1,721,023 research outputs found
Fluid Models in Performance Analysis
No full textStochastic fluid models have been applied to model and evaluate the performance of many important real systems. The automatic analysis tools to support of fluid models are still not as improved as the ones for discrete state Markov models, but there is a wide range of models which can be effectively described and analyzed with fluid models. Also the model support of hybrid models from various performance evaluation tools improves continuously. The aim of this work is to summarize the basic concepts and the potential use of Markov fluid models. The factors which determine the limits of solvability of fluid models are also discussed. Practical guidelines can be extracted from these factors to determine the applicability of fluid models in practical modeling examples. The work is supported by an example where Fluid Models, derived from an higher level modeling language (Fluid Stochastic Petri Nets), have been exploited to study the transfer time distribution in Peer-to-Peer file sharing applications
Stationary analysis of fluid level dependent bounded fluid models
No full textIn stochastic fluid models the drift at which the fluid level changes in the fluid buffer and the generator of the underlying process might depend on the discrete state of the system and on the fluid level itself. In this paper we analyse the stationary behaviour of finite buffer Markov fluid models in which the drift and the generator of the underlying continuous time Markov chain (CTMC) depends on both of these parameters. Especially, the case when the drift changes sign at a given fluid level is considered. This case requires a particular treatment, because at this fluid level probability mass might develop. When dealing with sign changes, new problems that were not addressed in previous works arises. The set of stationary equations is provided and a transformation of the unknowns is applied to obtain a solvable system description. Numerical examples introduce the behaviour of fluid systems with various discontinuities and sign changes of the drift
Analysis of large scale interacting systems by mean field method
No full textModeling and analysing very large stochastic systems composed of interacting entities is a very challenging and complex task. The usual approach, relying on the generation of the whole state space, is bounded by the state space explosion, even if symmetry properties, often included in the model, allow to apply lumping techniques and building the overall model by means of tensor algebra operations. In this paper we resort to the mean field theory. The main idea of the mean field theory is to focus on one particular tagged entity and to replace all interactions with the other entities with an average or effective interaction. The reduction of a multibody problem into an effective one-body problem makes the solution easier while at the same time taking into account the contribution of an averaged interdependence of the whole system on the specific entity. We apply the mean field approach to very large systems of interacting continuous time Markov chains, in which the averaged interaction depends on the distribution of the entity population in each state. We report several examples of interacting Markovian queues, showing the potentialities of the proposed techniqu
Second Order Fluid Models with General Boundary Behaviour
No full textFor applications of stochastic fluid models, such as those related to wildfire spread and containment, one wants a fast method to compute time dependent probabilities. Erlangization is an approximation method that replaces various distributions at a time t by the corresponding ones at a random time with Erlang distribution having mean t. Here, we develop an efficient version of that algorithm for various first passage time distributions of a fluid flow, exploiting recent results on fluid flows, probabilistic underpinnings, and some special structures. Some connections with a familiar Laplace transform inversion algorithm due to Jagerman are also noted up front
Acyclic Discrete Phase Type Distributions: properties and a Parameter Estimation Algorithm
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