2004 ◽  
Vol 41 (02) ◽  
pp. 557-569 ◽  
Author(s):  
Nail Akar ◽  
Khosrow Sohraby

In this paper, we study Markov fluid queues where the net fluid rate to a single-buffer system varies with respect to the state of an underlying continuous-time Markov chain. We present a novel algorithmic approach to solve numerically for the steady-state solution of such queues. Using this approach, both infinite- and finite-buffer cases are studied. We show that the solution of the infinite-buffer case is reduced to the solution of a generalized spectral divide-and-conquer (SDC) problem applied on a certain matrix pencil. Moreover, this SDC problem does not require the individual computation of any eigenvalues and eigenvectors. Via the solution for the SDC problem, a matrix-exponential representation for the steady-state queue-length distribution is obtained. The finite-buffer case, on the other hand, requires a similar but different decomposition, the so-called additive decomposition (AD). Using the AD, we obtain a modified matrix-exponential representation for the steady-state queue-length distribution. The proposed approach for the finite-buffer case is shown not to have the numerical stability problems reported in the literature.


2017 ◽  
Vol 31 (3) ◽  
pp. 265-283 ◽  
Author(s):  
Ewan Jacov Cahen ◽  
Michel Mandjes ◽  
Bert Zwart

This paper focuses on the evaluation of the probability that both components of a bivariate stochastic process ever simultaneously exceed some large level; a leading example is that of two Markov fluid queues driven by the same background process ever reaching the set (u, ∞)×(u, ∞), for u>0. Exact analysis being prohibitive, we resort to asymptotic techniques and efficient simulation, focusing on large values of u. The first contribution concerns various expressions for the decay rate of the probability of interest, which are valid under Gärtner–Ellis-type conditions. The second contribution is an importance-sampling-based rare-event simulation technique for the bivariate Markov modulated fluid model, which is capable of asymptotically efficiently estimating the probability of interest; the efficiency of this procedure is assessed in a series of numerical experiments.


2004 ◽  
Vol 41 (2) ◽  
pp. 557-569 ◽  
Author(s):  
Nail Akar ◽  
Khosrow Sohraby

In this paper, we study Markov fluid queues where the net fluid rate to a single-buffer system varies with respect to the state of an underlying continuous-time Markov chain. We present a novel algorithmic approach to solve numerically for the steady-state solution of such queues. Using this approach, both infinite- and finite-buffer cases are studied. We show that the solution of the infinite-buffer case is reduced to the solution of a generalized spectral divide-and-conquer (SDC) problem applied on a certain matrix pencil. Moreover, this SDC problem does not require the individual computation of any eigenvalues and eigenvectors. Via the solution for the SDC problem, a matrix-exponential representation for the steady-state queue-length distribution is obtained. The finite-buffer case, on the other hand, requires a similar but different decomposition, the so-called additive decomposition (AD). Using the AD, we obtain a modified matrix-exponential representation for the steady-state queue-length distribution. The proposed approach for the finite-buffer case is shown not to have the numerical stability problems reported in the literature.


2015 ◽  
Vol 52 (3) ◽  
pp. 826-840 ◽  
Author(s):  
Fabrice Guillemin ◽  
Bruno Sericola

We study congestion periods in a finite fluid buffer when the net input rate depends upon a recurrent Markov process; congestion occurs when the buffer content is equal to the buffer capacity. Similarly to O'Reilly and Palmowski (2013), we consider the duration of congestion periods as well as the associated volume of lost information. While these quantities are characterized by their Laplace transforms in that paper, we presently derive their distributions in a typical stationary busy period of the buffer. Our goal is to compute the exact expression of the loss probability in the system, which is usually approximated by the probability that the occupancy of the infinite buffer is greater than the buffer capacity under consideration. Moreover, by using general results of the theory of Markovian arrival processes, we show that the duration of congestion and the volume of lost information have phase-type distributions.


2020 ◽  
pp. 74-80
Author(s):  
Philippe Schweizer ◽  

We would like to show the small distance in neutropsophy applications in sciences and humanities, has both finally consider as a terminal user a human. The pace of data production continues to grow, leading to increased needs for efficient storage and transmission. Indeed, the consumption of this information is preferably made on mobile terminals using connections invoiced to the user and having only reduced storage capacities. Deep learning neural networks have recently exceeded the compression rates of algorithmic techniques for text. We believe that they can also significantly challenge classical methods for both audio and visual data (images and videos). To obtain the best physiological compression, i.e. the highest compression ratio because it comes closest to the specificity of human perception, we propose using a neutrosophical representation of the information for the entire compression-decompression cycle. Such a representation consists for each elementary information to add to it a simple neutrosophical number which informs the neural network about its characteristics relative to compression during this treatment. Such a neutrosophical number is in fact a triplet (t,i,f) representing here the belonging of the element to the three constituent components of information in compression; 1° t = the true significant part to be preserved, 2° i = the inderterminated redundant part or noise to be eliminated in compression and 3° f = the false artifacts being produced in the compression process (to be compensated). The complexity of human perception and the subtle niches of its defects that one seeks to exploit requires a detailed and complex mapping that a neural network can produce better than any other algorithmic solution, and networks with deep learning have proven their ability to produce a detailed boundary surface in classifiers.


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