{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,24]],"date-time":"2026-06-24T08:50:28Z","timestamp":1782291028291,"version":"3.54.5"},"reference-count":30,"publisher":"Cambridge University Press (CUP)","issue":"2","license":[{"start":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T00:00:00Z","timestamp":1764633600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":["cambridge.org"],"crossmark-restriction":true},"short-container-title":["J. Appl. Probab."],"published-print":{"date-parts":[[2026,6]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>\n                    We study a queueing system with a fixed number of parallel service stations of infinite servers, each having a dedicated arrival process, and one flexible arrival stream that is routed to one of the service stations according to a \u2018weighted\u2019 shortest queue policy. We consider the model with general arrival processes and general service time distributions. Assuming that the dedicated arrival rates are of order\n                    <jats:italic>n<\/jats:italic>\n                    and the flexible arrival rate is of order\n                    <jats:inline-formula>\n                      <jats:alternatives>\n                        <jats:inline-graphic xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" mime-subtype=\"png\" content-type=\"simple\" xlink:href=\"S0021900225100466_inline1.png\">\n                          <jats:alt-text content-type=\"machine-generated\">StartRoot n EndRoot<\/jats:alt-text>\n                        <\/jats:inline-graphic>\n                        <mml:math xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" xmlns:mnf=\"http:\/\/cambridge.org\/core\/manifest\" xmlns:cup=\"http:\/\/contentservices.cambridge.org\" xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" xmlns:m=\"http:\/\/cambridge.org\/core\/metadata\" xmlns:core=\"http:\/\/cambridge.org\/core\" xmlns:c=\"http:\/\/cambridge.org\/core\/content\">\n                          <mml:msqrt>\n                            <mml:mi>n<\/mml:mi>\n                          <\/mml:msqrt>\n                        <\/mml:math>\n                        <jats:tex-math>$\\sqrt{n}$<\/jats:tex-math>\n                      <\/jats:alternatives>\n                    <\/jats:inline-formula>\n                    , we show that the diffusion-scaled queueing processes converge to a stochastic Volterra integral equation with \u2018ranks\u2019 driven by a continuous Gaussian process. It reduces to the limiting diffusion with a discontinuous drift in the Markovian setting.\n                  <\/jats:p>","DOI":"10.1017\/jpr.2025.10046","type":"journal-article","created":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T08:55:54Z","timestamp":1764665754000},"page":"690-706","update-policy":"https:\/\/doi.org\/10.1017\/policypage","source":"Crossref","is-referenced-by-count":0,"title":["Stochastic Volterra integral equations with ranks as scaling limits of parallel infinite-server queues under weighted shortest queue policy"],"prefix":"10.1017","volume":"63","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2787-7569","authenticated-orcid":false,"given":"Tomoyuki","family":"Ichiba","sequence":"first","affiliation":[{"name":"University of California"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Guodong","family":"Pang","sequence":"additional","affiliation":[{"name":"Rice University"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"56","published-online":{"date-parts":[[2025,12,2]]},"reference":[{"key":"S0021900225100466_ref25","volume-title":"CDMA: Principles of Spread Spectrum Communication","author":"Viterbi","year":"1995"},{"key":"S0021900225100466_ref11","doi-asserted-by":"publisher","DOI":"10.1287\/ijoc.2021.1100"},{"key":"S0021900225100466_ref27","doi-asserted-by":"publisher","DOI":"10.1002\/nav.20243"},{"key":"S0021900225100466_ref21","doi-asserted-by":"publisher","DOI":"10.1214\/06-PS091"},{"key":"S0021900225100466_ref24","doi-asserted-by":"publisher","DOI":"10.1137\/1.9780898719017"},{"key":"S0021900225100466_ref20","doi-asserted-by":"publisher","DOI":"10.1080\/17442509408833896"},{"key":"S0021900225100466_ref19","first-page":"2383","article-title":"A strong order 1\/2 method for multidimensional SDEs with discontinuous drift","volume":"27","author":"Leobacher","year":"2017","journal-title":"Prob. 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F. (1988). Differential Equations with Discontinuous Right-Hand Sides (Math. Appl. (Soviet Ser.) 18). Kluwer, Dordrecht."},{"key":"S0021900225100466_ref7","doi-asserted-by":"publisher","DOI":"10.1137\/20M1323746"},{"key":"S0021900225100466_ref5","doi-asserted-by":"publisher","DOI":"10.1023\/A:1020105004865"},{"key":"S0021900225100466_ref14","doi-asserted-by":"publisher","DOI":"10.1214\/10-AAP706"},{"key":"S0021900225100466_ref1","doi-asserted-by":"publisher","DOI":"10.1214\/19-AAP1466"},{"key":"S0021900225100466_ref18","doi-asserted-by":"publisher","DOI":"10.1016\/S0304-4149(02)00181-3"},{"key":"S0021900225100466_ref2","doi-asserted-by":"publisher","DOI":"10.1007\/BF00960074"},{"key":"S0021900225100466_ref29","doi-asserted-by":"publisher","DOI":"10.1081\/STM-200046493"},{"key":"S0021900225100466_ref3","first-page":"187","article-title":"Volterra equations with It\u00f4 integrals I","volume":"2","author":"Berger","year":"1980","journal-title":"J. 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Published by Cambridge University Press on behalf of Applied Probability Trust","name":"copyright","label":"Copyright","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https:\/\/creativecommons.org\/licenses\/by\/4.0\/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.","name":"license","label":"License","group":{"name":"copyright_and_licensing","label":"Copyright and Licensing"}},{"value":"This content has been made available to all.","name":"free","label":"Free to read"}]}}