{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,2,27]],"date-time":"2024-02-27T00:11:00Z","timestamp":1708992660038},"reference-count":21,"publisher":"Walter de Gruyter GmbH","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,3,1]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>This paper proposes the nonparametric asymmetric kernel method in the study of strong stability of the PH\/M\/1 queuing system, after perturbation of arrival distribution to evaluate the proximity of the complex GI\/M\/1 system, where GI is a unknown general distribution.\nThe class of generalized gamma (GG) kernels is considered because of its several interesting properties and flexibility.\nA simulation for several models illustrates the performance of the GG asymmetric kernel estimators in the study of strong stability of the PH\/M\/1, by computing the variation distance and the stability error.<\/jats:p>","DOI":"10.1515\/mcma-2023-2023","type":"journal-article","created":{"date-parts":[[2023,12,12]],"date-time":"2023-12-12T23:05:39Z","timestamp":1702422339000},"page":"81-92","source":"Crossref","is-referenced-by-count":0,"title":["Asymmetric kernel method in the study of strong stability of the PH\/M\/1 queuing system"],"prefix":"10.1515","volume":"30","author":[{"given":"Yasmina","family":"Djabali","sequence":"first","affiliation":[{"name":"Research Unit LaMOS , University of Bejaia , 06000 Bejaia , Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sedda","family":"Hakmi","sequence":"additional","affiliation":[{"name":"Research Unit LaMOS , University of Bejaia , 06000 Bejaia , Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Nabil","family":"Zougab","sequence":"additional","affiliation":[{"name":"Research Unit LaMOS and Electrical Engineering Department , University of Bejaia , 06000 Bejaia , Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Djamil","family":"A\u00efssani","sequence":"additional","affiliation":[{"name":"Research Unit LaMOS , University of Bejaia , 06000 Bejaia , Algeria"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"374","published-online":{"date-parts":[[2023,12,13]]},"reference":[{"key":"2024022618254290367_j_mcma-2023-2023_ref_001","doi-asserted-by":"crossref","unstructured":"K. Abbas, B. Heidergott and D. A\u00efssani,\nA functional approximation for the M\/G\/1\/N queue,\nDiscrete Event Dyn. Syst. 23 (2013), no. 1, 93\u2013104.","DOI":"10.1007\/s10626-012-0135-1"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_002","unstructured":"S. Asmussen,\nApplied Probability and Queues, 2nd ed.,\nAppl. Math. (New York) 51,\nSpringer, New York, 2003"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_003","unstructured":"D. A\u012dssani and N. V. Kartashov,\nErgodicity and stability of Markov chains with respect to operator topologies in a space of transition kernels,\nDokl. Akad. Nauk Ukrain. SSR Ser. A (1983), no. 11, 3\u20135."},{"key":"2024022618254290367_j_mcma-2023-2023_ref_004","doi-asserted-by":"crossref","unstructured":"A. Bareche and D. A\u00efssani,\nKernel density in the study of the strong stability of the \n                  \n                     \n                        \n                           M\n                           \/\n                           M\n                           \/\n                           1\n                        \n                     \n                     \n                     M\/M\/1\n                  \n                queueing system,\nOper. Res. Lett. 36 (2008), no. 5, 535\u2013538.","DOI":"10.1016\/j.orl.2008.04.002"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_005","doi-asserted-by":"crossref","unstructured":"A. Bareche and D. A\u00efssani,\nStatistical techniques for a numerical evaluation of the proximity of \n                  \n                     \n                        \n                           G\n                           \/\n                           G\n                           \/\n                           1\n                        \n                     \n                     \n                     G\/G\/1\n                  \n                and \n                  \n                     \n                        \n                           G\n                           \/\n                           M\n                           \/\n                           1\n                        \n                     \n                     \n                     G\/M\/1\n                  \n                queueing systems,\nComput. Math. Appl. 61 (2011), no. 5, 1296\u20131304.","DOI":"10.1016\/j.camwa.2010.12.057"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_006","doi-asserted-by":"crossref","unstructured":"Z. Benouaret and D. A\u00efssani,\nStrong stability in a two-dimensional classical risk model with independent claims,\nScand. Actuar. J. (2010), no. 2, 83\u201392.","DOI":"10.1080\/03461230802673805"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_007","doi-asserted-by":"crossref","unstructured":"L. Berdjoudj and D. Aissani,\nStrong stability in retrial queues,\nTheory Probab. Math. Statist. 68 (2003), 11\u201317.","DOI":"10.1090\/S0094-9000-04-00595-2"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_008","doi-asserted-by":"crossref","unstructured":"L. Bouallouche-Medjkoune and D. Aissani,\nPerformance analysis approximation in a queueing system of type \n                  \n                     \n                        \n                           M\n                           \/\n                           G\n                           \/\n                           1\n                        \n                     \n                     \n                     M\/G\/1\n                  \n               ,\nMath. Methods Oper. Res. 63 (2006), no. 2, 341\u2013356.","DOI":"10.1007\/s00186-005-0022-8"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_009","doi-asserted-by":"crossref","unstructured":"R. Caldentey,\nApproximations for multi-class departure processes,\nQueueing Syst. 38 (2001), no. 2, 205\u2013212.","DOI":"10.1023\/A:1010910531975"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_010","unstructured":"Y. Djabali,\nStablit\u00e9 Forte dans les syst\u00e8mes d\u2019Attente de type Phase: Cas des Syst\u00e8mes PH\/M\/1 et M\/PH\/1,\nTh\u00e8se de Doctorat, Universit\u00e9 de Bejaia, 2017."