Estimating the Transmission Probability in Wireless Networks with Configuration Models

Bermolen, Paola; Jonckheere, Matthieu; Larroca, Federico; Moyal, Pascal

doi:10.1145/2858795

Cited by 10 publications

(10 citation statements)

References 19 publications

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“…Studying the jamming constant of uniformly chosen random graphs with a given asymptotic degree distribution (we make this notion more precise in the sequel) allows to make a first step in this direction, by studying a "first order" model which grasps only the bonds between points but no further correlations. The techniques and analysis presented here are at the core of the performance evaluation analysis of wireless systems, as developed in a companion applied paper [3].…”

Section: Introductionmentioning

confidence: 99%

“…Notice however that we do not construct a proper Erdös-Rényi graph and in fact, no uniform construction based on a prescribed degree distribution can do so, since the independence assumption for the existence of the various edges cannot be fulfilled. (Z) δ 3 3/8 0.37913944 (Honeycomb) δ 4 1/3 0.3641323 (Z 2 ) Table 1: Jamming constants for different degree distributions and their counterparts on deterministic graphs (simulation values for deterministic graphs are taken from [23]).…”

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confidence: 99%

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The jamming constant of uniform random graphs

Bermolen

Jonckheere

Moyal

2017

Stochastic Processes and their Applications

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By constructing jointly a random graph and an associated exploration process, we define the dynamics of a "parking process" on a class of uniform random graphs as a measure-valued Markov process, representing the empirical degree distribution of non-explored nodes. We then establish a functional law of large numbers for this process as the number of vertices grows to infinity, allowing us to assess the jamming constant of the considered random graphs, i.e. the size of the maximal independent set discovered by the exploration algorithm. This technique, which can be applied to any uniform random graph with a given degree distribution, can be seen as a generalization in the space of measures, of the differential equation method introduced by Wormald.

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Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

The jamming constant of uniform random graphs

Bermolen

Jonckheere

Moyal

2017

Stochastic Processes and their Applications

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“…En (Bermolen, 2016) se presenta una metodología para calcular la probabilidad de transmisión que optimice el desempeño de redes inalámbricas de acceso múltiple con monitoreo de señal portadora (CSMA por sus siglas en inglés, Carrier Sense Multiple Access). La metodología modela la interferencia entre usuarios por medio de grafos aleatorios.…”

Section: Trabajo Relacionadounclassified

Control de Acceso al Medio basado en Entropía para S-ALOHA en Redes Inalámbricas Ad-Hoc

González-Ambriz

Rivero-Ángeles

Menchaca-Mendez

2019

Rev. iberoam. autom. inform. ind.

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ResumenEn este artículo presentamos un nuevo enfoque de acceso al medio de capa cruzada que utiliza información topológica de la red para seleccionar la probabilidad de transmisión de cada nodo. En el esquema propuesto, la probabilidad de acceder al canal es asignada en función tanto de la entropía topológica de la red, como de la probabilidad individual de cada nodo de ser elegido por el algoritmo de enrutamiento como retransmisor en un flujo de datos de extremo-a-extremo. La entropía topológica de la red mide la capacidad de dicha red para distribuir el tráfico entre los nodos que la componen. Valores de entropía baja indican que el tráfico tenderá a concentrarse en regiones particulares de la red y que por lo tanto la probabilidad de que los nodos localizados en dichas regiones experimenten contención, es alta. En este caso, la probabilidad de acceso al medio de los nodos que se encuentran en esas regiones deberá ser seleccionada de forma tal que se reduzca la probabilidad de que experimenten contención. Experimentos de simulación muestran que el esquema propuesto logra ganancias de desempeño en términos del caudal, la tasa de colisiones y el retardo extremo-a-extremo. Palabras Clave:Tecnología inalámbrica y dispositivos móviles, control de acceso, comunicaciones y redes de comunicaciones, arquitecturas de control distribuido y descentralizado, control basado en eventos Entropy-Based Channel Access Control for S-ALOHA in Wireless Ad-Hoc Networks AbstractIn this paper we present a novel cross-layer medium access control scheme that uses information about the network topology in order to select the adequate transmission probability at the individual nodes. In the proposed Entropy-based Medium Acess Control protocol (EbMAC), the probability of accessing the channel of each node is a function of the topological network entropy and their individual probability of being selected as relay in an end-to-end path computed by the routing algorithm. The topological network entropy measures the ability of the network to distribute the data traffic among the nodes. High values of network entropy indicate that the data traffic will tend to concentrate around particular regions of the network and hence, that these regions are more likely to experience contention. In this case, the channel access probability has to be selected in such a way as to reduce the packet collision probability in such hot spots. Simulation-based experiments show that the proposed scheme attains performance gains in terms of throughput, collisions ratio and end-to-end delay.

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“…The size of the maximal greedy independent set of an Erdős-Rényi random graph was first considered in [15]; see Remark 1 below. Recently, jamming constants for the Erdős-Rényi random graph were studied in [3,23], and for random graphs with given degrees in [1,2,4]. In [1], random graphs were used to model wireless networks, in which nodes (mobile devices) try to activate after random times, and can only become active if none of their neighbors is active (transmitting).…”

Section: Introductionmentioning

confidence: 99%

“…Recently, jamming constants for the Erdős-Rényi random graph were studied in [3,23], and for random graphs with given degrees in [1,2,4]. In [1], random graphs were used to model wireless networks, in which nodes (mobile devices) try to activate after random times, and can only become active if none of their neighbors is active (transmitting). When the size of the wireless network becomes large and nodes try to activate after a short random time independently of each other, the jammed state with a maximal number of active nodes becomes the dominant state of the system.…”

Section: Introductionmentioning

confidence: 99%

Generalized Random Sequential Adsorption on Erdős–Rényi Random Graphs

Dhara¹,

Leeuwaarden²,

Mukherjee³

2016

J Stat Phys

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We investigate random sequential adsorption (RSA) on a random graph via the following greedy algorithm: Order the n vertices at random, and sequentially declare each vertex either active or frozen, depending on some local rule in terms of the state of the neighboring vertices. The classical RSA rule declares a vertex active if none of its neighbors is, in which case the set of active nodes forms an independent set of the graph. We generalize this nearest-neighbor blocking rule in three ways and apply it to the Erdős-Rényi random graph. We consider these generalizations in the large-graph limit n → ∞ and characterize the jamming constant, the limiting proportion of active vertices in the maximal greedy set.

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Estimating the Transmission Probability in Wireless Networks with Configuration Models

Cited by 10 publications

References 19 publications

The jamming constant of uniform random graphs

The jamming constant of uniform random graphs

Control de Acceso al Medio basado en Entropía para S-ALOHA en Redes Inalámbricas Ad-Hoc

Generalized Random Sequential Adsorption on Erdős–Rényi Random Graphs

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