We analyze a model of relay-augmented cellular wireless networks. The network users, who move according to a general mobility model based on a Poisson point process of continuous trajectories in a bounded domain, try to communicate with a base station located at the origin. Messages can be sent either directly or indirectly by relaying over a second user. We show that in a scenario of an increasing number of users, the probability that an atypically high number of users experiences bad quality of service over a certain amount of time decays at an exponential speed. This speed is characterized via a constrained entropy minimization problem. Further, we provide simulation results indicating that solutions of this problem are potentially nonunique due to symmetry breaking. Also, two general sources for bad quality of service can be detected, which we refer to as isolation and screening.
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Aizenman, M., Chayes, J.T., Chayes, L., Fröhlich, J., Russo, L.: On a sharp transition from area law to perimeter law in a system of random surfaces. Comm. Math. Phys. 92(1), 19–69 (1983)
Baccelli, F., Błaszczyszyn, B.: Stochastic Geometry and Wireless Networks: Vol. 1: Theory. Now Publishers Inc (2009)
Baccelli, F., Błaszczyszyn, B.: Stochastic Geometry and Wireless Networks: Vol. 2: Application. Now Publishers Inc (2009)
Bletsas, A., Khisti, A., Reed, D.P., Lippman, A.: A simple cooperative diversity method based on network path selection. IEEE J. Sel. Areas Commun. 24(3), 659–672 (2006)
Bletsas, A., Shin, H., Win, M.Z.: Cooperative communications with outage-optimal opportunistic relaying. IEEE Trans. Wirel. Commun. 6(9), 3450–3460 (2007)
Dembo, A., Zeitouni, O.: Large Deviations Techniques and Applications, 2nd edn. Springer, New York (1998)
Döring, H., Faraud, G., König, W.: Connection times in large ad-hoc mobile networks. Bernoulli 22(4), 2143–2176 (2016)
Dudley, R.M.: Real Analysis and Probability. Cambridge University Press, Cambridge (2002)
Federer, H.: Geometric Measure Theory. Springer, New York (1969)
Ganesh, A.J., Torrisi, G.L.: Large deviations of the interference in a wireless communication model. IEEE Trans. Inf. Theory 54(8), 3505–3517 (2008)
Gelfand, I.M., Fomin, S.V.: Calculus of Variations. Prentice-Hall, Englewood Cliffs (1963)
Kingman, J.F.C.: Poisson Processes. Oxford University Press, New York (1993)
Si, J., Li, Z., Liu, Z.: Outage probability of opportunistic relaying in Rayleigh fading channels with multiple interferers. IEEE Signal Process. Lett. 17(5), 445–448 (2010)
Torrisi, G.L., Leonardi, E.: Simulating the tail of the interference in a Poisson network model. IEEE Trans. Inf. Theory 59(3), 1773–1787 (2013)
The authors thank the anonymous referee for the comments and suggestions that helped to substantially improve the quality of the article. The authors thank W. König for interesting discussions and comments.
This research was supported by the Leibniz program Probabilistic Methods for Mobile Ad-Hoc Networks. This research publication was funded by LMU Munich’s Institutional Strategy LMUexcellent within the framework of the German Excellence Initiative.
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Hirsch, C., Jahnel, B., Keeler, P. et al. Large deviations in relay-augmented wireless networks. Queueing Syst 88, 349–387 (2018). https://doi.org/10.1007/s11134-017-9555-9
- Large deviations
- Wireless network
- Signal-to-interference ratio
- Symmetry breaking
Mathematics Subject Classification
- Primary 60F10
- Secondary 60K35