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Selfish users in energy constrained ALOHA systems with power capture

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Abstract

We consider a slotted ALOHA setting where backlogged, energy-constrained users selfishly select the probability with which they transmit packets. Packets are successfully received, even in case of collision, if the signal to interference plus noise ratio at the access point exceeds some threshold (power capture). The user problem of finding appropriate transmission probabilities is formulated as a static non-cooperative game and the performance limits for stationary and mobile scenarios are determined. The equilibrium analyses show that for stationary scenarios, users with high pathgains share the channel fairly while others never transmit. In the mobile case users utilize a binary strategy where they try to monopolize the channel when their pathgain exceeds some threshold that depends on system parameters (number of users, transmission costs, etc.). Otherwise they shut their transmitters off. Compared to traditional nondiscriminatory distributed multiaccess protocols the operating points achieved by selfish users generally increase sum-utility although this comes at the expense of larger user performance variations.

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Notes

  1. This means that users would need to meet before the game is played so as to coordinate their actions in order to successfully reach this class of Nash equilibria.

  2. From Fig. 2 it is evident that this situation is likely to occur when the propagation exponent α is low (and the received signal strength from different nodes do not differ by much at the access point) and/or when the signal to interference requirement is high.

  3. For example consider the Nash equilibrium where one of the users monopolizes the channel. This equilibrium would only be achieved if one user attempts to monopolize the channel while all others select not to transmit. Reaching such an equilibrium in a single-shot game would require that users have a “signalling device” that allows them to “coordinate” their actions (cf. correlated equilibria).

  4. Notice that the probability with which a randomly chosen user transmits a packet in PTG-I is \(\hbox{Pr}\left(g\geq F_g^{-1}\left(E^{1/N-1)}\right)\right)=1-\hbox{Pr}\left(g\leq F_g^{-1}\left(E^{1/N-1)}\right)\right)=1-F_g\left(F_g^{-1}\left(E^{1/(N-1)}\right)\right)=1-E^{1/(N-1)}\). This is the same probability with which a user transmits when capture prospects are not taken into consideration.

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  1. Wireless@KTH, Royal Institute of Technology, Electrum 418, SE-164 40, Kista, Sweden

    Johan Hultell, Ömer Ileri & Jens Zander

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  1. Johan Hultell
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  2. Ömer Ileri
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  3. Jens Zander
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Correspondence to Ömer Ileri.

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Hultell, J., Ileri, Ö. & Zander, J. Selfish users in energy constrained ALOHA systems with power capture. Wireless Netw 17, 199–212 (2011). https://doi.org/10.1007/s11276-010-0273-z

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