Throughput equalization in mean-field hard-core models for CSMA-based wireless networks
09 May 2016-pp 1-8
TL;DR: This paper considers the problem of equalizing throughput of nodes in CSMA-based wireless networks, and presents a distributed strategy based on a mean-field hard-core model of interference that equalizes the throughput of the nodes with different degrees.
Abstract: In this paper we consider the problem of equalizing throughput of nodes in CSMA-based wireless networks. We model interference in a network using conflict graph, where edges represent hard-core interaction, meaning that the two nodes an edge connects cannot be simultaneously active, or transmitting. In practice, the degrees of nodes in a conflict graph are not constant. In such cases, using CSMA leads to lack of fairness since nodes with larger degree have the potential of getting hold of the medium for smaller fraction of time than the nodes with smaller degree. We present a distributed strategy for throughput equalization. The proposed strategy is based on a mean-field hard-core model of interference, and it equalizes the throughput of the nodes with different degrees. We also show that the mean-field hard-core model exhibits a certain phase transition. We present results of Monte-Carlo simulations to evaluate the the proposed strategy in square grid networks and Poisson networks, in addition to mean-field networks.
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01 Jan 2001
TL;DR: In this paper, the Hessian B Parisi equation and channel coding theorem of K-Sat were derived for the mean field theory of phase transitions and the replica symmetry breaking theory of spin glasses.
Abstract: 1 Mean-field theory of phase transitions 2 Mean-field theory of spin glasses 3 Replica symmetry breaking 4 Gauge theory of spin glasses 5 Error-correcting codes 6 Image restoration 7 Associative memory 8 Learning in perceptron 9 Optimization problems A Eigenvalues of the Hessian B Parisi equation C Channel coding theorem D Distribution and free energy of K-Sat References Index
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TL;DR: In this article, the Erd\H{o}s-Gallai Linear Algorithm (EGL) was proposed, whose worst running time is O(n) in worst case.
Abstract: Havel in 1955, Erd\H{o}s and Gallai in 1960, Hakimi in 1962, Ruskey, Cohen, Eades and Scott in 1994, Barnes and Savage in 1997, Kohnert in 2004, Tripathi, Venugopalan and West in 2010 proposed a method to decide, whether a sequence of nonnegative integers can be the degree sequence of a simple graph. The running time of their algorithms is $\Omega(n^2)$ in worst case. In this paper we propose a new algorithm called EGL (Erd\H{o}s-Gallai Linear algorithm), whose worst running time is $\Theta(n).$ As an application of this quick algorithm we computed the number of the different degree sequences of simple graphs for $24, ...,29$ vertices.
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01 Jan 2011
TL;DR: It is shown that the stationary distribution of the CSMA system is in fact insensitive with respect to the transmission durations and the back-off times, and the stability conditions in a few relevant scenarios are identified.
Abstract: Random-access algorithms such as the Carrier-Sense Multiple-Access (CSMA) protocol provide a popular mechanism for distributed medium access control in large-scale wireless networks. In recent years, fairly tractable models have been shown to yield remarkably accurate throughput estimates for CSMA networks. These models typically assume that both the transmission durations and the back-off periods are exponentially distributed. We show that the stationary distribution of the system is in fact insensitive with respect to the transmission durations and the back-off times. These models primarily pertain to a saturated scenario where nodes always have packets to transmit. In reality however, the buffers may occasionally be empty as packets are randomly generated and transmitted over time. The resulting interplay between the activity states and the buffer contents gives rise to quite complicated queueing dynamics, and even establishing the stability criteria is usually a serious challenge. We explicitly identify the stability conditions in a few relevant scenarios, and illustrate the difficulties arising in other cases.
3 citations
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01 Jan 1988TL;DR: Probabilistic Reasoning in Intelligent Systems as mentioned in this paper is a complete and accessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty, and provides a coherent explication of probability as a language for reasoning with partial belief.
Abstract: From the Publisher:
Probabilistic Reasoning in Intelligent Systems is a complete andaccessible account of the theoretical foundations and computational methods that underlie plausible reasoning under uncertainty. The author provides a coherent explication of probability as a language for reasoning with partial belief and offers a unifying perspective on other AI approaches to uncertainty, such as the Dempster-Shafer formalism, truth maintenance systems, and nonmonotonic logic. The author distinguishes syntactic and semantic approaches to uncertaintyand offers techniques, based on belief networks, that provide a mechanism for making semantics-based systems operational. Specifically, network-propagation techniques serve as a mechanism for combining the theoretical coherence of probability theory with modern demands of reasoning-systems technology: modular declarative inputs, conceptually meaningful inferences, and parallel distributed computation. Application areas include diagnosis, forecasting, image interpretation, multi-sensor fusion, decision support systems, plan recognition, planning, speech recognitionin short, almost every task requiring that conclusions be drawn from uncertain clues and incomplete information.
