{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,8,24]],"date-time":"2025-08-24T01:43:52Z","timestamp":1755999832367,"version":"3.37.3"},"reference-count":30,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2019,10,10]],"date-time":"2019-10-10T00:00:00Z","timestamp":1570665600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,10,10]],"date-time":"2019-10-10T00:00:00Z","timestamp":1570665600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100003005","name":"Eindhoven University of Technology","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100003005","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Queueing Syst"],"published-print":{"date-parts":[[2019,12]]},"abstract":"<jats:title>Abstract<\/jats:title>\n<jats:p>We consider load balancing in service systems with affinity relations between jobs and servers. Specifically, an arriving job can be assigned to a fast, primary server from a particular selection associated with this job or to a secondary server to be processed at a slower rate. Such job\u2013server affinity relations can model network topologies based on geographical proximity, or data locality in cloud scenarios. We introduce load balancing schemes that assign jobs to primary servers if available, and otherwise to secondary servers. A novel coupling construction is developed to obtain stability conditions and performance bounds. We also conduct a fluid limit analysis for symmetric model instances, which reveals a delicate interplay between the model parameters and load balancing performance.<\/jats:p>","DOI":"10.1007\/s11134-019-09633-y","type":"journal-article","created":{"date-parts":[[2019,10,10]],"date-time":"2019-10-10T18:09:37Z","timestamp":1570730977000},"page":"227-268","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Job assignment in large-scale service systems with affinity relations"],"prefix":"10.1007","volume":"93","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1350-9346","authenticated-orcid":false,"given":"Ellen","family":"Cardinaels","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Sem C.","family":"Borst","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Johan S. H.","family":"van Leeuwaarden","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,10,10]]},"reference":[{"key":"9633_CR1","doi-asserted-by":"publisher","first-page":"873","DOI":"10.1214\/aoap\/1043862415","volume":"7","author":"N Bean","year":"1997","unstructured":"Bean, N., Gibbens, R., Zachary, S.: Dynamic and equilibrium behavior of controlled loss networks. Ann. Appl. Probab. 7, 873\u2013885 (1997)","journal-title":"Ann. Appl. Probab."},{"key":"9633_CR2","unstructured":"Bena\u00efm, M., Le Boudec, J.Y.: On mean field convergence and stationary regime. arXiv preprint arXiv:1111.5710 (2011)"},{"key":"9633_CR3","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4684-9477-8","volume-title":"Point Processes and Queues, Martingale Dynamics","author":"P Br\u00e9maud","year":"1981","unstructured":"Br\u00e9maud, P.: Point Processes and Queues, Martingale Dynamics. Springer, New York (1981)"},{"key":"9633_CR4","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4613-8643-8","volume-title":"Non-uniform Random Variate Generation","author":"L Devroye","year":"1986","unstructured":"Devroye, L.: Non-uniform Random Variate Generation. Springer, New York (1986)"},{"issue":"4","key":"9633_CR5","doi-asserted-by":"publisher","first-page":"690","DOI":"10.1109\/TAC.1980.1102445","volume":"25","author":"A Ephremides","year":"1980","unstructured":"Ephremides, A., Varaiya, P., Walrand, J.: A simple dynamic routing problem. IEEE Trans. Autom. Control 25(4), 690\u2013693 (1980)","journal-title":"IEEE Trans. Autom. Control"},{"key":"9633_CR6","volume-title":"Flows in Networks","author":"LR Ford","year":"2015","unstructured":"Ford, L.R., Fulkerson, D.R.: Flows in Networks. Princeton University Press, Princeton (2015)"},{"issue":"1","key":"9633_CR7","doi-asserted-by":"publisher","first-page":"55","DOI":"10.1023\/A:1019175812444","volume":"29","author":"S Foss","year":"1998","unstructured":"Foss, S., Chernova, N.: On the stability of a partially accessible multi-station queue with state-dependent routing. Queueing Syst. 29(1), 55\u201373 (1998)","journal-title":"Queueing Syst."