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The Markov-modulated Poisson process (MMPP) cookbook
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The impact of job arrival patterns on parallel scheduling
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Aggregate matrix-analytic techniques and their applications
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Grid resource management: state of the art and future trends
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Nonlinear Time Series Analysis
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Parallel computer workload modeling with markov chains
JSSPP'04 Proceedings of the 10th international conference on Job Scheduling Strategies for Parallel Processing
Workload characteristics of a multi-cluster supercomputer
JSSPP'04 Proceedings of the 10th international conference on Job Scheduling Strategies for Parallel Processing
Workload analysis of a cluster in a grid environment
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Long range dependent job arrival process and its implications in grid environments
Proceedings of the first international conference on Networks for grid applications
Workload dynamics on clusters and grids
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CCGRID '10 Proceedings of the 2010 10th IEEE/ACM International Conference on Cluster, Cloud and Grid Computing
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Proceedings of 2011 International Conference for High Performance Computing, Networking, Storage and Analysis
Towards Non-Stationary Grid Models
Journal of Grid Computing
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In this paper we present an initial analysis of job arrivals in a production data-intensive Grid and investigate several traffic models for the interarrival time processes. Our analysis focuses on the heavy-tail behavior and autocorrelations, and the modeling is carried out at three different levels: Grid, Virtual Organization (VO), and region. A set of m-state Markov modulated Poisson processes (MMPP) is investigated, while Poisson processes and hyperexponential renewal processes are evaluated for comparison studies. We apply the transportation distance metric from dynamical systems theory to further characterize the differences between the data trace and the simulated time series, and estimate errors by bootstrapping. The experimental results show that MMPPs with a certain number of states are successful to a certain extent in simulating the job traffic at different levels, fitting both the interarrival time distribution and the autocorrelation function. However, MMPPs are not able to match the autocorrelations for certain VOs, in which strong deterministic semi-periodic patterns are observed. These patterns are further characterized using different representations. Future work is needed to model both deterministic and stochastic components in order to better capture the correlation structure in the series.