On retrial queue with customer balking and feedback subject to server breakdowns
Motivated by some real stochastic service systems, we study a feedback retrial queue with customer balking and unreliable servers (servers subject to breakdowns). A customer will either join a retrial orbit or balk if all servers are busy upon his arrival. After a service completion, the customer ei...
Saved in:
| Published in | Communications in statistics. Theory and methods Vol. 51; no. 17; pp. 6049 - 6063 |
|---|---|
| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Philadelphia
Taylor & Francis
02.09.2022
Taylor & Francis Ltd |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0361-0926 1532-415X |
| DOI | 10.1080/03610926.2020.1852432 |
Cover
| Abstract | Motivated by some real stochastic service systems, we study a feedback retrial queue with customer balking and unreliable servers (servers subject to breakdowns). A customer will either join a retrial orbit or balk if all servers are busy upon his arrival. After a service completion, the customer either leave the system or enter the retrial group again for additional service. The customer who is interrupted by the server failure will be served by another server if available; otherwise, he will be contacted later and treated as leaving the system. We use a quasi-birth-and-death process to analyze this system with almost all possible uncertain factors and derive major performance measures of the system. We also develop a cost function determining the optimal parameter settings of the system under the stability condition. Probabilistic Global Search Lausanne approach is employed in solving the optimization issue. The effects of parameters on performance measures of the system are examined numerically. Finally, we discuss the application of the model in the telephone medical consulting service system. |
|---|---|
| AbstractList | Motivated by some real stochastic service systems, we study a feedback retrial queue with customer balking and unreliable servers (servers subject to breakdowns). A customer will either join a retrial orbit or balk if all servers are busy upon his arrival. After a service completion, the customer either leave the system or enter the retrial group again for additional service. The customer who is interrupted by the server failure will be served by another server if available; otherwise, he will be contacted later and treated as leaving the system. We use a quasi-birth-and-death process to analyze this system with almost all possible uncertain factors and derive major performance measures of the system. We also develop a cost function determining the optimal parameter settings of the system under the stability condition. Probabilistic Global Search Lausanne approach is employed in solving the optimization issue. The effects of parameters on performance measures of the system are examined numerically. Finally, we discuss the application of the model in the telephone medical consulting service system. |
| Author | Su, Siping Ke, Jau-Chuan Zhang, Zhe-George Liu, Tzu-Hsin |
