Numerical performance of an asynchronous Jacobi iteration

Bull, J. Mark; Freeman, T. L.

doi:10.1007/3-540-55895-0_431

Cited by 11 publications

(9 citation statements)

References 3 publications

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“…It performs an asynchronous Jacobi with local Gauss-Seidel method as in [2] on the system of linear equations in (6). This method converges for any initial estimate of r when T W − I is strictly or irreducibly diagonally dominant [3], [4], [5] and in fact in some cases the asynchronous version has been shown to converge faster than the synchronous version [2]. Thus, to prove that the risk calculations will converge, it is enough to show strict diagonal dominance for T W − I.…”

Section: A Convergencementioning

confidence: 99%

A system for coupled road traffic utility maximisation and risk management using VANET

Fitzgerald

Landfeldt

2012

2012 15th International IEEE Conference on Intelligent Transportation Systems

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We propose a system for dynamic, online management of traffic accident risk in which vehicles exchange information via a vehicular ad-hoc network and use received information in calculating an estimate of current risk levels. We test the system's effectiveness in increasing the utility of the road network while maintaining the accident rate. We further prove the convergence of our proposed algorithm and investigate the information propagation, convergence rate and bandwidth requirements of the system and find that the system is able to increase the utility at maintained accident rate while operating within the confines of the IEEE 802.11p radio standard.

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Section: A Convergencementioning

confidence: 99%

A system for coupled road traffic utility maximisation and risk management using VANET

Fitzgerald

Landfeldt

2012

2012 15th International IEEE Conference on Intelligent Transportation Systems

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“…In [3,5,7] the authors study the performance of APJ in terms of time to converge. In this paper we will make a similar study except that we record a complete log of all of the iterations and communications that take place in the implementation.…”

Section: X[i](k)=m[ii]*x[i](k-1)+c[i] For All Inputs J X[i](k)=x[i](kmentioning

confidence: 99%

Performance analysis of asynchronous parallel Jacobi

Hook

Dingle

2017

Numer Algor

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The directed acyclic graph (DAG) associated with a parallel algorithm captures the partial order in which separate local computations are completed and how their outputs are subsequently used in further computations. Unlike in a synchronous parallel algorithm the DAG associated with an asynchronous parallel algorithm is not predetermined. Instead it is a product of the asynchronous timing dynamics of the machine and cannot be known in advance, as such it is best thought of as a pseudorandom variable.In this paper we present a formalism for analyzing the performance of asynchronous parallel Jacobi's method in terms of its DAG. We use this approach to prove error bounds and bounds on the rate of convergence. The rate of convergence bounds are based on the statistical properties of the DAG and are valid for systems with a non-negative iteration matrix. We support our theoretical results with a suit of numerical examples, where we compare the performance of synchronous and asynchronous parallel Jacobi to certain statistical properties of the DAGs associated with the computations. We also present some examples of small matrices with elements of mixed sign, which demonstrate that determining whether a system will converge under asynchronous iteration in this more general setting is a far more difficult problem.

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“…The entire system of nodes is thus collectively solving a set of linear equations, in which each row corresponds to one node, in a distributed fashion by performing an asynchronous Jacobi with local Gauss-Seidel method, as in [6].…”

Section: Coupled Risk Estimation Algorithmmentioning

confidence: 99%

Trading accuracy and resource usage in highly dynamic vehicular networks

Fitzgerald

Landfeldt

2013

16th International IEEE Conference on Intelligent Transportation Systems (ITSC 2013)

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Abstract-Vehicular networks bring new ways of viewing road traffic management and safety applications. For the first time, it will be possible for vehicles to exchange information and build fine-grained knowledge about the current situation, estimating risks and adapting their driving. Central to these applications is the need to exchange information in a highly dynamic environment, building a view of the current situation before the conditions change. This is turn requires the distributed algorithms used to converge on low error margins quickly.In this paper, we investigate the performance of such a distributed algorithm which aims to build a common assessment of the risk level among vehicles to trade off accident risks with road throughput. In particular, we examine how the convergence rate is affected by network size and node density, and also how the error in the algorithm's output is affected by the rate at which nodes send out update beacons. We develop a variable-rate beaconing scheme in order to find a trade-off between accuracy of outputs and network resource usage. We then formulate this as a more general optimisation problem applicable to other applications or distributed algorithmic problems in highly dynamic distributed systems such as VANETs.

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Numerical performance of an asynchronous Jacobi iteration

Cited by 11 publications

References 3 publications

A system for coupled road traffic utility maximisation and risk management using VANET

A system for coupled road traffic utility maximisation and risk management using VANET

Performance analysis of asynchronous parallel Jacobi

Trading accuracy and resource usage in highly dynamic vehicular networks

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