Advertisement

The Queueing Problem and Its Generalizations

  • Youngsub ChunEmail author
Chapter
Part of the Studies in Economic Design book series (DESI)

Abstract

A group of agents must be served in a facility. The facility can serve one agent at a time and agents incur waiting costs. The queueing problem is concerned with finding the order to serve agents and the monetary transfers they should receive. In this paper, we summarize recent developments in the queueing problem and discuss its possible generalizations to indicate the directions for future research.

References

  1. Chun, Y. (2006a). A pessimistic approach to the queueing problem. Mathematical Social Sciences, 51, 171–181.CrossRefGoogle Scholar
  2. Chun, Y. (2006b). No-envy in queueing problems. Economic Theory, 29, 151–162.CrossRefGoogle Scholar
  3. Chun, Y. (2011). Consistency and monotonicity in sequencing problems. International Journal of Game Theory, 40, 29–41.CrossRefGoogle Scholar
  4. Chun, Y. (2016). Fair queueing. Berlin: Springer.CrossRefGoogle Scholar
  5. Chun, Y., & Heo, E. J. (2008). Queueing problems with two parallel servers. International Journal of Economic Theory, 4, 299–315.CrossRefGoogle Scholar
  6. Chun, Y., & Hokari, T. (2007). On the coincidence of the Shapley value and the nucleolus in queueing problems. Seoul Journal of Economics, 20(2), 223–237.Google Scholar
  7. Chun, Y., Mitra, M., & Mutuswami, S. (2014a). Characterizations of pivotal mechanisms in the queueing problem. Mathematical Social Sciences, 72, 62–66.CrossRefGoogle Scholar
  8. Chun, Y., Mitra, M., & Mutuswami, S. (2014b). Egalitarian equivalence and strategyproofness in the queueing problem. Economic Theory, 56(2), 425–442.CrossRefGoogle Scholar
  9. Chun, Y., Mitra, M., & Mutuswami, S. (2015). A characterization of the symmetrically balanced VCG rule in the queueing problem. Games and Economic Behavior.  https://doi.org/10.1016/j.geb.2015.04.001.
  10. Chun, Y., Mitra, M., & Mutuswami, S. (2017). Reordering an existing queue. Social Choice and Welfare, 49, 65–87.CrossRefGoogle Scholar
  11. Chun, Y., & Park, B. (2017). A graph theoretic approach to the slot allocation problem. Social Choice and Welfare, 48, 133–152.CrossRefGoogle Scholar
  12. Chun, Y., & Yengin, D. (2017). Welfare lower bounds and strategy-proofness in the queueing problem. Games and Economic Behavior, 102, 462–476.CrossRefGoogle Scholar
  13. Clarke, E. H. (1971). Multi-part pricing of public goods. Public Choice, 11, 17–33.CrossRefGoogle Scholar
  14. Curiel, I., Pederzoli, G., & Tijs, S. (1989). Sequencing games. European Journal of Operations Research, 40, 344–351.CrossRefGoogle Scholar
  15. Dolan, R. J. (1978). Incentive mechanisms for priority queuing problems. The Bell Journal of Economics, 9, 421–436.CrossRefGoogle Scholar
  16. Foley, D. (1967). Resource allocation and the public sector. Yale Economic Essays, 7, 45–98.Google Scholar
  17. Gershkov, A., & Schweinzer, P. (2010). When queueing is better than push and shove. International Journal of Game Theory, 39, 409–430.CrossRefGoogle Scholar
  18. Ghosh, S., Long, Y., & Mitra, M. (2014). Dynamic VCG mechanisms in queueing. New York: Mimeo.Google Scholar
  19. Groves, T. (1973). Incentives in teams. Econometrica, 41, 617–631.CrossRefGoogle Scholar
  20. Gul, F. (1989). Bargaining foundations of Shapely value. Econometrica, 57, 81–95.CrossRefGoogle Scholar
  21. Hart, S., & Mas-Colell, A. (1996). Bargaining and value. Econometrica, 64, 357–380.CrossRefGoogle Scholar
  22. Hashimoto, K., & Saitoh, H. (2012). Strategy-proof and anonymous rule in queueing problems: A relationship between equity and efficiency. Social Choice and Welfare, 38, 473–480.CrossRefGoogle Scholar
  23. Holmström, B. (1979). Groves’ schemes on restricted domains. Econometrica, 47, 1137–1144.CrossRefGoogle Scholar
