Advances in Applied Probability

Optimal paths on the space-time SINR random graph

François Baccelli, Bartłomiej Błaszczyszyn, and Mir-Omid Haji-Mirsadeghi

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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.

Article information

Adv. in Appl. Probab., Volume 43, Number 1 (2011), 131-150.

First available in Project Euclid: 15 March 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60D05: Geometric probability and stochastic geometry [See also 52A22, 53C65] 05C80: Random graphs [See also 60B20]
Secondary: 90C27: Combinatorial optimization 60G55: Point processes

Poisson point process random graph first passage percolation shot noise process SINR


Baccelli, François; Błaszczyszyn, Bartłomiej; Haji-Mirsadeghi, Mir-Omid. Optimal paths on the space-time SINR random graph. Adv. in Appl. Probab. 43 (2011), no. 1, 131--150. doi:10.1239/aap/1300198516.

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