143936150","type":"journal-article","created":{"date-parts":[[2006,4,4]],"date-time":"2006-04-04T03:51:16Z","timestamp":1144122676000},"page":"263-283","source":"Crossref","is-referenced-by-count":7,"title":["Perturbation analysis of a variable M\/M\/1 queue: a probabilistic approach"],"prefix":"10.1017","volume":"38","author":[{"given":"Nelson","family":"Antunes","sequence":"first","affiliation":[]},{"given":"Christine","family":"Fricker","sequence":"additional","affiliation":[]},{"given":"Fabrice","family":"Guillemin","sequence":"additional","affiliation":[]},{"given":"Philippe","family":"Robert","sequence":"additional","affiliation":[]}],"member":"56","published-online":{"date-parts":[[2016,7,1]]},"reference":[{"key":"S0001867800000902_ref13","doi-asserted-by":"publisher","DOI":"10.1155\/S1048953398000288"},{"key":"S0001867800000902_ref12","doi-asserted-by":"publisher","DOI":"10.1081\/STM-100001400"},{"key":"S0001867800000902_ref11","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019173523289"},{"key":"S0001867800000902_ref10","first-page":"1395","volume-title":"Proc. IEEE Infocom 1999","author":"Massouli\u00e9","year":"1999"},{"key":"S0001867800000902_ref8","doi-asserted-by":"publisher","DOI":"10.1017\/S0001867800028949"},{"key":"S0001867800000902_ref6","doi-asserted-by":"publisher","DOI":"10.1016\/S0166-5316(03)00115-9"},{"key":"S0001867800000902_ref5","volume-title":"The Single Server Queue","author":"Cohen","year":"1982"},{"key":"S0001867800000902_ref4","doi-asserted-by":"publisher","DOI":"10.1111\/1467-9574.00138"},{"key":"S0001867800000902_ref3","doi-asserted-by":"crossref","unstructured":"[3] Antunes N. , Fricker C. , Guillemin F. and Robert P. (2005). Integration of streaming services and TCP data transmission in the Internet. Submitted.","DOI":"10.1016\/j.peva.2005.07.006"},{"key":"S0001867800000902_ref9","first-page":"1316","volume-title":"Proc. IEEE Infocom 2002","author":"Jelenkovi\u0107","year":"2002"},{"key":"S0001867800000902_ref1","doi-asserted-by":"publisher","DOI":"10.1023\/A:1019111809660"},{"key":"S0001867800000902_ref2","doi-asserted-by":"publisher","DOI":"10.1017\/S0001867800013148"},{"key":"S0001867800000902_ref7","unstructured":"[7] Fricker C. , Guillemin F. and Robert P. (2004). Perturbation analysis of an M\/M\/1 queue in a diffusion random environment. Submitted."},{"key":"S0001867800000902_ref14","unstructured":"[14] Robert P. (2003). Stochastic Networks and Queues (Appl. Math. (New York) 52). Springer, New York."}],"container-title":["Advances in Applied Probability"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.cambridge.org\/core\/services\/aop-cambridge-core\/content\/view\/S0001867800000902","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,2]],"date-time":"2019-05-02T16:33:26Z","timestamp":1556814806000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.cambridge.org\/core\/product\/identifier\/S0001867800000902\/type\/journal_article"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,3]]},"references-count":14,"aliases":["10.1017\/s0001867800000902"],"journal-issue":{"issue":"1","published-print":{"date-parts":[[2006,3]]}},"alternative-id":["S0001867800000902"],"URL":"https:\/\/doi.org\/10.1239\/aap\/1143936150","relation":{},"ISSN":["0001-8678","1475-6064"],"issn-type":[{"value":"0001-8678","type":"print"},{"value":"1475-6064","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,3]]}}}