Abstract
Resource allocation problems are concerned with the allocation of limited resources among competing agents so as to achieve the best system performances. In systems which serve many users, like in networking, there is a need to respect some fairness rules while looking for the overall efficiency. The so-called Max-Min Fairness is widely used to meet these goals. However, allocating the resource to optimize the worst performance may cause a dramatic worsening of the overall system efficiency. Therefore, several other fair allocation schemes are searched and analyzed. In this paper we show how the scalar inequality measures can be consistently used in bicriteria models to search for fair and efficient allocations while taking into account importance weighting of the agents.
This work was partially supported by the Polish Ministry of Science and Higher Education under the grants N N516 4307 33 and 69/N-SINGAPUR/2007/0.
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References
Atkinson, A.B.: On the measurement of inequality. J. Economic Theory 2, 244–263 (1970)
Bansal, N., Sviridenko, M.: The Santa Claus problem. In: Proc. of STOC 2006, Seattle, pp. 31–41 (May 2006)
Bertsekas, D., Gallager, R.: Data Networks. Prentice-Hall, Englewood Cliffs (1987)
Bouveret, S., Lemaitre, M.: Computing leximin-optimal solutions in constraints networks. Artificial Intell. 173, 343–364 (2009)
Bouveret, S., Lang, J.: Efficiency and envy-freeness in fair division of indivisible goods: logical representation and complexity. In: Proc. IJCAI 2005, Edinburgh, pp. 935–940 (August 2005)
Bonald, T., Massoulie, L.: Impact of fairness on Internet performance. In: Proc. of ACM Sigmetrics, pp. 82–91 (June 2001)
Brams, S.J., Taylor, A.D.: Fair Division: From Cake Cutting to Dispute Resolution. Cambridge Univ. Press, New York (1996)
Dalton, H.: The measurement of the inequality of income. Economic J. 30, 348–361 (1920)
Denda, R., Banchs, A., Effelsberg, W.: The fairness challenge in computer networks. In: Crowcroft, J., Roberts, J., Smirnov, M.I. (eds.) QofIS 2000. LNCS, vol. 1922, pp. 208–220. Springer, Heidelberg (2000)
Golden, B., Perny, P.: Infinite order Lorenz dominance for fair multiagent optimization. In: Proc. of AAMAS 2010, Toronto, pp. 383–390 (May 2010)
Goldsmith, J., Sloan, R.: The AI conference paper assignment problem. In: Proc. AAAI Workshop on Preference Handling for Artificial Intelligence, Vancouver, pp. 53–57 (July 2007)
Ibaraki, T., Katoh, N.: Resource Allocation Problems, Algorithmic Approaches. MIT Press, Cambridge (1988)
Jaffe, J.: Bottleneck flow control. IEEE Trans. Communications 7, 207–237 (1980)
la Kelly, F., Mauloo, A., Tan, D.: Rate control for communication networks: shadow prices, proportional fairness and stability. J. Opnl. Res. Soc. 49, 206–217 (1997)
Kleinberg, J., Rabani, Y., Tardos, E.: Fairness in routing and load balancing. J. Comput. Syst. Sci. 63, 2–21 (2001)
Kostreva, M.M., Ogryczak, W.: Linear optimization with multiple equitable criteria. RAIRO Oper. Res. 33, 275–297 (1999)
Kostreva, M.M., Ogryczak, W., Wierzbicki, A.: Equitable aggregations and multiple criteria analysis. Eur. J. Opnl. Res. 158, 362–367 (2004)
Lesca, J., Perny, P.: LP Solvable Models for Multiagent Fair Allocation problems. In: Proc. of ECAI 2010, Lizbon (August 2010)
Luss, H.: On equitable resource allocation problems: A lexicographic minimax approach. Oper. Res. 47, 361–378 (1999)
Marchi, E., Oviedo, J.A.: Lexicographic optimality in the multiple objective linear programming: the nucleolar solution. Eur. J. Opnl. Res. 57, 355–359 (1992)
Marshall, A.W., Olkin, I.: Inequalities: Theory of Majorization and Its Applications. Academic Press, New York (1979)
Moulin, H.: Axioms of Cooperative Decision Making. Cambridge Univ. Press, New York (1988)
Nash, J.F.: The bargaining problem. Econometrica 18, 155–162 (1950)
Ogryczak, W.: On the Distribution Approach to Location Problems. Comp. Indust. Engg. 37, 595–612 (1999)
Ogryczak, W.: Inequality measures and equitable approaches to location problems. Eur. J. Opnl. Res. 122, 374–391 (2000)
Ogryczak, W.: Comments on properties of the minimax solutions in goal programming. Eur. J. Opnl. Res. 132, 17–21 (2001)
Ogryczak, W.: On principles of fair resource allocation for importance weighted agents. In: Proc. of SOCINFO 2009, Warsaw, pp. 57–62 (2009)
Ogryczak, W., Ruszczyński, A.: Dual stochastic dominance and related mean-risk models. SIAM J. Optimization 13, 60–78 (2002)
Ogryczak, W., Śliwiński, T.: On equitable approaches to resource allocation problems: the conditional minimax solution. J. Telecom. Info. Tech. 3(02), 40–48 (2002)
Ogryczak, W., Śliwiński, T.: On direct methods for lexicographic min-max optimization. In: Gavrilova, M.L., Gervasi, O., Kumar, V., Tan, C.J.K., Taniar, D., Laganá, A., Mun, Y., Choo, H. (eds.) ICCSA 2006. LNCS, vol. 3982, pp. 774–783. Springer, Heidelberg (2006)
Ogryczak, W., Wierzbicki, A.: On multi-criteria approaches to bandwidth allocation. Control and Cybernetics 33, 427–448 (2004)
Ogryczak, W., Wierzbicki, A., Milewski, M.: A multi-criteria approach to fair and efficient bandwidth allocation. OMEGA 36, 451–463 (2008)
Pigou, A.C.: Wealth and Welfare. Macmillan, London (1912)
Pióro, M., Medhi, D.: Routing, Flow and Capacity Design in Communication and Computer Networks. Morgan Kaufmann, San Francisco (2004)
Rawls, J.: Justice as fairness. Philosophical Review LXVII, 164–194 (1958)
Rawls, J.: The Theory of Justice. Harvard University Press, Cambridge (1971)
Rothschild, M., Stiglitz, J.E.: Some further results in the measurement of inequality. J. Econ. Theory 6, 188–204 (1973)
Rzadca, K., Trystram, D., Wierzbicki, A.: Fair Game-Theoretic Resource Management in Dedicated Grids. In: CCGRID 2007, pp. 343–350 (2007)
Sen, A.: On Economic Inequality. Clarendon Press, Oxford (1973)
Steinhaus, H.: Sur la division pragmatique. Econometrica 17, 315–319 (1949)
Young, H.P.: Equity in Theory and Practice. Princeton Univ. Press, Princeton (1994)
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Ogryczak, W. (2010). Bicriteria Models for Fair and Efficient Resource Allocation. In: Bolc, L., Makowski, M., Wierzbicki, A. (eds) Social Informatics. SocInfo 2010. Lecture Notes in Computer Science, vol 6430. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16567-2_11
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