| Author_xml | – sequence: 1 givenname: Jau-Chuan surname: Ke fullname: Ke, Jau-Chuan organization: Department of Applied Statistics, National Taichung University of Science and Technology – sequence: 2 givenname: Tzu-Hsin surname: Liu fullname: Liu, Tzu-Hsin organization: Department of Finance, Chaoyang University of Technology – sequence: 3 givenname: Siping surname: Su fullname: Su, Siping organization: Department of Decision Sciences, Western Washington University – sequence: 4 givenname: Zhe-George surname: Zhang fullname: Zhang, Zhe-George organization: Beedie School of Business, Simon Fraser University |
| BookMark | eNqFkEtLAzEUhYNUsFZ_ghBwPTXPeeBGKb6gUBcK7kJm5o6mnSY1yVj6752hdeNCVxcO3zn33nOKRtZZQOiCkiklObkiPKWkYOmUEdZLuWSCsyM0ppKzRFD5NkLjgUkG6ASdhrAkhMos52P0vLDYQ_RGt_izgw7w1sQPXHUhujV4XOp2Zew71rbGDUBd6mqFQ1cuoYo4OhzAfw2YB72q3daGM3Tc6DbA-WFO0Ov93cvsMZkvHp5mt_Ok4jyPicwYL0EwWmZCNprXUGRA60YUohchbVLINakpL3WmC5FzWdKCCSGrPO1_lnyCLve5G-_6w0NUS9d5269ULC0KQvuYoqfknqq8C8FDozberLXfKUrUUJ76KU8N5alDeb3v-pevMlFH42z02rT_um_2bmMb59d663xbq6h3rfON17YyQfG_I74BsO2JDg |
| CitedBy_id | crossref_primary_10_1080_16843703_2022_2092954 crossref_primary_10_3390_math9192415 crossref_primary_10_3934_math_20241022 crossref_primary_10_1051_ro_2025013 crossref_primary_10_3390_math12233695 crossref_primary_10_1080_03610918_2025_2464075 crossref_primary_10_3233_JIFS_231195 crossref_primary_10_1007_s10479_025_06547_2 crossref_primary_10_3390_math11163532 crossref_primary_10_3390_math9151797 |
| Cites_doi | 10.1051/ro/2017091 10.1007/BF01158472 10.1007/BF01158474 10.1016/S0898-1221(98)00160-6 10.1051/ro/2017029 10.1504/IJISE.2018.091900 10.1504/IJISE.2018.094608 10.1080/15598608.2016.1251365 10.1016/j.peva.2008.04.004 10.1007/BF02564721 10.1080/00207160.2010.498884 10.1016/S0307-904X(02)00061-6 10.1016/j.mcm.2009.12.011 10.1007/BF01720984 10.1504/IJOR.2017.10004610 10.1007/978-1-4899-2977-8 10.1080/16843703.2017.1320459 10.1080/16843703.2018.1510359 10.1016/j.apm.2017.10.025 10.1007/s10479-006-5300-1 10.1137/1.9780898719734 10.1007/s10479-007-0192-2 10.1016/j.ejor.2010.09.040 10.1049/iet-com.2017.0820 10.1080/00207160.2014.932908 10.1016/S0096-3003(02)00629-X 10.1002/j.1538-7305.1963.tb00510.x 10.1016/j.camwa.2011.03.109 10.1016/j.amc.2013.12.108 10.1016/j.camwa.2009.06.021 |
| ContentType | Journal Article |
| Copyright | 2020 Taylor & Francis Group, LLC 2020 2020 Taylor & Francis Group, LLC |
| Copyright_xml | – notice: 2020 Taylor & Francis Group, LLC 2020 – notice: 2020 Taylor & Francis Group, LLC |
| DBID | AAYXX CITATION 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| DOI | 10.1080/03610926.2020.1852432 |
| DatabaseName | CrossRef Computer and Information Systems Abstracts Mechanical & Transportation Engineering Abstracts Technology Research Database Engineering Research Database ProQuest Computer Science Collection Civil Engineering Abstracts Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Academic Computer and Information Systems Abstracts Professional |
