The value of shapley as a strategy for Resource Optimization on Power Line Communication (PLC)

Main Article Content

Juan C Vesga http://orcid.org/0000-0003-3764-7265
Gerardo Granados Acuña http://orcid.org/0000-0003-1787-0734
Javier E Sierra Carrillo http://orcid.org/0000-0001-9111-326X

Keywords

game theory, HPAV, OFDM, Power Line Communication, Shapley

Abstract

This article proposes the use of cooperative game theory, supported by the use of bankruptcy game of the and the Shapley value, as a strategy to optimize the allocation of resources in each node, according to service demand, the number of stations and the conditions of the PLC channel. The paper proposes a scenario under saturated traffic conditions, in order to assess the degree of optimization that the value of Shapley can perform in front of traffic and channel conditions clearly established. It is concluded that the use of cooperative game theory, supported on the Shapley value, can be considered as an excellent alternative when making resource optimization processes in a PLC channel y with the possibility to be implemented in economic embedded systems, because it does not require complex operations for its estimation.

MSC: 91A12,90C26 | PACS: 02.50.Le, 84.40.Ua, 02.50.Le

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References

[1] K. y. Y. L. y. G. S. Latchman Haniph y Srinivas, Homeplug AV and IEEE 1901: A Handbook for PLC Designers and Users, 1st ed. New Jersey, USA: Wiley-IEEE Press, 2013.

[2] N. Anatory, J. y Theethayi, Broadband Power-Line Communication Systems: Theory and Applications., 1st ed. Southampton, England: WIT Press, 2010.

[3] J. L. y. T. E. C. Pérez J y Jimeno, Teoría de juegos, 1st ed. Madrid, España: Pearson-Prentice Hall, 2003.

[4] D. Ramírez R., “Cooperación en la cadena de suministro de la energía eléctrica en Colombia,” Tesis de Maestría, Universidad del Norte, 2008.

[5] P. Peleg B y Sudhölter, Introduction to the theory of cooperative games. Springer, 2007. [Online]. Available: http://dx.doi.org/10.1007/978-3-540-72945-7

[6] B. O’Neill, “A problem of rights arbitration from the Talmud,” Mathematical Social Sciences, vol. 2, no. 4, pp. 345–371, 1982. [Online]. Available: http://dx.doi.org/10.1016/0165-4896(82)90029-4

[7] H. Moulin, “Axiomatic Cost and Surplus-Sharing,” in The Handbook of Social Choice and Welfare. Elsevier B.V., 2001, ch. 6, pp. 289–357. [Online]. Available: http://dx.doi.org/10.1016/S1574-0110(02)80010-8

[8] M. Aumann Robert J y Maschler, “Game theoretic analysis of a bankruptcy problem from the Talmud,” Journal of Economic Theory, vol. 36, no. 2, pp. 195–213, 1985. [Online]. Available: http://dx.doi.org/10.1016/0022-0531(85)90102-4

[9] I. Curiel, Cooperative game theory and applications: cooperative games arising from combinatorial optimization problems. Dordrecht: Kluwer Academic Publishers, 1997.

[10] M. y. V. A. Herrero C y Maschler, “Individual rights and collective responsibility: the rights egalitarian solution,” Mathematical Social Sciences, vol. 37, no. 1, pp. 59–77, 1999.

[11] W. Thomson, “Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: a survey,” 2003. [Online]. Available: http: //dx.doi.org/10.1016/S0165-4896(02)00070-7

[12] M. L. C. Rodríguez, Contribuciones a la teoría del valor en juegos en forma estratégica y en problemas de bancarrota, S. d. P. e. I. Científico, Ed. Universidad Santiago de Compostela, 2005.

[13] J. R. F. García, “Complejidad y algoritmos en juegos cooperativos,” Tesis Doctoral, Universidad de Sevilla, 2000. 192, 209 [14] L. S. Shapley, “A value for n-persons games in Contributions to the Theory of Games II,” Annals of Mathematics Studies, no. 28, pp. 307–317, 1953.

[15] A. Magaña, “Formación de coaliciones en los juegos cooperativos y juegos con múltiples alternativas,” Tesis Doctoral, Universidad Politécnica de Cataluña, 1996. [Online]. Available: http://www.tdx.cat/handle/10803/6700

[16] D. B. Gillies, “Some theorems on n-person games,” Tesis Doctoral, Princeton University, 1953.

[17] L. S. Shapley, “On balanced sets and cores,” Naval research logistics quarterly, vol. 14, no. 4, pp. 453–460, 1967. [Online]. Available: http://dx.doi.org/10.1002/nav.3800140404

[18] F. Canete, “User guide for PLC channel generator v. 2,” 2011. [Online]. Available: http://www.plc.uma.es/channel_generator/User_guide_v2.pdf

[19] J. A. Cortés, “Modulation and Multiple Access Techniques for Indoor Broadband Power-Line Communications,” Tesis Doctoral, Universidad de Málaga, 2007. [Online]. Available: http://www.biblioteca.uma.es/bbldoc/tesisuma/17114500.pdf

[20] P. Berens, “CircStat: a MATLAB toolbox for circular statistics,” Journal of Statistics Software, vol. 31, no. 10, pp. 1–21, 2009. [Online]. Available: http://www.jstatsoft.org/v31/i10/paper

[21] R. H. y. M. S. L. Walpole RE y Myers, Probabilidad y estadística para ingenieros. Mexico D.F., Mexico: Pearson-Prentice Hall, 2007.

[22] Minitab Inc, “Pareto chart basics,” 2015. [Online]. Available: http://support.minitab.com/en-us/minitab/17/topic-library/
quality-tools/quality-tools/pareto-chart-basics/