{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:52:14Z","timestamp":1777704734445,"version":"3.51.4"},"reference-count":28,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2018,12,6]],"date-time":"2018-12-06T00:00:00Z","timestamp":1544054400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2019,2,16]]},"abstract":"<jats:p>\n                    In this paper, we employ a cooperative game to study coalition performance of a parallel service system with nonexponential service times, which is comprised of\n                    <jats:italic>n<\/jats:italic>\n                    independent parallel M\/E\n                    <jats:sub>\n                      <jats:italic>k<\/jats:italic>\n                    <\/jats:sub>\n                    \/1 queues, where the service times of the coalitions are designed as a closed-form framework. For such a queueing cooperative game, we use the Erlang service time distributions to make analysis of various coalitions more feasible, and specifically, it is easy to set up a characteristic function for the coalitions under an Erlang closed-form framework. Once the characteristic function is given in the queueing cooperative game, we compute the Shapley value, the Owen value and the core whose aim is to suitably provide the cost allocation for the coalitions. Furthermore, we use numerical examples to give useful observation on the cost allocations for the coalitions through the Shapley value, the Owen value and the core.\n                  <\/jats:p>","DOI":"10.3233\/jifs-18101","type":"journal-article","created":{"date-parts":[[2018,12,11]],"date-time":"2018-12-11T12:59:54Z","timestamp":1544533194000},"page":"127-137","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":1,"title":["Cooperative game in parallel service systems with nonexponential service times"],"prefix":"10.1177","volume":"36","author":[{"given":"Cheng-Guo","family":"E","sequence":"first","affiliation":[{"name":"School of Economics and Management, Yanshan University, Qinhuangdao, China"},{"name":"Liren College, Yanshan University, Qinhuangdao, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Quan-Lin","family":"Li","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Yanshan University, Qinhuangdao, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Shiyong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Economics and Management, Yanshan University, Qinhuangdao, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2018,12,6]]},"reference":[{"key":"e_1_3_2_2_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.1070.0823"},{"key":"e_1_3_2_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.mathsocsci.2007.07.003"},{"key":"e_1_3_2_4_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1060.0346"},{"key":"e_1_3_2_5_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1090.0737"},{"key":"e_1_3_2_6_2","doi-asserted-by":"publisher","DOI":"10.1287\/opre.2014.1283"},{"key":"e_1_3_2_7_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.1040.0303"},{"key":"e_1_3_2_8_2","volume-title":"Models in Cooperative Game Theory","author":"Branzei R.","year":"2008","unstructured":"BranzeiR., DimitrovD., TijsS., Models in Cooperative Game Theory, Springer-Verlag, New York, 2008."},{"key":"e_1_3_2_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2017.02.010"},{"key":"e_1_3_2_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0899-8256(89)90014-6"},{"key":"e_1_3_2_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.ejor.2007.04.053"},{"key":"e_1_3_2_12_2","doi-asserted-by":"publisher","DOI":"10.1007\/s001860400350"},{"key":"e_1_3_2_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0165-4896(98)00028-6"},{"key":"e_1_3_2_14_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.1030.0166"},{"key":"e_1_3_2_15_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0269964814000102"},{"key":"e_1_3_2_16_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-11492-2"},{"key":"e_1_3_2_17_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.44.7.971"},{"key":"e_1_3_2_18_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0022-0531(02)00036-4"},{"key":"e_1_3_2_19_2","volume-title":"Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach","author":"Neuts M.F.","year":"1981","unstructured":"NeutsM.F., Matrix-Geometric Solutions in Stochastic Models: An Algorithmic Approach, Johns Hopkins University Press, Maryland, 1981."},{"key":"e_1_3_2_20_2","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.18.5.64"},{"key":"e_1_3_2_21_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-45494-3_7"},{"key":"e_1_3_2_22_2","volume-title":"Introduction to the Theory of Cooperative Games","author":"Peleg B.","year":"2007","unstructured":"PelegB., Sudh\u00f6lterP., Introduction to the Theory of Cooperative Games, Springer-Verlag, New York, 2007."},{"key":"e_1_3_2_23_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-6205-4"},{"key":"e_1_3_2_24_2","volume-title":"An Introduction to Game Theory","author":"Rasmusen E.","year":"2007","unstructured":"RasmusenE., An Introduction to Game Theory, Blackwell Publishing, New York, 2007."},{"key":"e_1_3_2_25_2","doi-asserted-by":"publisher","DOI":"10.2307\/1911680"},{"key":"e_1_3_2_26_2","first-page":"307","volume-title":"Annals of Mathematics Studies","author":"Shapley L.S.","year":"1953","unstructured":"ShapleyL.S., A value for n-person games, in contributions to the theory of games II, Annals of Mathematics Studies, H.W.Kuhn and A.W.Tucker eds., Princeton University Press, Princeton, 28, 1953, 307\u2013317."},{"key":"e_1_3_2_27_2","doi-asserted-by":"publisher","DOI":"10.1109\/ITC.2010.5608712"},{"key":"e_1_3_2_28_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0899-8256(03)00043-5"},{"key":"e_1_3_2_29_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2015.04.063"}],"container-title":["Journal of Intelligent &amp; 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