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Cost-Sharing Games in Real-Time Scheduling Systems

  • Tami TamirEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11316)

Abstract

We apply non-cooperative game theory to analyze the server’s activation cost in real-time scheduling systems. An instance of the game consists of a single server and a set of unit-length jobs. Every job needs to be processed along a specified time interval, defined by its release-time and due-date. Jobs may also have variable weights, which specify the amount of resource they require. We assume that jobs are controlled by selfish agents who act to minimize their own cost, rather than to optimize any global objective.

The jobs processed in a specific time-slot cover the server’s activation cost in this slot, with the cost being shared proportionally to the jobs’ weights. Known result on cost-sharing games do not exploit the special interval-structure of the strategy space in our game, and are therefore not tight. We present a complete analysis of equilibrium existence, computation, and inefficiency in real-time scheduling cost-sharing games. Our tight analysis covers various classes of instances, and distinguishes between unilateral and coordinated deviations.

References

  1. 1.
    Ackermann, H., Röglin, H., Vöcking, B.: On the impact of combinatorial structure on congestion games. J. ACM 55(6), 25:1–25:22 (2008)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Adany, R., Tamir, T.: Algorithms for battery utilization in electric vehicles. Appl. Artif. Intell. 28(3), 272–291 (2014)CrossRefGoogle Scholar
  3. 3.
    Albers, S.: On the value of coordination in network design. SIAM J. Comput. 38(6), 2273–2302 (2009)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Albers, S.: Energy-efficient algorithms. Commun. ACM 53(5), 86–96 (2010)CrossRefGoogle Scholar
  5. 5.
    Andelman, N., Feldman, M., Mansour, Y.: Strong price of anarchy. Games Econ. Behav. 65(2), 289–317 (2009)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Anshelevich, E., Dasgupta, A., Kleinberg, J., Tardos, E., Wexler, T., Roughgarden, T.: The price of stability for network design with fair cost allocation. SIAM J. Comput. 38(4), 1602–1623 (2008)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Aumann, R.: Acceptable points in general cooperative n-person games. In: Contributions to the Theory of Games IV, vol. 4 (1959)Google Scholar
  8. 8.
    Avni, G., Kupferman, O., Tamir, T.: Network-formation games with regular objectives. J. Inf. Comput. 251, 165–178 (2016)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Avni, G., Tamir, T.: Cost-sharing scheduling games on restricted unrelated machines. Theor. Comput. Sci. 646, 26–39 (2016)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Baptiste, P.: Batching identical jobs. Math. Methods Oper. Res. 52(3), 355–367 (2000)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Bar-Noy, A., Guha, S., Naor, J., Schieber, B.: Approximating the throughput of multiple machines in real-time scheduling. SIAM J. Comput. 31(2), 331–352 (2001)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Caragiannis, I., Flammini, M., Kaklamanis, C., Kanellopoulos, P., Moscardelli, L.: Tight bounds for selfish and greedy load balancing. Algorithmica 61(3), 606–637 (2011)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Chang, J., Erlebach, T., Gailis, R., Khuller, S.: Broadcast scheduling: algorithms and complexity. ACM Trans. Algorithms 7(4), 47:1–47:14 (2011).  https://doi.org/10.1145/2000807.2000815. Article No. 47MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Chang, J., Gabow, H.N., Khuller, S.: A model for minimizing active processor time. Algorithmica 70(3), 368–405 (2014)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Chekuri, C., Chuzhoy, J., Lewin-Eytan, L., Naor, J., Orda, A.: Non-cooperative multicast and facility location games. IEEE J. Sel. Areas Commun. 25(6), 1193–1206 (2007)CrossRefGoogle Scholar
