29,363 research outputs found
Dynamic Resource Management in Clouds: A Probabilistic Approach
Dynamic resource management has become an active area of research in the
Cloud Computing paradigm. Cost of resources varies significantly depending on
configuration for using them. Hence efficient management of resources is of
prime interest to both Cloud Providers and Cloud Users. In this work we suggest
a probabilistic resource provisioning approach that can be exploited as the
input of a dynamic resource management scheme. Using a Video on Demand use case
to justify our claims, we propose an analytical model inspired from standard
models developed for epidemiology spreading, to represent sudden and intense
workload variations. We show that the resulting model verifies a Large
Deviation Principle that statistically characterizes extreme rare events, such
as the ones produced by "buzz/flash crowd effects" that may cause workload
overflow in the VoD context. This analysis provides valuable insight on
expectable abnormal behaviors of systems. We exploit the information obtained
using the Large Deviation Principle for the proposed Video on Demand use-case
for defining policies (Service Level Agreements). We believe these policies for
elastic resource provisioning and usage may be of some interest to all
stakeholders in the emerging context of cloud networkingComment: IEICE Transactions on Communications (2012). arXiv admin note:
substantial text overlap with arXiv:1209.515
Moderate deviations and extinction of an epidemic
Consider an epidemic model with a constant flux of susceptibles, in a
situation where the corresponding deterministic epidemic model has a unique
stable endemic equilibrium. For the associated stochastic model, whose law of
large numbers limit is the deterministic model, the disease free equilibrium is
an absorbing state, which is reached soon or later by the process. However, for
a large population size, i.e. when the stochastic model is close to its
deterministic limit, the time needed for the stochastic perturbations to stop
the epidemic may be enormous. In this paper, we discuss how the Central Limit
Theorem, Moderate and Large Deviations allow us to give estimates of the
extinction time of the epidemic, depending upon the size of the population
Stochastic epidemics in a homogeneous community
These notes describe stochastic epidemics in a homogenous community. Our main
concern is stochastic compartmental models (i.e. models where each individual
belongs to a compartment, which stands for its status regarding the epidemic
under study : S for susceptible, E for exposed, I for infectious, R for
recovered) for the spread of an infectious disease. In the present notes we
restrict ourselves to homogeneously mixed communities. We present our general
model and study the early stage of the epidemic in chapter 1. Chapter 2 studies
the particular case of Markov models, especially in the asymptotic of a large
population, which leads to a law of large numbers and a central limit theorem.
Chapter 3 considers the case of a closed population, and describes the final
size of the epidemic (i.e. the total number of individuals who ever get
infected). Chapter 4 considers models with a constant influx of susceptibles
(either by birth, immigration of loss of immunity of recovered individuals),
and exploits the CLT and Large Deviations to study how long it takes for the
stochastic disturbances to stop an endemic situation which is stable for the
deterministic epidemic model. The document ends with an Appendix which presents
several mathematical notions which are used in these notes, as well as
solutions to many of the exercises which are proposed in the various chapters.Comment: Part I of "Stochastic Epidemic Models with Inference", T. Britton &
E. Pardoux eds., Lecture Notes in Mathematics 2255, Springer 201
The Hitting Times of A Stochastic Epidemic Model
In this paper, we focus on the hitting times of a stochastic epidemic model
presented by \cite{Gray}. Under the help of the auxiliary stopping times, we
investigate the asymptotic limits of the hitting times by the variations of
calculus and the large deviation inequalities when the noise is sufficiently
small. It can be shown that the relative position between the initial state and
the hitting state determines the scope of the hitting times greatly
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