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Impact of human mobility on the design of opportunistic forwarding algorithms
 In Proc. IEEE Infocom
, 2006
"... Abstract — Studying transfer opportunities between wireless devices carried by humans, we observe that the distribution of the intercontact time, that is the time gap separating two contacts of the same pair of devices, exhibits a heavy tail such as one of a power law, over a large range of value. ..."
Abstract

Cited by 153 (9 self)
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Abstract — Studying transfer opportunities between wireless devices carried by humans, we observe that the distribution of the intercontact time, that is the time gap separating two contacts of the same pair of devices, exhibits a heavy tail such as one of a power law, over a large range of value. This observation is confirmed on six distinct experimental data sets. It is at odds with the exponential decay implied by most mobility models. In this paper, we study how this new characteristic of human mobility impacts a class of previously proposed forwarding algorithms. We use a simplified model based on the renewal theory to study how the parameters of the distribution impact the delay performance of these algorithms. We make recommendation for the design of well founded opportunistic forwarding algorithms, in the context of human carried devices. I.
Impact of human mobility on opportunistic forwarding algorithms
 IEEE Trans. Mob. Comp
, 2007
"... Abstract — We study data transfer opportunities between wireless devices carried by humans. We observe that the distribution of the intercontact time (the time gap separating two contacts between the same pair of devices) may be well approximated by a power law over the range [10 minutes; 1 day]. T ..."
Abstract

Cited by 122 (19 self)
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Abstract — We study data transfer opportunities between wireless devices carried by humans. We observe that the distribution of the intercontact time (the time gap separating two contacts between the same pair of devices) may be well approximated by a power law over the range [10 minutes; 1 day]. This observation is confirmed using eight distinct experimental data sets. It is at odds with the exponential decay implied by the most commonly used mobility models. In this paper, we study how this newly uncovered characteristic of human mobility impacts one class of forwarding algorithms previously proposed. We use a simplified model based on the renewal theory to study how the parameters of the distribution impact the performance in terms of the delivery delay of these algorithms. We make recommendations for the design of well founded opportunistic forwarding algorithms, in the context of human carried devices. I.
Navigation on a Poisson point process
 RR, n o 5790, INRIA, Rocquencourt
, 2006
"... On a locally finite point set, a navigation defines a path through the point set from a point to another. The set of paths leading to a given point defines a tree, the navigation tree. In this article, we analyze the properties of the navigation tree when the point set is a Poisson point process on ..."
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Cited by 3 (0 self)
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On a locally finite point set, a navigation defines a path through the point set from a point to another. The set of paths leading to a given point defines a tree, the navigation tree. In this article, we analyze the properties of the navigation tree when the point set is a Poisson point process on R d. We examine the local weak convergence of the navigation tree, the asymptotic average of a functional along a path, the shape of the navigation tree and its topological ends. We illustrate our work in the small world graphs where new results are established. AMS Classification: Primary 60D05, 05C05; secondary 90C27, 60G55.
Applied Probability Trust (19 January 2006) THE DEAD LEAVES MODEL: A GENERAL TESSELLATION MODELING OCCLUSION
"... In this article, we study a particular example of general random tessellation, the dead leaves model. This model, first studied by the Mathematical Morphology school, is defined as a sequential superimposition of random closed sets, and provides the natural tool to study the occlusion phenomenon, es ..."
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In this article, we study a particular example of general random tessellation, the dead leaves model. This model, first studied by the Mathematical Morphology school, is defined as a sequential superimposition of random closed sets, and provides the natural tool to study the occlusion phenomenon, essential ingredient in the formation of visual images. We generalize results from G. Matheron, and in particular we compute the probability for n compact sets to be included in visible parts. This result characterizes the distribution of the boundary of the dead leaves tessellation.