Queueing Systems

, Volume 88, Issue 3–4, pp 349–387 | Cite as

Large deviations in relay-augmented wireless networks

  • Christian HirschEmail author
  • Benedikt Jahnel
  • Paul Keeler
  • Robert Patterson


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.


Large deviations Relay Wireless network Signal-to-interference ratio Symmetry breaking 

Mathematics Subject Classification

Primary 60F10 Secondary 60K35 



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.


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Copyright information

© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  • Christian Hirsch
    • 1
    Email author
  • Benedikt Jahnel
    • 2
  • Paul Keeler
    • 2
  • Robert Patterson
    • 2
  1. 1.Mathematisches InstitutLudwig-Maximilians-Universität MünchenMunichGermany
  2. 2.Weierstrass Institute BerlinBerlinGermany

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