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In this paper, we use the weak perturbation theory to establish analytic error bounds for the M\/G\/1 model. Numerical examples are carried out to illustrate the quality of the obtained error bounds.<\/jats:p>","DOI":"10.1051\/ro\/2018027","type":"journal-article","created":{"date-parts":[[2018,5,1]],"date-time":"2018-05-01T07:51:28Z","timestamp":1525161088000},"page":"1411-1428","source":"Crossref","is-referenced-by-count":1,"title":["A weak perturbation theory for approximations of invariant measures in M\/G\/1 model"],"prefix":"10.1051","volume":"52","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-0168-3192","authenticated-orcid":false,"given":"Badredine","family":"Issaadi","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Karim","family":"Abbas","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Djamil","family":"A\u00efssani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"250","published-online":{"date-parts":[[2018,12,6]]},"reference":[{"key":"R1","doi-asserted-by":"crossref","unstructured":"Abate J., \nChoudhury G.L. and \nWhitt W., An introduction to numerical transform inversion and its application to probability models, in \nComputational Probability, edited by \nGrassmann W.K.. \nKluwer Academic Publishers \n(2000) 257\u2013323.","DOI":"10.1007\/978-1-4757-4828-4_8"},{"key":"R2","doi-asserted-by":"crossref","first-page":"1444","DOI":"10.1109\/JSAC.2005.851779","volume":"23","author":"Bouabdallah","year":"2005","journal-title":"IEEE J. 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