Abstract
In this article, a new game theoretical method is proposed to model packet forwarding in relay networks. A simple case of relay network that consists of a source, a relay and a destination node communicating on a common channel is considered. A stationary Markovian game model is utilized to optimize the system performance in terms of throughput, delay and power consumption cost. Both cooperative and non-cooperative solutions are provided for this model. Best strategy set taken by players as well as system performance is studied for different system parameters. Also, the proposed method is extended to model a more general case of Ad-hoc networks considering different packet error rates in case of collision occurrence that improves the system performance further.
Simulation results show that performance of the non-cooperative solution, in which players do not require to know each other’s selected strategy, asymptotically approaches the cooperative system performance. Hence, the proposed model with non-cooperative solution is an appropriate method to apply in practical Ad-hoc networks.
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References
Han, B., & Lee, S. (2007). Efficient packet error rate estimation in wireless networks. In 3rd IEEE international conference on testbeds and research infrastructures for the development of networks and communities (TridentCom 2007) (pp. 1–9)
Elliot, E. O. (1963). Estimates of error rates for codes on burst-noise channels. Bell Systems Technical Journal, 42, 1977–1997.
Laneman, J., Tse, D., & Wornell, G. (2004). Cooperative diversity in wireless networks: efficient protocols and outage behavior. IEEE Transactions on Information Theory, 50(12), 3062–3080.
Srivastava, V., Neel, J., MacKenzie, A. B., Menon, R., DaSilva, L. A., Hicks, J. E., Reed, J. H., & Gilles, R. P. (2005). Using game theory to analyze wireless ad hoc networks. IEEE Communications Surveys and Tutorials, 7(5), 46–56.
MacKenzie, A. B., & DaSilva, L. A. Game theory for wireless engineers. Morgan and Claypool Publishers.
Agarwal, S., Krishnamurthy, S. V., Katz, R. H., & Dao, S. K. (2001). Distributed Power Control in Ad-hoc Wireless Networks. In IEEE international symposium on personal, indoor and mobile radio communications (PIMRC) (pp. 59–66).
Felegyhazi, M., Hubaux, J.-P., & Buttyan, L. (2006). Nash equilibria of packet forwarding strategies in wireless ad hoc networks. IEEE Transactions on Mobile Computing, 5(5), 463–476.
Yan, L., Hailes, S., & Capra, L. (2008). Analysis of packet relaying models and incentive strategies in wireless ad hoc networks with game theory. In 22nd international conference on advanced information networking and applications (pp. 1062–1069).
Feng, D., Zhu, Y., & Luo, X. (2009). Cooperative incentive mechanism based on game theory in MANET. In 2009 international conference on networking and digital society (pp. 201–204).
Michiardi, P., & Molva, R. (2002). Core: a collaborative reputation mechanism to enforce node cooperation in mobile ad hoc networks. In Communication and multimedia security (pp. 107–121).
Felegyhazi, M., Buttyan, L., & Hubaux, J.-P. (2004). Equilibrium analysis of packet forwarding strategies in wireless ad hoc networks—the dynamic case. In 2nd workshop on modeling and optimization in mobile, ad hoc and wireless networks.
Refaei, M. T., Srivastava, V., DaSilva, L. A., & Eltoweissy, M. (2005). A reputation-based mechanism for isolating selfish nodes in ad hoc networks. In IEEE second annual international conference on mobile and ubiquitous systems: networking and services (MOBIQUITOUS 2005) (Vol. 7(5), pp. 3–11).
Han, Z., Pandana, C., & Liu, K. J. R. (2005). A self-learning repeated game framework for optimizing packet forwarding networks. In IEEE wireless communications and networking conference (Vol. 4, pp. 2131–2136).
Sagduyu, Y. E., & Ephremides, A. (2006). A game-theoretic look at simple relay channel. Journal of Wireless Networks, 12(5), 545–560.
Gau, R.-H. (2006). Performance analysis of slotted Aloha in interference-dominating wireless ad-hoc networks. IEEE Communications Letters, 10(5), 402–404.
Fudenberg, D., & Tirole, J. (1991). Game theory. Cambridge: MIT Press.
Osborne, M., & Rubinstein, A. (1994). A course in game theory. Cambridge: MIT Press.
Shapley, L. S. (1953). Stochastic games. Proceedings of the National Academy of Sciences, 39, 1095–1100.
Maskin, E., & Tirole, J. (2001). Markov perfect equilibrium: I. Observable actions. Journal of Economic Theory, 100(2), 191–219.
Nowak, A. S., & Szajowski, K. (1999). Nonzero-sum stochastic games. Annals of the International Society of Dynamic Games, 4, 297–342.
Choudhury, S., & Gibson, J. D. (2008). Throughput optimization for wireless LANs in the presence of packet error rate constraints. IEEE Communications Letters, 12(1), 11–13.
Bultan, A., Tazebay, M. V., & Akansu, A. N. (1988). A comparative performance study of excisers for various interference classes. In IEEE-SP international symposium on digital object identifier (pp. 381–384).
Sagduyu, Y. E., & Ephremides, A. (2003). Power control and rate adaptation as stochastic games for random access. In 42nd IEEE conference on decision and control (Vol. 4, pp. 4202–4207).
MacKenzie, A. B., & Wicker, S. B. (2001). Selfish users in Aloha: a game-theoretic approach. In IEEE vehicular technology conference (VTC2001) (Vol. 3, pp. 1354–1357).
Ghez, S., Verdu, S., & Schwartz, S. C. (1988). Stability properties of slotted aloha with multipacket reception capability. IEEE Transactions on Automatic Control, 33(7), 640–649.
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Afghah, F., Razi, A. & Abedi, A. Stochastic game theoretical model for packet forwarding in relay networks. Telecommun Syst 52, 1877–1893 (2013). https://doi.org/10.1007/s11235-011-9471-y
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DOI: https://doi.org/10.1007/s11235-011-9471-y