{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,14]],"date-time":"2026-02-14T09:01:05Z","timestamp":1771059665800,"version":"3.50.1"},"reference-count":26,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T00:00:00Z","timestamp":1614902400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T00:00:00Z","timestamp":1614902400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Queueing Syst"],"published-print":{"date-parts":[[2021,4]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Pay-for-priority is a common practice in congestion-prone service systems. The extant literature on this topic restricts attention to the case where the only epoch for customers to purchase priority is <jats:italic>upon arrival<\/jats:italic>, and if customers choose not to upgrade when they arrive, they cannot do so later during their wait. A natural alternative is to let customers pay and upgrade to priority at any time during their stay in the queue, even if they choose not to do so initially. This paper builds a queueing-game-theoretic model that explicitly captures self-interested customers\u2019 dynamic <jats:italic>in-queue<\/jats:italic> priority-purchasing behavior. When all customers (who have not upgraded yet) <jats:italic>simultaneously<\/jats:italic> decide whether to upgrade, we find in our model that pure-strategy equilibria do not exist under some intuitive criteria, contrasting the findings in classical models where customers can only purchase priority upon arrival. However, when customers <jats:italic>sequentially<\/jats:italic> decide whether to upgrade, threshold-type pure-strategy equilibria may exist. In particular, under sufficiently light traffic, if the number of ordinary customers accumulates to a certain threshold, then it is always the second last customer who upgrades, but in general, it could be a customer from another position, and the queue-length threshold that triggers an upgrade can also vary with the traffic intensity. Finally, we find that in-queue priority purchase subject to the sequential rule yields less revenue than upon-arrival priority purchase in systems with small buffers.<\/jats:p>","DOI":"10.1007\/s11134-021-09694-y","type":"journal-article","created":{"date-parts":[[2021,3,5]],"date-time":"2021-03-05T18:03:53Z","timestamp":1614967433000},"page":"343-381","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["In-queue priority purchase: a dynamic game approach"],"prefix":"10.1007","volume":"97","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1154-5861","authenticated-orcid":false,"given":"Zhongbin","family":"Wang","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5370-6926","authenticated-orcid":false,"given":"Luyi","family":"Yang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6643-6865","authenticated-orcid":false,"given":"Shiliang","family":"Cui","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jinting","family":"Wang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,3,5]]},"reference":[{"issue":"5","key":"9694_CR1","doi-asserted-by":"publisher","first-page":"1051","DOI":"10.1287\/opre.22.5.1051","volume":"22","author":"I Adiri","year":"1974","unstructured":"Adiri, I., Yechiali, U.: Optimal priority-purchasing and pricing decisions in nonmonopoly and monopoly queues. Oper. Res. 22(5), 1051\u20131066 (1974)","journal-title":"Oper. Res."},{"issue":"3","key":"9694_CR2","doi-asserted-by":"publisher","first-page":"423","DOI":"10.1287\/msom.2013.0449","volume":"15","author":"P Af\u00e8che","year":"2013","unstructured":"Af\u00e8che, P.: Incentive-compatible revenue management in queueing systems: optimal strategic delay. Manuf. Serv. Oper. Manag. 15(3), 423\u2013443 (2013)","journal-title":"Manuf. Serv. Oper. Manag."},{"key":"9694_CR3","doi-asserted-by":"crossref","unstructured":"Af\u00e8che, P., Sarhangian, V.: Rational abandonment from priority queues: equilibrium strategy and pricing implications. Working paper, University of Toronto (2015)","DOI":"10.2139\/ssrn.2679328"},{"issue":"12","key":"9694_CR4","doi-asserted-by":"publisher","first-page":"2727","DOI":"10.1287\/mnsc.2013.1730","volume":"59","author":"Z Ak\u015fin","year":"2013","unstructured":"Ak\u015fin, Z., Ata, B., Emadi, S.M., Su, C.L.: Structural estimation of callers\u2019 delay sensitivity in call centers. Manag. Sci. 59(12), 2727\u20132746 (2013)","journal-title":"Manag. Sci."