Formulation of the simple Markovian model using fractional calculus approach and its application to analysis of queue behavior of severe patients

Soma Dhar; Lipi B. Mahanta; Kishore Kumar Das

doi:10.21307/stattrans-2019-007

Formulation of the simple Markovian model using fractional calculus approach and its application to analysis of queue behavior of severe patients

Soma Dhar Gauhati University , Lipi B. Mahanta Institute of Advanced Study in Science and Technology. E-mail:. ORCID:https://orcid.org/0000-0002-7733-5461 , Kishore Kumar Das Department of Statistics, Gauhati University, Guwahati, India Statistics in Transition new series, vol. 20, 2019, 1, pages: 117-129 Published online: 25 April 2019 DOI 10.21307/stattrans-2019-007

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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 E^V_0.5,0.5(t), for different fractional values of server activity status, n = 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.

KEYWORDS

fractional order, arrival rate, patients, fractional calculus

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