Probabilistic Reasoning in Intelligent Systems will be of special interest to scholars and researchers in AI, decision theory, statistics, logic, philosophy, cognitive psychology, and the management sciences. Professionals in the areas of knowledge-based systems, operations research, engineering, and statistics will find theoretical and computational tools of immediate practical use. The book can also be used as an excellent text for graduate-level courses in AI, operations research, or applied probability.
15,671 citations
TL;DR: Two protocols are described for CSMA and their throughput-delay characteristics are given and results show the large advantage CSMA provides as compared to the random ALOHA access modes.
Abstract: Radio communication is considered as a method for providing remote terminal access to computers. Digital byte streams from each terminal are partitioned into packets (blocks) and transmitted in a burst mode over a shared radio channel. When many terminals operate in this fashion, transmissions may conflict with and destroy each other. A means for controlling this is for the terminal to sense the presence of other transmissions; this leads to a new method for multiplexing in a packet radio environment: carrier sense multiple access (CSMA). Two protocols are described for CSMA and their throughput-delay characteristics are given. These results show the large advantage CSMA provides as compared to the random ALOHA access modes.
2,361 citations
"Throughput equalization in mean-fie..." refers background in this paper
...Although CSMA is somewhat old [3], there has been renewed interest in the analysis of CSMA, primarily because of recent research results, but also due to the development of new wireless systems using CSMA, such as cognitive radio....
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Book•
18 Oct 2012TL;DR: This rigorous introduction to stochastic geometry will enable you to obtain powerful, general estimates and bounds of wireless network performance and make good design choices for future wireless architectures and protocols that efficiently manage interference effects.
Abstract: Covering point process theory, random geometric graphs and coverage processes, this rigorous introduction to stochastic geometry will enable you to obtain powerful, general estimates and bounds of wireless network performance and make good design choices for future wireless architectures and protocols that efficiently manage interference effects. Practical engineering applications are integrated with mathematical theory, with an understanding of probability the only prerequisite. At the same time, stochastic geometry is connected to percolation theory and the theory of random geometric graphs and accompanied by a brief introduction to the R statistical computing language. Combining theory and hands-on analytical techniques with practical examples and exercises, this is a comprehensive guide to the spatial stochastic models essential for modelling and analysis of wireless network performance.
2,327 citations
"Throughput equalization in mean-fie..." refers methods in this paper
...Stochastic geometry [4] offers one such approach where spatial point processes are used to model the locations of wireless nodes [5], [6]....
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TL;DR: For a large number of natural counting problems for which there was no previous indication of intractability, that they belong to the class of computationally eqivalent counting problems that are at least as difficult as the NP-complete problems.
Abstract: The class of $# P$-complete problems is a class of computationally eqivalent counting problems (defined by the author in a previous paper) that are at least as difficult as the $NP$-complete problems. Here we show, for a large number of natural counting problems for which there was no previous indication of intractability, that they belong to this class. The technique used is that of polynomial time reduction with oracles via translations that are of algebraic or arithmetic nature.
2,147 citations
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TL;DR: This summary of the state-of-the-art in iterative coding makes this decision more straightforward, with emphasis on the underlying theory, techniques to analyse and design practical iterative codes systems.
Abstract: Having trouble deciding which coding scheme to employ, how to design a new scheme, or how to improve an existing system? This summary of the state-of-the-art in iterative coding makes this decision more straightforward. With emphasis on the underlying theory, techniques to analyse and design practical iterative coding systems are presented. Using Gallager's original ensemble of LDPC codes, the basic concepts are extended for several general codes, including the practically important class of turbo codes. The simplicity of the binary erasure channel is exploited to develop analytical techniques and intuition, which are then applied to general channel models. A chapter on factor graphs helps to unify the important topics of information theory, coding and communication theory. Covering the most recent advances, this text is ideal for graduate students in electrical engineering and computer science, and practitioners. Additional resources, including instructor's solutions and figures, available online: www.cambridge.org/9780521852296.
2,100 citations