  16. 16.
    Chen, H., Roughgarden, T.: Network design with weighted players. Theory Comput. Syst. 45(2), 302–324 (2009)MathSciNetCrossRefGoogle Scholar
  17. 17.
    de Jong, J., Klimm, M., Uetz, M.: Efficiency of equilibria in uniform matroid congestion games. In: Gairing, M., Savani, R. (eds.) SAGT 2016. LNCS, vol. 9928, pp. 105–116. Springer, Heidelberg (2016).  https://doi.org/10.1007/978-3-662-53354-3_9CrossRefGoogle Scholar
  18. 18.
    von Falkenhausen, P., Harks, T.: Optimal cost sharing for resource selection games. Math. Oper. Res. 38(1), 184–208 (2013)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Flammini, M., Monaco, G., Moscardelli, L., Shachnai, H., Shalom, M., Tamir, T., Zaks, S.: Minimizing total busy time in parallel scheduling with application to optical networks. Theor. Comput. Sci. 411(40–42), 3553–3562 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Fotakis, D., Kontogiannis, S., Spirakis, P.: Selfish unsplittable flows. Theor. Comput. Sci. 348(2–3), 226–239 (2005)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Gairing, M., Schoppmann, F.: Total latency in singleton congestion games. In: Deng, X., Graham, F.C. (eds.) WINE 2007. LNCS, vol. 4858, pp. 381–387. Springer, Heidelberg (2007).  https://doi.org/10.1007/978-3-540-77105-0_42CrossRefGoogle Scholar
  22. 22.
    Gkatzelis, V., Kollias, K., Roughgarden, T.: Optimal cost-sharing in general resource selection games. J. Oper. Res. 64(6), 1230–1238 (2016)MathSciNetCrossRefGoogle Scholar
  23. 23.
    Harks, T., Klimm, M.: On the existence of pure nash equilibria in weighted congestion games. Math. Oper. Res. 37(3), 419–436 (2012)MathSciNetCrossRefGoogle Scholar
  24. 24.
    Harks, T., Miller, K.: The worst-case efficiency of cost sharing methods in resource allocation games. Oper. Res. 59(6), 1491–1503 (2011)MathSciNetCrossRefGoogle Scholar
  25. 25.
    Ieong, S., McGrew, R., Nudelman, E., Shoham, Y., Sun, Q.: Fast and compact: a simple class of congestion games. In: Proceedings of the 20th AAAI, pp. 489–494 (2005)Google Scholar
  26. 26.
    Irani, S., Pruhs, K.R.: Algorithmic problems in power management. SIGACT News 36(2), 63–76 (2005)CrossRefGoogle Scholar
  27. 27.
    Jensen, J.L.W.V.: Sur les fonctions convexes et les ingalits entre les valeurs moyennes. Acta Math. 30, 175–193 (1906)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Khandekar, R., Schieber, B., Shachnai, H., Tamir, T.: Real-time scheduling to minimize machine busy time. J. Sched. 18(6), 561–573 (2015)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Koutsoupias, E., Papadimitriou, C.: Worst-case equilibria. Comput. Sci. Rev. 3(2), 65–69 (2009)CrossRefGoogle Scholar
  30. 30.
    Leung, J., Kelly, L., Anderson, J.H.: Handbook of Scheduling: Algorithms, Models, and Performance Analysis. CRC Press Inc., Boca Raton (2004)Google Scholar
  31. 31.
    Milchtaich, I.: Congestion games with player-specific payoff functions. Games Econ. Behav. 13(1), 111–124 (1996)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Rosenthal, R.W.: A class of games possessing pure-strategy nash equilibria. Int. J. Game Theory 2, 65–67 (1973)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Syrgkanis, V.: The complexity of equilibria in cost sharing games. In: Saberi, A. (ed.) WINE 2010. LNCS, vol. 6484, pp. 366–377. Springer, Heidelberg (2010).  https://doi.org/10.1007/978-3-642-17572-5_30CrossRefGoogle Scholar
  34. 34.
    Vöcking, B.: Selfish load balancing. In: Algorithmic Game Theory. Cambridge University Press (2007)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.School of Computer ScienceThe Interdisciplinary Center (IDC)HerzliyaIsrael

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