5,992 research outputs found
Compact Markov-modulated models for multiclass trace fitting
Markov-modulated Poisson processes (MMPPs) are stochastic models for fitting empirical traces for simulation, workload characterization and queueing analysis purposes. In this paper, we develop the first counting process fitting algorithm for the marked MMPP (M3PP), a generalization of the MMPP for modeling traces with events of multiple types. We initially explain how to fit two-state M3PPs to empirical traces of counts. We then propose a novel form of composition, called interposition, which enables the approximate superposition of several two-state M3PPs without incurring into state space explosion. Compared to exact superposition, where the state space grows exponentially in the number of composed processes, in interposition the state space grows linearly in the number of composed M3PPs. Experimental results indicate that the proposed interposition methodology provides accurate results against artificial and real-world traces, with a significantly smaller state space than superposed processes
Markovian Workload Characterization for QoS Prediction in the Cloud.
Resource allocation in the cloud is usually driven by performance predictions, such as estimates of the future incoming load to the servers or of the quality-of-service (QoS) offered by applications to end users. In this context, characterizing web workload fluctuations in an accurate way is fundamental to understand how to provision cloud resources under time-varying traffic intensities. In this paper, we investigate the Markovian Arrival Processes (MAP) and the related MAP/MAP/1 queueing model as a tool for performance prediction of servers deployed in the cloud. MAPs are a special class of Markov models used as a compact description of the time-varying characteristics of workloads. In addition, MAPs can fit heavy-tail distributions, that are common in HTTP traffic, and can be easily integrated within analytical queueing models to efficiently predict system performance without simulating. By comparison with trace-driven simulation, we observe that existing techniques for MAP parameterization from HTTP log files often lead to inaccurate performance predictions. We then define a maximum likelihood method for fitting MAP parameters based on data commonly available in Apache log files, and a new technique to cope with batch arrivals, which are notoriously difficult to model accurately. Numerical experiments demonstrate the accuracy of our approach for performance prediction of web systems. © 2011 IEEE
Sequences of regressions and their independences
Ordered sequences of univariate or multivariate regressions provide
statistical models for analysing data from randomized, possibly sequential
interventions, from cohort or multi-wave panel studies, but also from
cross-sectional or retrospective studies. Conditional independences are
captured by what we name regression graphs, provided the generated distribution
shares some properties with a joint Gaussian distribution. Regression graphs
extend purely directed, acyclic graphs by two types of undirected graph, one
type for components of joint responses and the other for components of the
context vector variable. We review the special features and the history of
regression graphs, derive criteria to read all implied independences of a
regression graph and prove criteria for Markov equivalence that is to judge
whether two different graphs imply the same set of independence statements.
Knowledge of Markov equivalence provides alternative interpretations of a given
sequence of regressions, is essential for machine learning strategies and
permits to use the simple graphical criteria of regression graphs on graphs for
which the corresponding criteria are in general more complex. Under the known
conditions that a Markov equivalent directed acyclic graph exists for any given
regression graph, we give a polynomial time algorithm to find one such graph.Comment: 43 pages with 17 figures The manuscript is to appear as an invited
discussion paper in the journal TES
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