Large deviations for discrete and continuous percolation

Penrose, Mathew D.; Pisztora, Ágoston

doi:10.2307/1427912

Cited by 76 publications

(54 citation statements)

References 14 publications

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“…The connectivity of ad hoc networks has been extensively studied using percolation theory (Penrose and Pisztora, 1996;Santi and Blough, 2003), connected components (Dousse et al, 2006), temporal clustering coefficients (Tang et al, 2009) as well as other metrics (OvalleMartínez et al, 2005;Scellato et al, 2011).…”

Section: Connectivity Modellingmentioning

confidence: 99%

Worst-case latency of broadcast in intermittently connected networks

Asplund

Nadjm‐Tehrani

2012

IJAHUC

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Worst-case latency is an important characteristic of information dissemination protocols. However, in sparse mobile ad hoc networks where end-to-end connectivity cannot be achieved and store-carry-forward algorithms are needed, such worst-case analyses have not been possible to perform on real mobility traces due to lack of suitable models. We propose a new metric called delay expansion that reflects connectivity and reachability properties of intermittently connected networks. Using the delay expansion, we show how bounds on worst-case latency can be derived for a general class of broadcast protocols and a wide range of real mobility patterns. The paper includes theoretical results that show how worst-case latency can be related with delay expansion for a given mobility scenario, as well as simulations to validate the theoretical model.

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Section: Connectivity Modellingmentioning

confidence: 99%

Worst-case latency of broadcast in intermittently connected networks

Asplund

Nadjm‐Tehrani

2012

IJAHUC

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“…Some analysis of the two aspects are performed through simulations: as examples, Stuedi et al (2005) related to ad hoc networks, and Buratti & Verdone (2006), to WSN. Many papers based on random graph theory, continuum percolation and geometric probability Bollobàs (2001); Meester & Roy (1996);Penrose (1993;1999); Penrose & Pistztora (1996) addressed connectivity issues of networks. In particular, wireless ad hoc and sensor networks have recently attracted a growing attention Bettstetter (2002); Bettstetter & Zangl (2002);Pishro-Nik et al (2004); Salbaroli & Zanella (2006); Santi & Blough (2003); Vincze et al (2007).…”

Section: Related Workmentioning

confidence: 99%

Throughput Analysis of Wireless Sensor Networks via Evaluation of Connectivity and MAC Performance

Fabbri¹,

Buratti²

2011

Emerging Communications for Wireless Sensor Networks

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“…Related problems to graph theoretic results in this paper have been studied in the context of random graph theory [5], continuum percolation and geometric probability [6][7][8][9][10] and the study of wireless network graphs [11][12][13][14][15][16]. In random graph theory, the model G(n, p) is extensively studied, in which edges appear in a graph of n vertices with probability p independently of each other.…”

Section: Related Workmentioning

confidence: 99%

Connectivity properties of large-scale sensor networks

2009

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In wireless sensor networks, both nodes and links are prone to failures. In this paper we study connectivity properties of large-scale wireless sensor networks and discuss their implicit effect on routing algorithms and network reliability. We assume a network model of n sensors which are distributed randomly over a field based on a given distribution function. The sensors may be unreliable with a probability distribution, which possibly depends on n and the location of sensors. Two active sensor nodes are connected with probability p e (n) if they are within communication range of each other. We prove a general result relating unreliable sensor networks to reliable networks. We investigate different graph theoretic properties of sensor networks such as k-connectivity and the existence of the giant component. While connectivity (i.e. k = 1) insures that all nodes can communicate with each other, k-connectivity for k [ 1 is required for multipath routing. We analyze the average shortest path of the k paths from a node in the sensing field back to a base station. It is found that the lengths of these multiple paths in a k-connected network are all close to the shortest path.These results are shown through graph theoretical derivations and are also verified through simulations.

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Large deviations for discrete and continuous percolation

Cited by 76 publications

References 14 publications

Worst-case latency of broadcast in intermittently connected networks

Worst-case latency of broadcast in intermittently connected networks

Throughput Analysis of Wireless Sensor Networks via Evaluation of Connectivity and MAC Performance

Connectivity properties of large-scale sensor networks

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