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Fair Queuing and Other Probabilistic Allocation Methods

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  • Moulin, Herve

    (Rice U)

  • Stong, Richard

Abstract

A server processes one job per unit of time and randomly schedules the jobs requested by a given set of users; each user may request a different number of jobs. Fair queuing (Shenker 1989) schedules jobs in successive round-robin fashion, where each agent receives one unit in each round until his demand is met and the ordering is random in each round. Fair queuing *, the reverse scheduling of fair queuing, serves first (with uniform probability) one of the users with the largest remaining demand. We characterize fair queuing * by the combination of lower composition--LC--(the scheduling sequence is history independent), demand monotonicity--DM--(increasing my demand cannot result in increased delay) and two equity axioms, equal treatment ex ante--ETEA (two identical demands give the same probability distribution of service) and equal treatment ex post--ETEP (two identical demands must be served in alternating fashion). The set of dual axioms (in which ETEA and ETEP are unchanged) characterizes fair queuing. We also characterize the rich family of methods satisfying LC, DM, and the familiar consistency--CSY--axiom. They work by fixing a standard of comparison (preordering) between a demand of xi units by agent i and one of xj units by agent j. The first job scheduled is drawn from the agents whose demand has the highest standard.

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Bibliographic Info

Paper provided by Rice University, Department of Economics in its series Working Papers with number 2000-09.

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Date of creation: Mar 2001
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Handle: RePEc:ecl:riceco:2000-09

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References

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  1. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September.
  2. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
  3. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
  4. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  5. Moulin, Herve, 2000. "The Proportional Random Allocation of Indivisible Units," Working Papers 2000-02, Rice University, Department of Economics.
  6. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
  7. Barbera, Salvador & Jackson, Matthew O. & Neme, Alejandro, 1997. "Strategy-Proof Allotment Rules," Games and Economic Behavior, Elsevier, vol. 18(1), pages 1-21, January.
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Citations

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Cited by:
  1. Moulin, Herve & Sprumont, Yves, 2003. "On Demand Responsiveness in Additive Cost Sharing," Working Papers 2003-10, Rice University, Department of Economics.
  2. Carmen Herrero & Ricardo Martínez, 2008. "Balanced allocation methods for claims problems with indivisibilities," Social Choice and Welfare, Springer, vol. 30(4), pages 603-617, May.
  3. Chambers, Christopher P., 2006. "Asymmetric rules for claims problems without homogeneity," Games and Economic Behavior, Elsevier, vol. 54(2), pages 241-260, February.
  4. Moulin, Herve, 2000. "The Proportional Random Allocation of Indivisible Units," Working Papers 2000-02, Rice University, Department of Economics.
  5. Moulin, Herve, 2005. "Split-Proof Probabilistic Scheduling," Working Papers 2004-06, Rice University, Department of Economics.
  6. EHLERS, Lars & KLAUS, Bettina, 2001. "Probabilistic Assignments of Identical Indivisible Objects and Uniform Probabilistic Rules," Cahiers de recherche 2001-27, Universite de Montreal, Departement de sciences economiques.
  7. Moulin, Herve, 2001. "Filling a Multicolor Urn: An Axiomatic Analysis," Working Papers 2001-01, Rice University, Department of Economics.
  8. Carmen Herrero & Ricardo Martínez, 2008. "Up methods in the allocation of indivisibilities when preferences are single-peaked," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 16(2), pages 272-283, December.
  9. Francis Bloch & David Cantala, 2010. "Markovian assignment rules," Serie documentos de trabajo del Centro de Estudios Económicos 2010-18, El Colegio de México, Centro de Estudios Económicos.
  10. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357 Elsevier.

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