},{"issue":"1","key":"9633_CR8","doi-asserted-by":"publisher","first-page":"1","DOI":"10.1145\/2964791.2901478","volume":"44","author":"D Gamarnik","year":"2016","unstructured":"Gamarnik, D., Tsitsiklis, J.N., Zubeldia, M.: Delay, memory, and messaging tradeoffs in distributed service systems. ACM SIGMETRICS Perform. Eval. Rev. 44(1), 1\u201312 (2016)","journal-title":"ACM SIGMETRICS Perform. Eval. Rev."},{"key":"9633_CR9","doi-asserted-by":"crossref","unstructured":"Gardner, K., Stephens, C.: Smart dispatching in heterogeneous systems. In: Workshop on Mathematical Performance Modeling and Analysis. Phoenix, AZ (2019)","DOI":"10.1145\/3374888.3374894"},{"issue":"2","key":"9633_CR10","doi-asserted-by":"publisher","first-page":"69","DOI":"10.1145\/2825236.2825263","volume":"43","author":"N Gast","year":"2015","unstructured":"Gast, N.: The power of two choices on graphs: the pair-approximation is accurate? ACM SIGMETRICS Perform. Eval. Rev. 43(2), 69\u201371 (2015)","journal-title":"ACM SIGMETRICS Perform. Eval. Rev."},{"key":"9633_CR11","unstructured":"Gibbens, R., Hunt, P., Kelly, F.: Bistability in communication networks. Disorder in physical systems pp. 113\u2013128 (1990)"},{"issue":"4","key":"9633_CR12","doi-asserted-by":"publisher","first-page":"339","DOI":"10.1023\/A:1019188531950","volume":"33","author":"JM Harrison","year":"1999","unstructured":"Harrison, J.M., L\u00f3pez, M.J.: Heavy traffic resource pooling in parallel-server systems. Queueing Syst. 33(4), 339\u2013368 (1999)","journal-title":"Queueing Syst."},{"issue":"2","key":"9633_CR13","first-page":"220","volume":"5","author":"P Hartman","year":"1960","unstructured":"Hartman, P.: On local homeomorphisms of Euclidean spaces. Bol. Soc. Mat. Mexicana 5(2), 220\u2013241 (1960)","journal-title":"Bol. Soc. Mat. Mexicana"},{"issue":"2","key":"9633_CR14","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/0304-4149(94)90071-X","volume":"53","author":"P Hunt","year":"1994","unstructured":"Hunt, P., Kurtz, T.: Large loss networks. Stoch. Process. Appl. 53(2), 363\u2013378 (1994)","journal-title":"Stoch. Process. Appl."},{"issue":"3\u20134","key":"9633_CR15","doi-asserted-by":"publisher","first-page":"293","DOI":"10.1007\/BF01149166","volume":"21","author":"Z Liu","year":"1995","unstructured":"Liu, Z., Nain, P., Towsley, D.: Sample path methods in the control of queues. Queueing Syst. 21(3\u20134), 293\u2013335 (1995)","journal-title":"Queueing Syst."},{"issue":"11","key":"9633_CR16","doi-asserted-by":"publisher","first-page":"1056","DOI":"10.1016\/j.peva.2011.07.015","volume":"68","author":"Y Lu","year":"2011","unstructured":"Lu, Y., Xie, Q., Kliot, G., Geller, A., Larus, J.R., Greenberg, A.: Join-idle-queue: a novel load balancing algorithm for dynamically scalable web services. Perform. Eval. 68(11), 1056\u20131071 (2011)","journal-title":"Perform. Eval."},{"key":"9633_CR17","unstructured":"Martirosyan, D., Robert, P.: The equilibrium states of large networks of Erlang queues. arXiv preprint arXiv:1811.04763 (2018)"},{"issue":"10","key":"9633_CR18","doi-asserted-by":"publisher","first-page":"1094","DOI":"10.1109\/71.963420","volume":"12","author":"M Mitzenmacher","year":"2001","unstructured":"Mitzenmacher, M.: The power of two choices in randomized load balancing. IEEE Trans. Parallel Distrib. Syst. 12(10), 1094\u20131104 (2001)","journal-title":"IEEE Trans. Parallel Distrib. Syst."},{"issue":"1","key":"9633_CR19","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1145\/3179417","volume":"2","author":"D Mukherjee","year":"2018","unstructured":"Mukherjee, D., Borst, S.C., Van Leeuwaarden, J.S.H.: Asymptotically optimal load balancing topologies. Proc. ACM Meas. Anal. Comput. Syst. 2(1), 14 (2018)","journal-title":"Proc. ACM Meas. Anal. Comput. Syst."},{"issue":"4","key":"9633_CR20","doi-asserted-by":"publisher","first-page":"265","DOI":"10.1287\/stsy.2018.0016","volume":"8","author":"D Mukherjee","year":"2018","unstructured":"Mukherjee, D., Borst, S.C., Van Leeuwaarden, J.S.H., Whiting, P.A.: Universality of power-of-d load balancing in many-server systems. Stoch. Syst. 8(4), 265\u2013292 (2018). \nhttps:\/\/doi.org\/10.1287\/stsy.2018.0016","journal-title":"Stoch. Syst."