Analysis of Fluid Queues in Saturation with Additive Decomposition

Frailty models have been developed to quantify both heterogeneity as well as association in multivariate time-to-event data. In recent years, numerous shared and correlated frailty models have been proposed in the survival literature allowing for different association structures and frailty distributions. A bivariate correlated gamma frailty model with an additive decomposition of the frailty variables into a sum of independent gamma components was introduced before. Although this model has a very convenient closed-form representation for the bivariate survival function, the correlation among event- or subject-specific frailties is bounded above which becomes a severe limitation when the values of the two frailty variances differ substantially. In this article, we review existing correlated gamma frailty models and propose novel ones based on bivariate gamma frailty distributions. Such models are found to be useful for the analysis of bivariate survival time data regardless of the censoring type involved. The frailty methodology was applied to right-censored and left-truncated Danish twins mortality data and serological survey current status data on varicella zoster virus and parvovirus B19 infections in Belgium. From our analyses, it has been shown that fitting more flexible correlated gamma frailty models in terms of the imposed association and correlation structure outperforms existing frailty models including the one with an additive decomposition.

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Volume and duration of losses in finite buffer fluid queues

Journal of Applied Probability ◽

10.1239/jap/1445543849 ◽

2015 ◽

Vol 52 (3) ◽

pp. 826-840 ◽

Cited By ~ 1

Author(s):

Fabrice Guillemin ◽

Bruno Sericola

Keyword(s):

Busy Period ◽

Buffer Capacity ◽

Exact Expression ◽

Loss Probability ◽

Finite Buffer ◽

Fluid Queues ◽

Buffer Content ◽

Phase Type ◽

Phase Type Distributions ◽

Arrival Processes

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.

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Least Squares Smoothers and Additive Decomposition

New Approaches in Classification and Data Analysis - Studies in Classification, Data Analysis, and Knowledge Organization ◽

10.1007/978-3-642-51175-2_64 ◽

1994 ◽

pp. 549-555

Author(s):

Ulrich Halekoh ◽

Paul O. Degens

Keyword(s):

Least Squares ◽

Additive Decomposition

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Overflow probability upper bound for heterogeneous fluid queues handling general on-off sources

The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks - Teletraffic Science and Engineering ◽

10.1016/b978-0-444-82031-0.50015-9 ◽

1994 ◽

pp. 65-74 ◽

Cited By ~ 4

Author(s):

J. Guibert

Keyword(s):

Upper Bound ◽

Fluid Queues ◽

Overflow Probability

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Additive decompositions of polynomials over unique factorization domains

Journal of Algebra and Its Applications ◽

10.1142/s0219498820501509 ◽

2019 ◽

Vol 19 (08) ◽

pp. 2050150

Author(s):

Leila Benferhat ◽

Safia Manar Elislam Benoumhani ◽

Rachid Boumahdi ◽

Jesse Larone

Keyword(s):

Finite Fields ◽

Unique Factorization ◽

Additive Decomposition ◽

Unique Factorization Domains

Additive decompositions over finite fields were extensively studied by Brawely and Carlitz. In this paper, we study the additive decomposition of polynomials over unique factorization domains.

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