Renewal Theory and Queueing Algorithms for Matrix-Exponential Distributions

2016 ◽  
pp. 333-362
Keyword(s):  
Renewal Theory ◽  
Matrix Exponential ◽  
Exponential Distributions

scholarly journals An alternative characterization for matrix exponential distributions

2009 ◽  
Vol 41 (04) ◽  
pp. 1005-1022
Author(s):  
Mark Fackrell
Keyword(s):  
Continuous Function ◽  
Exponential Distribution ◽  
Matrix Exponential ◽  
Necessary Condition ◽  
Stieltjes Transform ◽  
Real Numbers ◽  
Exponential Distributions ◽  
Alternative Characterization

A necessary condition for a rational Laplace–Stieltjes transform to correspond to a matrix exponential distribution is that the pole of maximal real part is real and negative. Given a rational Laplace–Stieltjes transform with such a pole, we present a method to determine whether or not the numerator polynomial admits a transform that corresponds to a matrix exponential distribution. The method relies on the minimization of a continuous function of one variable over the nonnegative real numbers. Using this approach, we give an alternative characterization for all matrix exponential distributions of order three.

Fitting with Matrix-Exponential Distributions

2005 ◽  
Vol 21 (2-3) ◽  
pp. 377-400 ◽  
Author(s):  
Mark Fackrell
Keyword(s):  
Matrix Exponential ◽  
Exponential Distributions

Numerical inverse Laplace transformation using concentrated matrix exponential distributions

2020 ◽  
Vol 137 ◽  
pp. 102067 ◽  
Author(s):  
Gábor Horváth ◽  
Illés Horváth ◽  
Salah Al-Deen Almousa ◽  
Miklós Telek
Keyword(s):  
Laplace Transformation ◽  
Matrix Exponential ◽  
Exponential Distributions ◽  
Inverse Laplace Transformation

Bilateral matrix-exponential distributions (abstract only)

2012 ◽  
Vol 39 (4) ◽  
pp. 25-25
Author(s):  
Mogens Bladt ◽  
Luz Judith R. Esparza ◽  
Bo Friis Nielsen
Keyword(s):  
Matrix Exponential ◽  
Exponential Distributions

Reliability of the two-unit priority standby system revisited

2021 ◽  
pp. 1748006X2110518
Author(s):  
Serkan Eryilmaz ◽  
Maxim Finkelstein
Keyword(s):  
Laplace Transform ◽  
Reliability Assessment ◽  
Repair Time ◽  
Matrix Exponential ◽  
Exponential Distributions ◽  
Reliability Indices ◽  
Cold Standby ◽  
The Matrix ◽  
The Laplace Transform ◽  
Standby System

This paper deals with reliability assessment of the repairable two-unit cold standby system when the first, main unit has the better performance level than the second one. Therefore, after its repair, the main unit is always switched into operation. The new Laplace transform representation for the system’s lifetime is obtained for arbitrary operation and repair time distributions of the units. For some particular cases, the Laplace transform of the system is shown to be rational, which enables the use of the matrix-exponential distributions for obtaining relevant reliability indices. The discrete setup of the model is also considered through the corresponding matrix-geometric distributions, which are the discrete analogs of the matrix-exponential distributions.

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