Formulation of the Simple Markovian Model Using Fractional Calculus Approach and Its Application to Analysis of Queue Behaviour of Severe Patients (original) (raw)

2019, Statistics in Transition New Series

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 ν 0.5,0.5 (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.

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