| DatabaseTitle | CrossRef Civil Engineering Abstracts Technology Research Database Computer and Information Systems Abstracts – Academic Mechanical & Transportation Engineering Abstracts ProQuest Computer Science Collection Computer and Information Systems Abstracts Engineering Research Database Advanced Technologies Database with Aerospace Computer and Information Systems Abstracts Professional |
| DatabaseTitleList | Civil Engineering Abstracts |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Statistics Mathematics |
| EISSN | 1532-415X |
| EndPage | 6063 |
| ExternalDocumentID | 10_1080_03610926_2020_1852432 1852432 |
| Genre | Research Article |
| GrantInformation_xml | – fundername: Natural Sciences and Engineering Research Council of Canada grantid: RGPIN197319 |
| GroupedDBID | -~X .7F .QJ 0BK 0R~ 29F 2DF 30N 4.4 5GY 5VS 8VB AAENE AAJMT AALDU AAMIU AAPUL AAQRR ABCCY ABEHJ ABFIM ABHAV ABJNI ABLIJ ABPAQ ABPEM ABTAI ABXUL ABXYU ACGEJ ACGFS ACIWK ACTIO ADCVX ADGTB ADXPE AEISY AEOZL AEPSL AEYOC AFKVX AGDLA AGMYJ AIJEM AJWEG AKBVH AKOOK ALMA_UNASSIGNED_HOLDINGS ALQZU AQRUH AVBZW AWYRJ BLEHA CCCUG CE4 CS3 DGEBU DKSSO EBS E~A E~B F5P GTTXZ H13 HF~ HZ~ H~P IPNFZ J.P K1G KYCEM LJTGL M4Z NA5 NY~ O9- QWB RIG RNANH ROSJB RTWRZ S-T SNACF TBQAZ TDBHL TEJ TFL TFT TFW TN5 TTHFI TUROJ TWF TWZ UPT UT5 UU3 WH7 ZGOLN ZL0 ~02 ~S~ AAGDL AAHIA AAYXX AFRVT AIYEW AMVHM CITATION TASJS TOXWX 7SC 7TB 8FD FR3 JQ2 KR7 L7M L~C L~D |
| ID | FETCH-LOGICAL-c338t-5723be421b745fa3de97e1df494421e6f6e8a0d13ba7a94835b192445c8608053 |
| ISSN | 0361-0926 |
| IngestDate | Wed Aug 13 04:27:59 EDT 2025 Thu Apr 24 23:00:01 EDT 2025 Wed Oct 01 01:23:25 EDT 2025 Thu Jan 23 04:34:12 EST 2025 |
| IsPeerReviewed | true |
| IsScholarly | true |
| Issue | 17 |
| Language | English |
| LinkModel | OpenURL |
| MergedId | FETCHMERGED-LOGICAL-c338t-5723be421b745fa3de97e1df494421e6f6e8a0d13ba7a94835b192445c8608053 |
| Notes | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| PQID | 2699014219 |
| PQPubID | 186202 |
| PageCount | 15 |
| ParticipantIDs | crossref_citationtrail_10_1080_03610926_2020_1852432 informaworld_taylorfrancis_310_1080_03610926_2020_1852432 crossref_primary_10_1080_03610926_2020_1852432 proquest_journals_2699014219 |
| ProviderPackageCode | CITATION AAYXX |
| PublicationCentury | 2000 |
| PublicationDate | 2022-09-02 |
| PublicationDateYYYYMMDD | 2022-09-02 |
| PublicationDate_xml | – month: 09 year: 2022 text: 2022-09-02 day: 02 |
| PublicationDecade | 2020 |
| PublicationPlace | Philadelphia |
| PublicationPlace_xml | – name: Philadelphia |
| PublicationTitle | Communications in statistics. Theory and methods |
| PublicationYear | 2022 |
| Publisher | Taylor & Francis Taylor & Francis Ltd |
| Publisher_xml | – name: Taylor & Francis – name: Taylor & Francis Ltd |
| References | e_1_3_2_27_1 e_1_3_2_28_1 e_1_3_2_29_1 e_1_3_2_20_1 e_1_3_2_21_1 Artalejo J. R. (e_1_3_2_4_1) 2002; 15 e_1_3_2_22_1 e_1_3_2_23_1 e_1_3_2_24_1 e_1_3_2_25_1 Choi B. D. (e_1_3_2_10_1) 1992 Neuts M. F. (e_1_3_2_26_1) 1981 e_1_3_2_16_1 e_1_3_2_9_1 e_1_3_2_17_1 e_1_3_2_8_1 e_1_3_2_18_1 e_1_3_2_7_1 e_1_3_2_19_1 e_1_3_2_2_1 e_1_3_2_31_1 e_1_3_2_30_1 e_1_3_2_33_1 e_1_3_2_11_1 e_1_3_2_32_1 e_1_3_2_6_1 e_1_3_2_12_1 e_1_3_2_5_1 e_1_3_2_13_1 e_1_3_2_34_1 e_1_3_2_14_1 e_1_3_2_3_1 e_1_3_2_15_1 |
