6th International ICST Symposium on Modeling and Optimization

Research Article

Battery-state dependent power control as a dynamic game

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  • @INPROCEEDINGS{10.4108/ICST.WIOPT2008.3233,
        author={Ishai  Menache and Eitan  Altman},
        title={Battery-state dependent power control as a dynamic game},
        proceedings={6th International ICST Symposium on Modeling and Optimization},
        keywords={Battery lifetime Dynamic power control Max-min fairness Nash equilibrium Schur convexity and Majorization},
  • Ishai Menache
    Eitan Altman
    Year: 2008
    Battery-state dependent power control as a dynamic game
    DOI: 10.4108/ICST.WIOPT2008.3233
Ishai Menache1, Eitan Altman2
  • 1: Faculty of Electrical Engineering, Technion, Haifa 32000, Israel.
  • 2: INRIA, Sophia-Antipolis, 2004 Route des Lucioles, 06902 Sophia-Antipolis Cedex, France.


Consider an uplink cellular network shared by a finite number of mobile users with limited batteries. Whenever the battery drains out, the user pays a fixed price to recharge the battery. Users, assumed to have always traffic to send, control their transmission power in a noncooperative way. The novelty of our model is in considering the dynamic game in which the transmission power of a player may depend on the amount of energy left in its battery. We consider various models and various types of constraints and derive for each one the structure of the equilibrium. A particular interesting structure is obtained when there are constraints on the maximum transmission power which become tighter as the battery drains out. Using Schur convexity and majorization, we identify an equilibrium where each mobile distributes the power of each battery along the batterypsilas lifetime in a way equivalent to a max-min assignment.