},{"key":"9633_CR21","doi-asserted-by":"publisher","first-page":"193","DOI":"10.1214\/06-PS091","volume":"4","author":"G Pang","year":"2007","unstructured":"Pang, G., Talreja, R., Whitt, W.: Martingale proofs of many-server heavy-traffic limits for Markovian queues. Probab. Surv. 4, 193\u2013267 (2007)","journal-title":"Probab. Surv."},{"issue":"1","key":"9633_CR22","doi-asserted-by":"publisher","first-page":"155","DOI":"10.2307\/1427584","volume":"26","author":"PD Sparaggis","year":"1994","unstructured":"Sparaggis, P.D., Towsley, D., Cassandras, C.G.: Sample path criteria for weak majorization. Adv. Appl. Probab. 26(1), 155\u2013171 (1994)","journal-title":"Adv. Appl. Probab."},{"issue":"2","key":"9633_CR23","doi-asserted-by":"publisher","first-page":"141","DOI":"10.1017\/S0269964805050096","volume":"19","author":"AL Stolyar","year":"2005","unstructured":"Stolyar, A.L.: Optimal routing in output-queued flexible server systems. Probab. Eng. Inf. Sci. 19(2), 141\u2013189 (2005)","journal-title":"Probab. Eng. Inf. Sci."},{"key":"9633_CR24","volume-title":"Comparison Methods for Queues and Other Stochastic Models","author":"D Stoyan","year":"1983","unstructured":"Stoyan, D., Daley, D.J.: Comparison Methods for Queues and Other Stochastic Models. Wiley, New York (1983)"},{"issue":"1","key":"9633_CR25","doi-asserted-by":"publisher","first-page":"109","DOI":"10.1017\/S0269964800005088","volume":"12","author":"SR Turner","year":"1998","unstructured":"Turner, S.R.: The effect of increasing routing choice on resource pooling. Probab. Eng. Inf. Sci. 12(1), 109\u2013124 (1998)","journal-title":"Probab. Eng. Inf. Sci."},{"key":"9633_CR26","unstructured":"Van der Boor, M., Borst, S.C., Van Leeuwaarden, J.S.H., Mukherjee, D.: Scalable load balancing in networked systems: Universality properties and stochastic coupling methods. arXiv preprint arXiv:1712.08555 (2017)"},{"issue":"1","key":"9633_CR27","first-page":"20","volume":"32","author":"ND Vvedenskaya","year":"1996","unstructured":"Vvedenskaya, N.D., Dobrushin, R.L., Karpelevich, F.I.: Queueing system with selection of the shortest of two queues: an asymptotic approach. Problemy Peredachi Informatsii 32(1), 20\u201334 (1996)","journal-title":"Problemy Peredachi Informatsii"},{"issue":"1","key":"9633_CR28","doi-asserted-by":"publisher","first-page":"181","DOI":"10.2307\/3213271","volume":"14","author":"W Winston","year":"1977","unstructured":"Winston, W.: Optimality of the shortest line discipline. J. Appl. Probab. 14(1), 181\u2013189 (1977)","journal-title":"J. Appl. Probab."},{"issue":"2","key":"9633_CR29","doi-asserted-by":"publisher","first-page":"2","DOI":"10.1145\/3199524.3199528","volume":"45","author":"A Yekkehkhany","year":"2018","unstructured":"Yekkehkhany, A., Hojjati, A., Hajiesmaili, M.H.: GB-pandas: throughput and heavy-traffic optimality analysis for affinity scheduling. ACM SIGMETRICS Perform. Eval. Rev. 45(2), 2\u201314 (2018)","journal-title":"ACM SIGMETRICS Perform. Eval. Rev."},{"key":"9633_CR30","doi-asserted-by":"crossref","unstructured":"Zachary, S., Ziedins, I.: Loss networks. In: Queueing Networks, pp. 701\u2013728. Springer (2011)","DOI":"10.1007\/978-1-4419-6472-4_16"}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-019-09633-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11134-019-09633-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-019-09633-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,10,8]],"date-time":"2020-10-08T23:24:49Z","timestamp":1602199489000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11134-019-09633-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,10,10]]},"references-count":30,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2019,12]]}},"alternative-id":["9633"],"URL":"https:\/\/doi.org\/10.1007\/s11134-019-09633-y","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"type":"print","value":"0257-0130"},{"type":"electronic","value":"1572-9443"}],"subject":[],"published":{"date-parts":[[2019,10,10]]},"assertion":[{"value":"21 December 2018","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"15 September 2019","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 October 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}