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Priority Auctions and Queue Disciplines That Depend on Processing Time

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  • Thomas Kittsteiner

    () (Nuffield College, Oxford University, Oxford OX1 1NF, United Kingdom, and Department of Economics, University of Bonn, Lennéstrasse 37, 53113 Bonn, Germany)

  • Benny Moldovanu

    () (Department of Economics, University of Bonn, Lennéstrasse 37, 53113 Bonn, Germany)

Abstract

We analyze the allocation of priority in queues via simple bidding mechanisms. In our model, the stochastically arriving customers are privately informed about their own processing time. They make bids upon arrival at a queue whose length is unobservable. We consider two bidding schemes that differ in the definition of bids (these may reflect either total payments or payments per unit of time) and in the timing of payments (before or after service). In both schemes, a customer obtains priority over all customers, waiting in the queue or arriving while he is waiting, who make lower bids. Our main results show how the convexity/concavity of the function expressing the costs of delay determines the queue discipline (i.e., shortest-processing-time-first (SPT), longest-processing-time-first (LPT)) arising in a bidding equilibrium.

Suggested Citation

  • 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.
  • Handle: RePEc:inm:ormnsc:v:51:y:2005:i:2:p:236-248
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    File URL: http://dx.doi.org/10.1287/mnsc.1040.0301
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    References listed on IDEAS

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    1. 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.
    2. Jehiel, Philippe & Moldovanu, Benny, 2001. "Efficient Design with Interdependent Valuations," Econometrica, Econometric Society, pages 1237-1259.
    3. Hain, Roland & Mitra, Manipushpak, 2004. "Simple sequencing problems with interdependent costs," Games and Economic Behavior, Elsevier, vol. 48(2), pages 271-291, August.
    4. K. R. Balachandran, 1972. "Purchasing Priorities in Queues," Management Science, INFORMS, vol. 18(5-Part-1), pages 319-326, January.
    5. Tilt, Borge & Balachandran, K. R., 1979. "Stable and superstable customer policies in queues with balking and priority options," European Journal of Operational Research, Elsevier, vol. 3(6), pages 485-498, November.
    6. Naor, P, 1969. "The Regulation of Queue Size by Levying Tolls," Econometrica, Econometric Society, vol. 37(1), pages 15-24, January.
    7. McAfee, R. Preston, 1991. "Efficient allocation with continuous quantities," Journal of Economic Theory, Elsevier, vol. 53(1), pages 51-74, February.
    8. Partha Dasgupta & Eric Maskin, 2000. "Efficient Auctions," The Quarterly Journal of Economics, Oxford University Press, vol. 115(2), pages 341-388.
    9. Lui, Francis T, 1985. "An Equilibrium Queuing Model of Bribery," Journal of Political Economy, University of Chicago Press, vol. 93(4), pages 760-781, August.
    10. Robert J. Dolan, 1978. "Incentive Mechanisms for Priority Queuing Problems," Bell Journal of Economics, The RAND Corporation, vol. 9(2), pages 421-436, Autumn.
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    Citations

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    Cited by:

    1. 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.
    2. Gershkov, Alex & Moldovanu, Benny, 2012. "Optimal search, learning and implementation," Journal of Economic Theory, Elsevier, vol. 147(3), pages 881-909.
    3. Dirk Bergemann & Maher Said, 2010. "Dynamic Auctions: A Survey," Cowles Foundation Discussion Papers 1757, Cowles Foundation for Research in Economics, Yale University.
    4. Becker, Kai Helge, 2016. "An outlook on behavioural OR – Three tasks, three pitfalls, one definition," European Journal of Operational Research, Elsevier, vol. 249(3), pages 806-815.
    5. Benjamin Edelman & Michael Ostrovsky & Michael Schwarz, 2007. "Internet Advertising and the Generalized Second-Price Auction: Selling Billions of Dollars Worth of Keywords," American Economic Review, American Economic Association, vol. 97(1), pages 242-259, March.
    6. Heidrun C. Hoppe & Benny Moldovanu & Aner Sela, 2009. "The Theory of Assortative Matching Based on Costly Signals," Review of Economic Studies, Oxford University Press, vol. 76(1), pages 253-281.
    7. Jehiel, Philippe & Moldovanu, Benny, 2005. "Allocative and Informational Externalities in Auctions and Related Mechanisms," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 142, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    8. Moldovanu, Benny & Dizdar, Deniz & Gershkov, Alex, 2011. "Revenue maximization in the dynamic knapsack problem," Theoretical Economics, Econometric Society.
    9. Moulin, Hervé, 2008. "Proportional scheduling, split-proofness, and merge-proofness," Games and Economic Behavior, Elsevier, vol. 63(2), pages 567-587, July.
    10. Hervé Moulin, 2007. "On Scheduling Fees to Prevent Merging, Splitting, and Transferring of Jobs," Mathematics of Operations Research, INFORMS, vol. 32(2), pages 266-283, May.
    11. 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.
    12. Moulin, Herve, 2005. "Split-Proof Probabilistic Scheduling," Working Papers 2004-06, Rice University, Department of Economics.
    13. Ryuji Sano, 2015. "A Dynamic Mechanism Design for Scheduling with Different Use Lengths," KIER Working Papers 924, Kyoto University, Institute of Economic Research.
    14. Benny Moldovanu & Alex Gershkov, 2008. "The Trade-off Between Fast Learning and Dynamic Efficiency," 2008 Meeting Papers 348, Society for Economic Dynamics.

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