},{"issue":"1","key":"9694_CR5","doi-asserted-by":"publisher","first-page":"242","DOI":"10.1287\/opre.2016.1542","volume":"65","author":"Z Ak\u015fin","year":"2016","unstructured":"Ak\u015fin, Z., Ata, B., Emadi, S.M., Su, C.L.: Impact of delay announcements in call centers: an empirical approach. Oper. Res. 65(1), 242\u2013265 (2016)","journal-title":"Oper. Res."},{"issue":"5","key":"9694_CR6","doi-asserted-by":"publisher","first-page":"666","DOI":"10.1287\/mnsc.34.5.666","volume":"34","author":"H Alperstein","year":"1988","unstructured":"Alperstein, H.: Note-optimal pricing policy for the service facility offering a set of priority prices. Manag. Sci. 34(5), 666\u2013671 (1988)","journal-title":"Manag. Sci."},{"issue":"1","key":"9694_CR7","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1287\/moor.15.1.129","volume":"15","author":"D Assaf","year":"1990","unstructured":"Assaf, D., Haviv, M.: Reneging from processor sharing systems and random queues. Math. Oper. Res. 15(1), 129\u2013138 (1990)","journal-title":"Math. Oper. Res."},{"issue":"1","key":"9694_CR8","doi-asserted-by":"publisher","first-page":"163","DOI":"10.1287\/opre.2017.1638","volume":"66","author":"B Ata","year":"2018","unstructured":"Ata, B., Peng, X.: An equilibrium analysis of a multiclass queue with endogenous abandonments in heavy traffic. Oper. Res. 66(1), 163\u2013183 (2018)","journal-title":"Oper. Res."},{"issue":"5\u2013part\u20131","key":"9694_CR9","doi-asserted-by":"publisher","first-page":"319","DOI":"10.1287\/mnsc.18.5.319","volume":"18","author":"K Balachandran","year":"1972","unstructured":"Balachandran, K.: Purchasing priorities in queues. Manag. Sci. 18(5\u2013part\u20131), 319\u2013326 (1972)","journal-title":"Manag. Sci."},{"key":"9694_CR10","doi-asserted-by":"crossref","unstructured":"Cui, S., Veeraraghavan, S., Wang, J., Zhang, Y.: In-queue observation and abandonment. Working paper, Georgetown University (2018)","DOI":"10.2139\/ssrn.3290868"},{"issue":"1","key":"9694_CR11","doi-asserted-by":"publisher","first-page":"227","DOI":"10.1287\/mnsc.2018.3212","volume":"66","author":"S Cui","year":"2020","unstructured":"Cui, S., Wang, Z., Yang, L.: The economics of line-sitting. Manag. Sci. 66(1), 227\u2013242 (2020)","journal-title":"Manag. Sci."},{"issue":"6","key":"9694_CR12","doi-asserted-by":"publisher","first-page":"979","DOI":"10.1111\/poms.12520","volume":"25","author":"S Gavirneni","year":"2016","unstructured":"Gavirneni, S., Kulkarni, V.G.: Self-selecting priority queues with burr distributed waiting costs. Product. Oper. Manag. 25(6), 979\u2013992 (2016)","journal-title":"Product. Oper. Manag."},{"issue":"3","key":"9694_CR13","doi-asserted-by":"publisher","first-page":"1061","DOI":"10.1287\/mnsc.2017.2987","volume":"65","author":"I Gurvich","year":"2019","unstructured":"Gurvich, I., Lariviere, M.A., Ozkan, C.: Coverage, coarseness, and classification: determinants of social efficiency in priority queues. Manag. Sci. 65(3), 1061\u20131075 (2019)","journal-title":"Manag. Sci."},{"key":"9694_CR14","doi-asserted-by":"publisher","DOI":"10.1201\/b20014","volume-title":"Rational Queueing","author":"R Hassin","year":"2016","unstructured":"Hassin, R.: Rational Queueing. Chapman and Hall\/CRC, Boca Raton (2016)"},{"issue":"6","key":"9694_CR15","doi-asserted-by":"publisher","first-page":"966","DOI":"10.1287\/opre.45.6.966","volume":"45","author":"R Hassin","year":"1997","unstructured":"Hassin, R., Haviv, M.: Equilibrium threshold strategies: the case of queues with priorities. Oper. Res. 45(6), 966\u2013973 (1997)","journal-title":"Oper. Res."