March 2011 Optimal paths on the space-time SINR random graph
François Baccelli, Bartłomiej Błaszczyszyn, Mir-Omid Haji-Mirsadeghi
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Adv. in Appl. Probab. 43(1): 131-150 (March 2011). DOI: 10.1239/aap/1300198516


We analyze a class of signal-to-interference-and-noise-ratio (SINR) random graphs. These random graphs arise in the modeling packet transmissions in wireless networks. In contrast to previous studies on SINR graphs, we consider both a space and a time dimension. The spatial aspect originates from the random locations of the network nodes in the Euclidean plane. The time aspect stems from the random transmission policy followed by each network node and from the time variations of the wireless channel characteristics. The combination of these random space and time aspects leads to fluctuations of the SINR experienced by the wireless channels, which in turn determine the progression of packets in space and time in such a network. In this paper we study optimal paths in such wireless networks in terms of first passage percolation on this random graph. We establish both `positive' and `negative' results on the associated time constant. The latter determines the asymptotics of the minimum delay required by a packet to progress from a source node to a destination node when the Euclidean distance between the two tends to ∞. The main negative result states that this time constant is infinite on the random graph associated with a Poisson point process under natural assumptions on the wireless channels. The main positive result states that, when adding a periodic node infrastructure of arbitrarily small intensity to the Poisson point process, the time constant is positive and finite.


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François Baccelli. Bartłomiej Błaszczyszyn. Mir-Omid Haji-Mirsadeghi. "Optimal paths on the space-time SINR random graph." Adv. in Appl. Probab. 43 (1) 131 - 150, March 2011.


Published: March 2011
First available in Project Euclid: 15 March 2011

zbMATH: 1223.60011
MathSciNet: MR2761151
Digital Object Identifier: 10.1239/aap/1300198516

Primary: 05C80 , 60D05
Secondary: 60G55 , 90C27

Keywords: first passage percolation , Poisson point process , random graph , shot noise process , SINR

Rights: Copyright © 2011 Applied Probability Trust


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Vol.43 • No. 1 • March 2011
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