  24. Hougaard, J., Moreno-Ternero, J., & Østerdal, L. P. (2014). Assigning agents to a line. Games and Economic Behavior, 87, 539–553.CrossRefGoogle Scholar
  25. Ju, Y. (2013). Efficiency and compromise: A bid-offer counteroffer mechanism with two players. International Journal of Game Theory, 42, 501–520.CrossRefGoogle Scholar
  26. Ju, Y., Chun, Y., & van den Brink, R. (2014). Auctioning and selling positions: A non-cooperative approach to queueing conflicts. Journal of Economic Theory, 153, 33–45.CrossRefGoogle Scholar
  27. Ju, Y., & Wettstein, D. (2009). Implementing cooperative solution concepts: A generalized bidding approach. Economic Theory, 39, 307–330.CrossRefGoogle Scholar
  28. Kayi, C., & Ramaekers, E. (2010). Characterizations of Pareto-efficient, fair, and strategy-proof allocation rules in queueing problems. Games and Economic Behavior, 68, 220–232.CrossRefGoogle Scholar
  29. Maniquet, F. (2003). A characterization of the Shapley value in queueing problems. Journal of Economic Theory, 109, 90–103.CrossRefGoogle Scholar
  30. Mitra, M. (2001). Mechanism design in queueing problems. Economic Theory, 17, 277–305.CrossRefGoogle Scholar
  31. Mitra, M. (2002). Achieving the first best in sequencing problems. Review of Economic Design, 7, 75–91.CrossRefGoogle Scholar
  32. Mitra, M. (2005). Incomplete information and multiple machine queueing problems. European Journal of Operational Research, 165, 251–266.CrossRefGoogle Scholar
  33. Mitra, M., & Mutuswami, S. (2011). Group strategyproofness in queueing models. Games and Economic Behavior, 72, 242–254.CrossRefGoogle Scholar
  34. Moulin, H. (1990). Fair division under joint ownership: recent results and open problems. Social Choice and Welfare, 7, 149–170.CrossRefGoogle Scholar
  35. Moulin, H. (1991). Welfare bounds in the fair division problem. Journal of Economic Theory, 54, 321–337.CrossRefGoogle Scholar
  36. Moulin, H. (2007). On scheduling fees to prevent merging, splitting, and transferring of jobs. Mathematics of Operations Research, 32, 266–283.CrossRefGoogle Scholar
  37. Mukherjee, C. (2013). Weak group strategy-proof and queue-efficient mechanisms for the queueing problem with multiple machines. International Journal of Game Theory, 42, 131–163.CrossRefGoogle Scholar
  38. Parikshit, D., & Mitra, M. (2017). Incentives and justice for sequencing problems. Economic Theory, 64, 239–264.CrossRefGoogle Scholar
  39. Pazner, E., & Schmeidler, D. (1978). Egalitarian equivalent allocations: A new concept of equity. Quarterly Journal of Economics, 92, 671–687.CrossRefGoogle Scholar
  40. Pérez-Castrillo, D., & Wettstein, D. (2001). Bidding for the surplus: A non-cooperative approach to the Shapley value. Journal of Economic Theory, 100, 274–294.CrossRefGoogle Scholar
  41. Schummer, J., & Abizada, A. (2017). Incentives in landing slot problems. Journal of Economic Theory, 170, 29–55.CrossRefGoogle Scholar
  42. Schummer, J., & Vohra, R. (2013). Assignment of arrival slsots. American Economic Journal: Microeconomics, 5(2), 164–185.Google Scholar
  43. Shapley, L. S. (1953). A value for \(n\)-person Games. In H. W. Kuhn & A. W. Tucker (Eds.), Contributions to the theory of games II (Vol. 28, pp. 307–317), Annals of Mathematical Studies. USA: Princeton University Press.Google Scholar
  44. Suijs, J. (1996). On incentive compatibility and budget balancedness in public decision making. Economic Design, 2, 193–209.CrossRefGoogle Scholar
  45. Thomson, W. (2013). The theory of fair allocation. Book Manuscript. University of Rochester.Google Scholar
  46. Vickrey, W. (1961). Counterspeculation, auctions and competitive sealed tenders. Journal of Finance, 16, 8–37.CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of EconomicsSeoul National UniversitySeoulKorea

Personalised recommendations