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A General Graph Model For Representing Exact Communication Volume in Parallel Sparse Matrix–Vector Multiplication
, 2006
"... In this paper, we present a new graph model of sparse matrix decomposition for parallel sparse matrix–vector multiplication. Our model differs from previous graphbased approaches in two main respects. Firstly, our model is based on edge colouring rather than vertex partitioning. Secondly, our mod ..."
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In this paper, we present a new graph model of sparse matrix decomposition for parallel sparse matrix–vector multiplication. Our model differs from previous graphbased approaches in two main respects. Firstly, our model is based on edge colouring rather than vertex partitioning. Secondly, our model is able to correctly quantify and minimise the total communication volume of the parallel sparse matrix– vector multiplication while maintaining the computational load balance across the processors. We show that our graph edge colouring model is equivalent to the finegrained hypergraph partitioningbased sparse matrix decomposition model. We conjecture that the existence of such a graph model should lead to faster serial and parallel sparse matrix decomposition heuristics and associated tools.
Extracting StateBased Performance Metrics using Asynchronous Iterative Techniques
"... Solution of large sparse linear fixedpoint problems lies at the heart of many important performance analysis calculations. These calculations include steadystate, transient and passagetime computations in discretetime Markov chains, continuoustime Markov chains and semiMarkov chains. In recent ..."
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Solution of large sparse linear fixedpoint problems lies at the heart of many important performance analysis calculations. These calculations include steadystate, transient and passagetime computations in discretetime Markov chains, continuoustime Markov chains and semiMarkov chains. In recent years, much work has been done to extend the application of asynchronous iterative solution methods to different contexts. This work has been motivated by the potential for faster solution, more efficient use of the communication channel and access to memory, and simplification of task management and programming. In this paper, we show how the key performance metrics mentioned abovecanbetransformedintoproblemswhichcanbesolvedusingasynchronousiterative methods with guaranteed convergence—using the full breadth of Chazan and Miranker’s classesofasynchronousiterations.Weintroducetheapplicationofasynchronousiterative solution methods within this context by applying several algorithm variants to steadystate analysis of a GSPN model of a flexible manufacturing system. We show that for varying numbers of processors and different problem sizes one of these algorithm variants offers consistently better wall time until convergence, a consistently better communication profile, and often requires fewer update iterations than a standard parallel Jacobi algorithm, seemingly benefiting from a form of Gauss–Seidel effect. Key words: Asynchronous iterative solution; performance analysis; continuoustime Markov chain; semiMarkov chain; steadystate analysis; transient analysis; passagetime analysis 1
Response Times in Healthcare Systems
, 2007
"... It is a goal universally acknowledged that a healthcare system should treat its patients – and especially those in need of critical care – in a timely manner. However, this is often not achieved in practice, particularly in staterun public healthcare systems that suffer from high patient demand and ..."
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It is a goal universally acknowledged that a healthcare system should treat its patients – and especially those in need of critical care – in a timely manner. However, this is often not achieved in practice, particularly in staterun public healthcare systems that suffer from high patient demand and limited resources. In particular, Accident and Emergency (A&E) departments in England have been placed under increasing pressure, with attendances rising year on year, and a national government target whereby 98 % of patients should spend 4 hours or less in an A&E department from arrival to admission, transfer or discharge. This thesis presents techniques and tools to characterise and forecast patient arrivals, to model patient flow and to assess the responsetime impact of different resource allocations, patient treatment schemes and workload scenarios. Having obtained ethical approval to access five years of pseudonymised patient timing data from a large case study A&E department, we present a number of time series models that characterise and forecast daily A&E patient arrivals. Patient arrivals are
Asynchronous Iterative Solution for Dominant Eigenvectors with Applications in Performance Modelling and . . .
, 2009
"... Performance analysis calculations, for models of any complexity, require a distributed computation effort that can easily occupy a large compute cluster for many days. Producing a simple steadystate measure involves an enormous dominant eigenvector calculation, with even modest performance models h ..."
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Performance analysis calculations, for models of any complexity, require a distributed computation effort that can easily occupy a large compute cluster for many days. Producing a simple steadystate measure involves an enormous dominant eigenvector calculation, with even modest performance models having upwards of 10 12 variables. Computations such as passagetime analysis are an order of magnitude more difficult, producing many hundreds of repeated linear system calculations. As models describe greater concurrency, so the state space of the model increases and with it the magnitude of any performance analysis problem that may be being attempted. The PageRank algorithm is used by Google to measure the relative importance of web pages. It does this by formulating and solving a similarly enormous dominant eigenvector problem, with one variable for every page on the web. As with performance problems, as the number of web pages grows, so the size of the underlying system calculation grows also. With the number of web pages currently estimated to exceed one trillion, the PageRank problem requires many thousands of computers running concurrently over many different clusters. Both problems share the same underlying mathematical type and also the same requirement
Network
"... We developed analogous parallel algorithms to implement CostRank for distributed memory parallel computers using multi processors. Our intent is to make CostRank calculations for the growing number of hosts in a fast and a scalable way. In the same way we intent to secure large scale networks that r ..."
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We developed analogous parallel algorithms to implement CostRank for distributed memory parallel computers using multi processors. Our intent is to make CostRank calculations for the growing number of hosts in a fast and a scalable way. In the same way we intent to secure large scale networks that require fast and reliable computing to calculate the ranking of enormous graphs with thousands of vertices (states) and millions or arcs (links). In our proposed approach we focus on a parallel CostRank computational architecture on a cluster of PCs networked via Gigabit Ethernet LAN to evaluate the performance and scalability of our implementation. In particular, a partitioning of input data, graph files, and ranking vectors with load balancing technique can improve the runtime and scalability of largescale parallel computations. An application case study of analogous Cost Rank computation is presented. Applying parallel environment models for onedimensional sparse matrix partitioning on a modified research page, results in a significant reduction in communication overhead and in periteration runtime.We provide an analytical discussion of analogous algorithms performance in terms of I/O and synchronization cost, as well as of memory usage.