Modelling parallel and distributed virtual reality systems for performance analysis and comparison

Most Virtual Reality systems employ some form of parallel processing, making use of multiple processors which are often distributed over large areas geographically, and which communicate via various forms of message passing. The approaches to parallel decomposition differ for each system, as do the performance implications of each approach. Previous comparisons have only identified and categorized the different approaches. None have examined the performance issues involved in the different parallel decompositions. Performance measurement for a Virtual Reality system differs from that of other parallel systems in that some measure of the delays involved with the interaction of the separate components is required, in addition to the measure of the throughput of the system. Existing performance analysis approaches are typically not well suited to providing both these measures. This thesis describes the development of a performance analysis technique that is able to provide measures of both interaction latency and cycle time for a model of a Virtual Reality system. This technique allows performance measures to be generated as symbolic expressions describing the relationships between the delays in the model. It automatically generates constraint regions, specifying the values of the system parameters for which performance characteristics change. The performance analysis technique shows strong agreement with values measured from implementation of three common decomposition strategies on two message passing architectures. The technique is successfully applied to a range of parallel decomposition strategies found in Parallel and Distributed Virtual Reality systems. For each system, the primary decomposition techniques are isolated and analysed to determine their performance characteristics. This analysis allows a comparison of the various decomposition techniques, and in many cases reveals trends in their behaviour that would have gone unnoticed with alternative analysis techniques. The work described in this thesis supports the Performance Analysis and Comparison of Parallel and Distributed Virtual Reality systems. In addition it acts as a reference, describing the performance characteristics of decomposition strategies used in Virtual Reality systems

Hierarchical fractional-step approximations and parallel kinetic Monte Carlo algorithms

We present a mathematical framework for constructing and analyzing parallel algorithms for lattice Kinetic Monte Carlo (KMC) simulations. The resulting algorithms have the capacity to simulate a wide range of spatio-temporal scales in spatially distributed, non-equilibrium physiochemical processes with complex chemistry and transport micro-mechanisms. The algorithms can be tailored to specific hierarchical parallel architectures such as multi-core processors or clusters of Graphical Processing Units (GPUs). The proposed parallel algorithms are controlled-error approximations of kinetic Monte Carlo algorithms, departing from the predominant paradigm of creating parallel KMC algorithms with exactly the same master equation as the serial one. Our methodology relies on a spatial decomposition of the Markov operator underlying the KMC algorithm into a hierarchy of operators corresponding to the processors' structure in the parallel architecture. Based on this operator decomposition, we formulate Fractional Step Approximation schemes by employing the Trotter Theorem and its random variants; these schemes, (a) determine the communication schedule} between processors, and (b) are run independently on each processor through a serial KMC simulation, called a kernel, on each fractional step time-window. Furthermore, the proposed mathematical framework allows us to rigorously justify the numerical and statistical consistency of the proposed algorithms, showing the convergence of our approximating schemes to the original serial KMC. The approach also provides a systematic evaluation of different processor communicating schedules.Comment: 34 pages, 9 figure