| References_xml | – ident: e_1_3_2_28_1 doi: 10.1051/ro/2017091 – ident: e_1_3_2_15_1 doi: 10.1007/BF01158472 – ident: e_1_3_2_23_1 doi: 10.1007/BF01158474 – ident: e_1_3_2_9_1 doi: 10.1016/S0898-1221(98)00160-6 – ident: e_1_3_2_27_1 doi: 10.1051/ro/2017029 – ident: e_1_3_2_29_1 doi: 10.1504/IJISE.2018.091900 – volume: 15 start-page: 101 year: 2002 ident: e_1_3_2_4_1 article-title: Standard publication-title: Revista Matemática Complutense – ident: e_1_3_2_7_1 doi: 10.1504/IJISE.2018.094608 – ident: e_1_3_2_31_1 doi: 10.1080/15598608.2016.1251365 – ident: e_1_3_2_11_1 doi: 10.1016/j.peva.2008.04.004 – ident: e_1_3_2_2_1 doi: 10.1007/BF02564721 – ident: e_1_3_2_25_1 doi: 10.1080/00207160.2010.498884 – ident: e_1_3_2_22_1 doi: 10.1016/S0307-904X(02)00061-6 – ident: e_1_3_2_3_1 doi: 10.1016/j.mcm.2009.12.011 – ident: e_1_3_2_16_1 doi: 10.1007/BF01720984 – ident: e_1_3_2_19_1 doi: 10.1504/IJOR.2017.10004610 – ident: e_1_3_2_17_1 doi: 10.1007/978-1-4899-2977-8 – ident: e_1_3_2_6_1 doi: 10.1080/16843703.2017.1320459 – ident: e_1_3_2_34_1 doi: 10.1080/16843703.2018.1510359 – ident: e_1_3_2_8_1 doi: 10.1016/j.apm.2017.10.025 – ident: e_1_3_2_21_1 doi: 10.1007/s10479-006-5300-1 – volume-title: Matrix geometric solutions in stochastic models: An algorithmic approach year: 1981 ident: e_1_3_2_26_1 – ident: e_1_3_2_24_1 doi: 10.1137/1.9780898719734 – ident: e_1_3_2_5_1 doi: 10.1007/s10479-007-0192-2 – start-page: 93 volume-title: Feedback retrial queueing systems, in Queueing and Related Models year: 1992 ident: e_1_3_2_10_1 – ident: e_1_3_2_14_1 doi: 10.1016/j.ejor.2010.09.040 – ident: e_1_3_2_20_1 doi: 10.1049/iet-com.2017.0820 – ident: e_1_3_2_33_1 doi: 10.1080/00207160.2014.932908 – ident: e_1_3_2_30_1 doi: 10.1016/S0096-3003(02)00629-X – ident: e_1_3_2_32_1 doi: 10.1002/j.1538-7305.1963.tb00510.x – ident: e_1_3_2_18_1 doi: 10.1016/j.camwa.2011.03.109 – ident: e_1_3_2_12_1 doi: 10.1016/j.amc.2013.12.108 – ident: e_1_3_2_13_1 doi: 10.1016/j.camwa.2009.06.021 |
| SSID | ssj0015783 |
| Score | 2.3668952 |
| Snippet | Motivated by some real stochastic service systems, we study a feedback retrial queue with customer balking and unreliable servers (servers subject to... |
| SourceID | proquest crossref informaworld |
| SourceType | Aggregation Database Enrichment Source Index Database Publisher |
| StartPage | 6049 |
| SubjectTerms | Balking Breakdown cost Cost function Customer services Customers Feedback matrix-analytical approach Optimization Parameters Queues retrial queue Servers |
| Title | On retrial queue with customer balking and feedback subject to server breakdowns |
| URI | https://www.tandfonline.com/doi/abs/10.1080/03610926.2020.1852432 https://www.proquest.com/docview/2699014219 |
| Volume | 51 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAWR databaseName: Taylor & Francis Science and Technology Library-DRAA customDbUrl: eissn: 1532-415X dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0015783 issn: 0361-0926 databaseCode: 30N dateStart: 19970101 isFulltext: true titleUrlDefault: http://www.tandfonline.com/page/title-lists providerName: Taylor & Francis |
