Percolation in the signal to interference ratio graph

Dousse, Olivier; Franceschetti, Massimo; Macris, Nicolas; Meester, Ronald; Thiran, Patrick

doi:10.1017/s0021900200001820

Cited by 42 publications

(91 citation statements)

References 3 publications

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“…It is then the shot-noise field of received powers that plays important role in determining the connectivity and the capacity of the network in a broad sense. The foundations of the theory of SINR coverage processes are quite recent (see [1,2,8,10]). In what follows, we shall study the impact of structure of the p.p.…”

Section: Interference In Wireless Communicationsmentioning

confidence: 99%

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Directionally convex ordering of random measures, shot noise fields, and some applications to wireless communications

Błaszczyszyn

Yogeshwaran

2009

Adv. Appl. Probab.

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Directionally convex (dcx) ordering is a tool for comparison of dependence structure of random vectors that also takes into account the variability of the marginal distributions. When extended to random fields it concerns comparison of all finite dimensional distributions. Viewing locally finite measures as nonnegative fields of measure-values indexed by the bounded Borel subsets of the space, in this paper we formulate and study the dcx ordering of random measures on locally compact spaces. We show that the dcx order is preserved under some of the natural operations considered on random measures and point processes, such as independent superposition and thinning. Further operations such as independent marking and displacement, though do not preserve the dcx order on all point processes, are shown to preserve the order on Cox point processes. We also examine the impact of dcx order on the second moment properties, in particular on clustering and on Palm distributions. Comparisons of Ripley's functions, pair correlation functions as well as examples seem to indicate that p.p. higher in dcx order cluster more.As the main result, we show that non-negative integral (shot-noise) fields with respect to dcx ordered random measures inherit this ordering from the measures. Numerous applications of this result are shown, in particular to comparison of various Cox processes and some performance measures of wireless networks, in both of which shot-noise fields appear as key ingredients. We also mention a few pertinent open questions.

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Section: Interference In Wireless Communicationsmentioning

confidence: 99%

“…[12]), have stochastic intensity fields, which are shot-noise fields. They are also key ingredients of the recently proposed, so-called "physical" models for wireless networks, as we will explain in what follows (see also [1,8,10]). It is thus particularly appealing to study the shot-noise fields generated by dcx ordered random measures.…”

Section: Introductionmentioning

confidence: 99%

Directionally convex ordering of random measures, shot noise fields, and some applications to wireless communications

Błaszczyszyn

Yogeshwaran

2009

Adv. Appl. Probab.

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“…This implies that every node can be reached in a time that is linear with the distance. The result shows that one does not require full connectivity in a single instant; hence the requirement of a giant connected component (percolation) in a network with interference [10] is greatly relaxed. Hence, e.g., in a route discovery flooding algorithm, the time to find the route scales linearly with the diameter of the network.…”

Section: ) Inmentioning

confidence: 99%

“…Their model does not consider interference and thus allows the use of Kingman's subadditive ergodic theorem [9] while ours does not. Percolation in signal-to-interference ratio graphs was analyzed in [10] where the nodes are assumed to be full-duplex. In practice, radios do not transmit and receive at the same time (at the same frequency), and hence the instantaneous network graph is always disconnected.…”

Section: Introductionmentioning

confidence: 99%

“…We observe that the random graph g(k) is a snapshot of the ALOHA network at time instant k. The random graph process G(0, m) captures the entire connectivity history up to time m. The graph g(k) has the flavor of the interference graph analyzed in [10] where the authors consider only bidirectional links (full-duplex radios). They proved that such a graph percolates with respect to the density of the nodes if the processing gain is high enough.…”

Section: Introductionmentioning

confidence: 99%

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Bounds on the information propagation delay in interference-limited ALOHA networks

Ganti

Haenggi

2009

2009 7th International Symposium on Modeling and Optimization in Mobile, Ad Hoc, and Wireless Networks

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Abstract-In a wireless network the set of transmitting nodes changes frequently because of the MAC scheduler and the traffic load. Analyzing the connectivity of such a network using static graphs would lead to pessimistic performance results. In this paper, we consider an ad hoc network with half-duplex radios that uses multihop routing and slotted ALOHA for the network MAC contention, and introduce a random dynamic multi-digraph to model its connectivity. We first provide analytical results about the degree distribution of the graph. Next, defining the path formation time as the minimum time required for a causal path to form between the source and destination on the dynamic graph, we derive the distributional properties of the connection delay using techniques from first passage percolation and epidemic processes. We show that the delay scales linearly with the distance and provide asymptotic results (with respect to time) for the positions of the nodes which are able to receive information from a transmitter located at the origin. We also provide simulation results to support the theoretical results.

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Absence of percolation in graphs based on stationary point processes with degrees bounded by two

Jahnel

Tóbiás

2022

Random Struct Algorithms

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We consider undirected graphs that arise as deterministic functions of stationary point processes such that each point has degree bounded by two. For a large class of point processes and edge‐drawing rules, we show that the arising graph has no infinite connected component, almost surely. In particular, this extends our previous result for signal‐to‐interference ratio graphs based on stabilizing Cox point processes and verifies the conjecture of Balister and Bollobás that the bidirectional k$$ k $$‐nearest neighbor graph of a two‐dimensional homogeneous Poisson point process does not percolate for k=2$$ k=2 $$.

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Percolation in the signal to interference ratio graph

Cited by 42 publications

References 3 publications

Directionally convex ordering of random measures, shot noise fields, and some applications to wireless communications

Directionally convex ordering of random measures, shot noise fields, and some applications to wireless communications

Bounds on the information propagation delay in interference-limited ALOHA networks

Absence of percolation in graphs based on stationary point processes with degrees bounded by two

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