},{"key":"9694_CR16","doi-asserted-by":"publisher","DOI":"10.1007\/978-1-4615-0359-0","volume-title":"To Queue Or Not To Queue: Equilibrium Behavior in Queueing Systems","author":"R Hassin","year":"2003","unstructured":"Hassin, R., Haviv, M.: To Queue Or Not To Queue: Equilibrium Behavior in Queueing Systems, vol. 59. Springer, New York (2003)"},{"issue":"3\u20134","key":"9694_CR17","doi-asserted-by":"publisher","first-page":"419","DOI":"10.1007\/s11134-017-9535-0","volume":"86","author":"Y Kerner","year":"2017","unstructured":"Kerner, Y., Sherzer, E., Yanco, M.A.: On non-equilibria threshold strategies in ticket queues. Queueing Syst. 86(3\u20134), 419\u2013431 (2017)","journal-title":"Queueing Syst."},{"key":"9694_CR18","unstructured":"Maglaras, C., Yao, J., Zeevi, A.: Observational learning and abandonment in a congested queue. Working paper, Columbia University (2017)"},{"issue":"5","key":"9694_CR19","doi-asserted-by":"publisher","first-page":"870","DOI":"10.1287\/opre.38.5.870","volume":"38","author":"H Mendelson","year":"1990","unstructured":"Mendelson, H., Whang, S.: Optimal incentive-compatible priority pricing for the M\/M\/1 queue. Oper. Res. 38(5), 870\u2013883 (1990)","journal-title":"Oper. Res."},{"key":"9694_CR20","first-page":"15","volume":"37","author":"P Naor","year":"1969","unstructured":"Naor, P.: The regulation of queue size by levying tolls. Econ. J. Econ. Soc. 37, 15\u201324 (1969)","journal-title":"Econ. J. Econ. Soc."},{"issue":"3","key":"9694_CR21","doi-asserted-by":"publisher","first-page":"578","DOI":"10.1111\/poms.12818","volume":"27","author":"H Nazerzadeh","year":"2018","unstructured":"Nazerzadeh, H., Randhawa, R.S.: Near-optimality of coarse service grades for customer differentiation in queueing systems. Prod. Oper. Manag. 27(3), 578\u2013595 (2018)","journal-title":"Prod. Oper. Manag."},{"issue":"1","key":"9694_CR22","doi-asserted-by":"publisher","first-page":"43","DOI":"10.1111\/poms.12889","volume":"28","author":"J Wang","year":"2019","unstructured":"Wang, J., Cui, S., Wang, Z.: Equilibrium strategies in M\/M\/1 priority queues with balking. Prod. Oper. Manag. 28(1), 43\u201362 (2019)","journal-title":"Prod. Oper. Manag."},{"key":"9694_CR23","unstructured":"Webb, E.M., Yu, Q., Bretthauer, K.M.: Linking delay announcements, abandonment, and service time. Working paper, Indiana University (2017)"},{"issue":"5","key":"9694_CR24","first-page":"2231","volume":"65","author":"L Yang","year":"2019","unstructured":"Yang, L., Debo, L.: Referral priority program: leveraging social ties via operational incentives. Manag. Sci. 65(5), 2231\u20132248 (2019)","journal-title":"Manag. Sci."},{"issue":"7","key":"9694_CR25","doi-asserted-by":"publisher","first-page":"2377","DOI":"10.1287\/mnsc.2016.2436","volume":"63","author":"L Yang","year":"2017","unstructured":"Yang, L., Debo, L., Gupta, V.: Trading time in a congested environment. Manag. Sci. 63(7), 2377\u20132395 (2017)","journal-title":"Manag. Sci."},{"key":"9694_CR26","doi-asserted-by":"crossref","unstructured":"Yang, L., Wang, Z., Cui, S.: A model of queue-scalping. Manag. Sci. https:\/\/doi.org\/10.1287\/mnsc.2020.3865 (2021)","DOI":"10.1287\/mnsc.2020.3865"}],"container-title":["Queueing Systems"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-021-09694-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s11134-021-09694-y\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s11134-021-09694-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,3,31]],"date-time":"2021-03-31T04:19:05Z","timestamp":1617164345000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s11134-021-09694-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,3,5]]},"references-count":26,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2021,4]]}},"alternative-id":["9694"],"URL":"https:\/\/doi.org\/10.1007\/s11134-021-09694-y","relation":{},"ISSN":["0257-0130","1572-9443"],"issn-type":[{"value":"0257-0130","type":"print"},{"value":"1572-9443","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,3,5]]},"assertion":[{"value":"29 October 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"3 February 2021","order":2,"name":"revised","label":"Revised","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 February 2021","order":3,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"5 March 2021","order":4,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}