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Fair Queuing and Other Probabilistic Allocation Methods

  • Moulin, Herve

    (Rice U)

  • Stong, Richard

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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File URL: http://www.ruf.rice.edu/~econ/papers/2000papers/09Moulin.pdf
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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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  1. Hervé Moulin, 2002. "The proportional random allocation of indivisible units," Social Choice and Welfare, Springer, vol. 19(2), pages 381-413.
  2. Kaminski, Marek M., 2000. "'Hydraulic' rationing," Mathematical Social Sciences, Elsevier, vol. 40(2), pages 131-155, September.
  3. Young, H. P., 1988. "Distributive justice in taxation," Journal of Economic Theory, Elsevier, vol. 44(2), pages 321-335, April.
  4. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  5. Salvador Barbera, 1995. "Strategy-Proof Allotment Rules," Discussion Papers 1142, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. 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.
  7. Hervé Moulin, 2000. "Priority Rules and Other Asymmetric Rationing Methods," Econometrica, Econometric Society, vol. 68(3), pages 643-684, May.
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