WIAS Preprint No. 1811, (2013)

Connection times in large ad hoc mobile networks


  • Döring, Hanna
  • Faraud, Gabriel
  • König, Wolfgang
    ORCID: 0000-0002-7673-4364

2010 Mathematics Subject Classification

  • 60K35 82C21 60J20 60F10


  • ad-hoc networks, connectivity, random waypoint model, dynamic continuum percolation, large deviations




We study connectivity properties in a probabilistic model for a large mobile ad-hoc network. We consider a large number of participants of the system moving randomly, independently and identically distributed in a large domain, with a space-dependent population density of finite, positive order and with a fixed time horizon. Messages are instantly transmitted according to a relay principle, i.e., they are iteratedly forwarded from participant to participant over distances $leq 2R$, with $2R$ the communication radius, until they reach the recipient. In mathematical terms, this is a dynamic continuum percolation model. We consider the connection time of two sample participants, the amount of time over which these two are connected with each other. In the above thermodynamic limit, we find that the connectivity induced by the system can be described in terms of the counterplay of a local, random, and a global, deterministic mechanism, and we give a formula for the limiting behaviour. A prime example of the movement schemes that we consider is the well-known random waypoint model (RWP). Here we describe the decay rate, in the limit of large time horizons, of the probability that the portion of the connection time is less than the expectation.

Appeared in

  • Bernoulli, 22 (2016) pp. 2143--2176.

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