},{"key":"2024022618254290367_j_mcma-2023-2023_ref_011","unstructured":"E. Gelenbe and G. Pujolle,\nIntroduction to Queueing Networks,\nWiley, New York, 1998."},{"key":"2024022618254290367_j_mcma-2023-2023_ref_012","doi-asserted-by":"crossref","unstructured":"L. Harfouche, N. Zougab and S. Adjabi,\nMultivariate generalised gamma kernel density estimators and application to non-negative data,\nInt. J. Comput. Sci. Math. 11 (2020), no. 2, 137\u2013157.","DOI":"10.1504\/IJCSM.2020.106391"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_013","doi-asserted-by":"crossref","unstructured":"B. R. Haverkort,\nApproximate analysis of networks of \n                  \n                     \n                        \n                           \n                              \n                                 \n                                    P\n                                    \u2062\n                                    H\n                                 \n                                 \/\n                                 P\n                              \n                              \u2062\n                              H\n                           \n                           \/\n                           1\n                           \/\n                           K\n                        \n                     \n                     \n                     PH\/PH\/1\/K\n                  \n                queues with customer losses: Test results,\nAnn. Oper. Res. 79 (1998), 271\u2013291.","DOI":"10.1023\/A:1018926806371"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_014","doi-asserted-by":"crossref","unstructured":"M. Hirukawa and M. Sakudo,\nFamily of the generalised gamma kernels: a generator of asymmetric kernels for nonnegative data,\nJ. Nonparametr. Stat. 27 (2015), no. 1, 41\u201363.","DOI":"10.1080\/10485252.2014.998669"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_015","unstructured":"N. V. Kartashov,\nCriteria for uniform ergodicity and strong stability of Markov chains with a common phase space,\nTheory Probab. Math. Statist. 30 (1984), 71\u201389."},{"key":"2024022618254290367_j_mcma-2023-2023_ref_016","doi-asserted-by":"crossref","unstructured":"N. V. Kartashov,\nStrong Stable Markov Chains,\nVSP, Utrecht, 1996.","DOI":"10.1515\/9783110917765"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_017","doi-asserted-by":"crossref","unstructured":"G. Latouche and V. Ramaswami,\nIntroduction to Matrix Analytic Methods in Stochastic Modeling,\nSociety for Industrial and Applied Mathematics, Philadelphia, 1999.","DOI":"10.1137\/1.9780898719734"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_018","doi-asserted-by":"crossref","unstructured":"B. Rabta and D. A\u00efssani,\nStrong stability in an \n                  \n                     \n                        \n                           (\n                           R\n                           ,\n                           s\n                           ,\n                           S\n                           )\n                        \n                     \n                     \n                     (R,s,S)\n                  \n                inventory model,\nInt. J. Prod. Econ. 97 (2005), 159\u2013171.","DOI":"10.1016\/j.ijpe.2004.06.050"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_019","doi-asserted-by":"crossref","unstructured":"V. Rabta, O. Lekadir and D. Aissani,\nStrong Stability of queueing systems and networks: A survey and perspectives,\nQueueing Theory,\nWiley, New York (2021), 259\u2013292.","DOI":"10.1002\/9781119755432.ch9"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_020","doi-asserted-by":"crossref","unstructured":"B. Sengupta,\nPhase-type representations for matrix-geometric solutions,\nComm. Statist. Stochastic Models 6 (1990), no. 1, 163\u2013167.","DOI":"10.1080\/15326349908807142"},{"key":"2024022618254290367_j_mcma-2023-2023_ref_021","doi-asserted-by":"crossref","unstructured":"N. Zougab, L. Harfouche, Y. Ziane and S. Adjabi,\nMultivariate generalized Birnbaum\u2013Saunders kernel density estimators,\nComm. Statist. Theory Methods 47 (2018), no. 18, 4534\u20134555.","DOI":"10.1080\/03610926.2017.1377252"}],"container-title":["Monte Carlo Methods and Applications"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2023-2023\/xml","content-type":"application\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2023-2023\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,2,26]],"date-time":"2024-02-26T18:26:02Z","timestamp":1708971962000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.degruyter.com\/document\/doi\/10.1515\/mcma-2023-2023\/html"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,13]]},"references-count":21,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2024,3,1]]},"published-print":{"date-parts":[[2024,3,1]]}},"alternative-id":["10.1515\/mcma-2023-2023"],"URL":"https:\/\/doi.org\/10.1515\/mcma-2023-2023","relation":{},"ISSN":["0929-9629","1569-3961"],"issn-type":[{"value":"0929-9629","type":"print"},{"value":"1569-3961","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,13]]}}}