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Pricing and Priority Auctions in Queueing Systems with a Generalized Delay Cost Structure


  • Philipp Afèche

    () (Kellogg School of Management, Northwestern University, Evanston, Illinois 60208-2009)

  • Haim Mendelson

    () (Graduate School of Business, Stanford University, Stanford, California 94305)


This paper studies alternative price-service mechanisms for a provider that serves customers whose delay cost depends on their service valuations. We propose a generalized delay cost structure that augments the standard additive model with a multiplicative component, capturing the interdependence between delay cost and values. We derive and compare the revenue-maximizing and socially optimal equilibria under uniform pricing, preemptive, and nonpreemptive priority auctions with an admission price. We find that the delay cost structure has a paramount effect on system behavior. The classical result that the revenue-maximizing admission price is higher and the utilization lower than is socially optimal can be reversed under our generalized structure, and we identify the conditions driving this reversal under each mechanism. We show that the conditional bid equilibria are unique and induce the socially optimal allocations. The auctions yield gains in system net value and provider profit over uniform pricing, which are dramatically larger for the preemptive mechanism. Both auctions perform better under multiplicative compared to additive delay costs. The highest-value customers always gain under the preemptive, but may lose under the nonpreemptive auction. The lowest-value customers always gain in either auction.

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  • Philipp Afèche & Haim Mendelson, 2004. "Pricing and Priority Auctions in Queueing Systems with a Generalized Delay Cost Structure," Management Science, INFORMS, vol. 50(7), pages 869-882, July.
  • Handle: RePEc:inm:ormnsc:v:50:y:2004:i:7:p:869-882

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    References listed on IDEAS

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    Cited by:

    1. Philipp Afèche & J. Michael Pavlin, 2016. "Optimal Price/Lead-Time Menus for Queues with Customer Choice: Segmentation, Pooling, and Strategic Delay," Management Science, INFORMS, vol. 62(8), pages 2412-2436, August.
    2. Lian, Zhaotong & Gu, Xinhua & Wu, Jinbiao, 2016. "A re-examination of experience service offering and regular service pricing under profit maximization," European Journal of Operational Research, Elsevier, vol. 254(3), pages 907-915.
    3. Ryan W. Buell & Dennis Campbell & Frances X. Frei, 2016. "How Do Customers Respond to Increased Service Quality Competition?," Manufacturing & Service Operations Management, INFORMS, vol. 18(4), pages 585-607, October.
    4. Pengfei Guo & Paul Zipkin, 2007. "Analysis and Comparison of Queues with Different Levels of Delay Information," Management Science, INFORMS, vol. 53(6), pages 962-970, June.
    5. Gérard P. Cachon & Pnina Feldman, 2011. "Pricing Services Subject to Congestion: Charge Per-Use Fees or Sell Subscriptions?," Manufacturing & Service Operations Management, INFORMS, vol. 13(2), pages 244-260, June.
    6. Apostolos Burnetas, 2013. "Customer equilibrium and optimal strategies in Markovian queues in series," Annals of Operations Research, Springer, vol. 208(1), pages 515-529, September.
    7. Thomas Kittsteiner & Benny Moldovanu, 2005. "Priority Auctions and Queue Disciplines That Depend on Processing Time," Management Science, INFORMS, vol. 51(2), pages 236-248, February.
    8. Haim Mendelson & Ali K. Parlaktürk, 2008. "Product-Line Competition: Customization vs. Proliferation," Management Science, INFORMS, vol. 54(12), pages 2039-2053, December.
    9. Baric{s} Ata & Shiri Shneorson, 2006. "Dynamic Control of an M/M/1 Service System with Adjustable Arrival and Service Rates," Management Science, INFORMS, vol. 52(11), pages 1778-1791, November.
    10. Güler, M. Güray & Bilgiç, Taner & Güllü, Refik, 2014. "Joint inventory and pricing decisions when customers are delay sensitive," International Journal of Production Economics, Elsevier, vol. 157(C), pages 302-312.
    11. Alex Gershkov & Paul Schweinzer, 2010. "When queueing is better than push and shove," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(3), pages 409-430, July.
    12. Anouar El Haji & Sander Onderstal, 2015. "Trading Places: An Experimental Comparison of Reallocation Mechanisms for Priority Queuing," Tinbergen Institute Discussion Papers 15-063/VII, Tinbergen Institute.
    13. Philipp Afèche, 2013. "Incentive-Compatible Revenue Management in Queueing Systems: Optimal Strategic Delay," Manufacturing & Service Operations Management, INFORMS, vol. 15(3), pages 423-443, July.
    14. Maxim Afanasyev & Haim Mendelson, 2010. "Service Provider Competition: Delay Cost Structure, Segmentation, and Cost Advantage," Manufacturing & Service Operations Management, INFORMS, vol. 12(2), pages 213-235, May.
    15. repec:eee:ejores:v:262:y:2017:i:1:p:239-250 is not listed on IDEAS
    16. Liu, Tieming & Methapatara, Chinnatat & Wynter, Laura, 2010. "Revenue management model for on-demand IT services," European Journal of Operational Research, Elsevier, vol. 207(1), pages 401-408, November.
    17. Eric T. Anderson & James D. Dana, Jr., 2009. "When Is Price Discrimination Profitable?," Management Science, INFORMS, vol. 55(6), pages 980-989, June.
    18. Jayaswal, Sachin & Jewkes, Elizabeth & Ray, Saibal, 2011. "Product differentiation and operations strategy in a capacitated environment," European Journal of Operational Research, Elsevier, vol. 210(3), pages 716-728, May.
    19. Zhou, Wenhui & Lian, Zhaotong & Wu, Jinbiao, 2014. "When should service firms provide free experience service?," European Journal of Operational Research, Elsevier, vol. 234(3), pages 830-838.
    20. Yina Lu & Andrés Musalem & Marcelo Olivares & Ariel Schilkrut, 2013. "Measuring the Effect of Queues on Customer Purchases," Management Science, INFORMS, vol. 59(8), pages 1743-1763, August.
    21. Ke-Wei Huang & Arun Sundararajan, 2006. "Pricing Digital Goods: Discontinuous Costs and Shared Infrastructure," Working Papers 06-11, NET Institute, revised Sep 2006.
    22. Ying-Ju Chen & Ke-Wei Huang, 2016. "Pricing Data Services: Pricing by Minutes, by Gigs, or by Megabytes per Second?," Information Systems Research, INFORMS, vol. 27(3), pages 596-617.
    23. repec:spr:annopr:v:244:y:2016:i:2:d:10.1007_s10479-016-2141-4 is not listed on IDEAS
    24. Barış Ata & Tava Lennon Olsen, 2009. "Near-Optimal Dynamic Lead-Time Quotation and Scheduling Under Convex-Concave Customer Delay Costs," Operations Research, INFORMS, vol. 57(3), pages 753-768, June.
    25. Gad Allon & Awi Federgruen, 2007. "Competition in Service Industries," Operations Research, INFORMS, vol. 55(1), pages 37-55, February.


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