| link | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwnV1NbxMxELVCuZQDggKitCAf6KlylLW9X0dUGkWQJkhJpNxWdtaGKiUtze6l_6n_kZm1d7NRIwpcVpGz3iSel_HMeOYNIR8BQlYoo5lSJmdSWclUGucM9jqV2kCGvCKevxhFg5n8Mg_nnc59K2upLHR3cbezruR_pApjIFeskv0HyTYPhQF4DfKFK0gYrn8l4zHWori-G6DeS-MTyUsw6H6a21OtrpZ1DaKFXUqrxfJ0XWoMvaDNiQFZvA3sxmWOUea2pbpVOVIlzWLtkaN17vqS_urJrgf1JhNRlezsRwlq42uDmeFlWeHirmSD9WUDx0k1OsHu2d83AWzDXJy-OjbBcHY7MAE-LR6zbNzY6YMeIa1EJVevFcAU7omwa_XLGZgU87Z-9oS0HodxS9tGPUd36ndu8MXEzl3Bp1EKpJbnmJfCYTAJufSh1S0W7tE468-Gw2x6Pp-eiP7NL4YtyvAo_0R8dhh6Qp7yOIqwYYbojZpDK1B-rhu3_2F1wRhSue_67C1TaIso94FhUFk70xfkuXdT6CeHuZekY1YH5NlFw_G7PiD7kwYPr8i38Yp6KNIKihShSGsoUg9FCoChNRSphyItrqmDIt1A8TWZ9c-nZwPmm3WwhRBJwcKYC20kD3QsQ6tEbtLYBLmVqYRBE9nIJKqXB0KrWKUSDH-Nvr8MF0kEKxSKN2Rvdb0ybwm1PBeyF8M3sQncEIPRasEODVWYROAf6EMi63XLFp7JHhuqXGVBTXjrlzvD5c78ch-SbjPtxlG5PDYhbQslKypEWwfmTDwy97iWYOY1xjrjEZ5Cw3Kk7_789hHZ3_yjjslecVua92D8FvpDBbnfNIGppQ |
| linkProvider | Taylor & Francis |
| linkToHtml | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV25TgMxELUQFISCI4C4cUG7IetjjxIhonAkUCRSOsvetZvAgpLdhq9nZo-IgBBFWsu2xtf4zdjzhpAr2EKOa2s8rW3qCe2Ep-Mw9eCu07HzhWQl8fxgGPTH4mEiJ99iYfBbJdrQriKKKHU1Hm50Rjdf4q5B6_rdmOEPAwZFkWSCgxrekMg0gmEc3eHiJQF2ZJUiOQCzGdo0UTx_dbN0Py2xl_7S1uUV1NshSSN89fNk2ily00k-f_A6rja6XbJdI1R6U22pPbJmszbZGizoXedt0kKIWjE875OX54zObJn9g4LYhaXo26VJAbDyzc6o0a_ojqcgEHVwVxqdTOm8MOgAovk7RbcwVgP0Ok3R131Axr270W3fq_M0eAkYuLknQ8aNFcw3oZBO89TGofVTJ2IBhTZwgY10N_W50aGOBWA-g2afkEkUwIAlPyTr2Xtmjwh1LOVgYoIkLoIKIeAVBxBEahkFAA3NMRHN6qikJjHHXBqvym-4TuvZUzh7qp69Y9JZNPuoWDz-axB_X3qVl-4TV-U6UfyftmfNPlG1QpgrFuADJExHfLJC15dksz8aPKmn--HjKWkxDMXAxy12RtbzWWHPASDl5qI8AV8Quv8M |
| linkToPdf | http://utb.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwpV1LTwIxEG4MJgYPPlAjitqD10W22-7jaFSCD5CDJN6adre9gEBg9-Kvd2YfxEcMB65N23Tb2ek305lvCLkGEbKeMtpRyiQOV5Y7KgoSB-46FVmXC5YTz_cHfm_En95FFU24LMMq0Ya2BVFErqvx554ntoqIuwGl63YihgEGDJpCwbgHWnjbxzxTzOLoDFYPCSCQRYVkH6xmGFMl8fw3zY_r6Qd56R9lnd9A3X2iq7UXgSfjdpbqdvz5i9Zxo487IHslPqW3hUAdki0zbZDd_orcddkgdQSoBb_zERm-TunC5LU_KKw6MxQ9uzTOAFR-mAXVaoLOeArroRZuSq3iMV1mGt0_NJ1RdApjN8Cu4wQ93cdk1H14u-s5ZZUGJwbzNnVEwDxtOHN1wIVVXmKiwLiJ5RGHRuNb34Sqk7ieVoGKOCA-jUYfF3HowwcL74TUprOpOSXUssQDAxNWYkPoEABasQBAhBKhD8BQNwmvDkfGJYU5VtKYSLdiOi13T-LuyXL3mqS9GjYvODzWDYi-n7xMc-eJLSqdSG_N2FYlJrJUB0vJfHx-hO2IzjaY-orsDO-78uVx8HxO6gzzMPBli7VILV1k5gLQUaovc_n_AvZ-_bk |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=On+retrial+queue+with+customer+balking+and+feedback+subject+to+server+breakdowns&rft.jtitle=Communications+in+statistics.+Theory+and+methods&rft.au=Jau-Chuan+Ke&rft.au=Liu%2C+Tzu-Hsin&rft.au=Su%2C+Siping&rft.au=Zhe-George%2C+Zhang&rft.date=2022-09-02&rft.pub=Taylor+%26+Francis+Ltd&rft.issn=0361-0926&rft.eissn=1532-415X&rft.volume=51&rft.issue=17&rft.spage=6049&rft.epage=6063&rft_id=info:doi/10.1080%2F03610926.2020.1852432&rft.externalDBID=NO_FULL_TEXT |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=0361-0926&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=0361-0926&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=0361-0926&client=summon |