In the present communication, we have studied different variations in the entropy measures in the different states of queueing processes. In case of steady state queuing process, it has been shown that as the arrival rate increases, the uncertainty increases whereas in the case of non-steady birth-death process, it is shown that the uncertainty varies differently. In this pattern, it first incr...

We are interested in describing the infected size of SIS Epidemic model using Birth-Death Markov process. The Susceptible-Infected-Susceptible (SIS) is defined within a population constant $M$; kept by replacing each death with newborn healthy individual. life span individual modelled an exponential distribution parameter $\alpha$; and disease spreads Poisson process rate $\lambda_{I}$. $\lambd...

Key-words: population dynamics, quasi-stationarity, Yaglom’s limit, birth and death process, logistic Feller diffusion.

The polynomial birth-death (PBD) distribution on non-negative integers introduced in Brown & Xia (2001) is the equilibrium distribution of the birth-death process with birth rates {αi} and death rates {βi}, where αi ≥ 0 and βi ≥ 0 are polynomial functions of i. The family unifies many well-known distributions such as Poisson, negative binomial and binomial. In this talk, I’ll explain how a nice...

Classic works of Karlin-McGregor and Jones-Magnus have established a general correspondence between continuous-time birth-and-death processes and continued fractions of the Stieltjes-Jacobi type together with their associated orthogonal polynomials. This fundamental correspondence is revisited here in the light of the basic relation between weighted lattice paths and continued fractions otherwi...

We consider a birth-death process {X(t), t ≥ 0} on the positive integers for which the origin is an absorbing state with birth coefficients λn, n ≥ 0 and death coefficients μn, n ≥ 0. We recall that the series A = ∑∞ n=1 1 λnπn and the series S = ∑∞ n=1 1 λnπn ∑∞ i=n+1 πi, where {πn, n ≥ 1} is the potential coefficients. It is well-known fact (see van Doorn [13]) that if the A = ∞ and S < ∞, th...