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Author
Dhar Soma (Gauhati University, India), Mahanta Lipi B. (nstitute of Advanced Study in Science and Technology, India), Das Kishore Kumar (Gauhati University, Guwahati, India)
Title
Formulation of the Simple Markovian Model Using Fractional Calculus Approach and its Application to Analysis of Queue Behaviour of Severe Patients
Source
Statistics in Transition, 2019, vol. 20, nr 1, s. 117-129, rys., tab., bibliogr. s. 127-129
Keyword
Rozkład Poissona, Równania różniczkowe, Modele Markowa
Poisson distribution, Differential equations, Markov models
Note
summ.
Abstract
In this paper, we introduce a fractional order of a simple Markovian model where the arrival rate of the patient is Poisson, i.e. independent of the patient size. Fraction is obtained by replacing the first order time derivative in the difference differential equations which govern the probability law of the process with the Mittag-Leffler function. We derive the probability distribution of the number N(t) of patients suffering from severe disease at an arbitrary time t. We also obtain the mean size (number) of the patients suffering from severe disease waiting for service at any given time t, in the form of E0 ν 5,0.5(t), for different fractional values of server activity status, ν = 1,0.95,0.90 and for arrival rates α = β = 0.5. A numerical example is also evaluated and analysed by using the simple Markovian model with the help of simulation techniques. (original abstract)
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The Library of Warsaw School of Economics
The Library of University of Economics in Katowice
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ISSN
1234-7655
Language
eng
URI / DOI
http://dx.doi.org/10.21307/stattrans-2019-007
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