We consider the stationary distribution of the M/GI/1 type queue when background states are countable. We are interested in its tail behavior. To this end, we derive a Markov renewal equation for characterizing the stationary distribution using a Markov additive process that describes the number of customers in system when the system is not empty. Variants of this Markov renewal equation are al...

Abstract The presented work summarizes the relationships between stability results and separation theorems. We prove equivalence different types of theorems on by an additive map concerning Cauchy functional equation.

Luce and Marley [2005. Ranked additive utility representations of gambles: Old and new axiomatizations. Journal of Risk and Uncertainty, 30, 21–62] examined various relations between mathematical forms for the utility of joint receipt of gambles and for the utility of uncertain gambles. Their assumptions lead to a bisymmetry functional equation which, when the gambles are ranked, is defined on ...

in  this paper, we investigate the generalizedhyers-ulam-rassias stability for the quartic, cubic and additivefunctional equation$$f(x+ky)+f(x-ky)=k^2f(x+y)+k^2f(x-y)+(k^2-1)[k^2f(y)+k^2f(-y)-2f(x)]$$ ($k in mathbb{z}-{0,pm1}$) in $p-$banach spaces.

This paper shows how to calculate solutions to Poisson's equation for the waiting time sequence of the recurrent M/G/1 queue. The solutions are used to construct martingales that permit us to study additive functionals associated with the waiting time sequence. These martingales provide asymptotic expressions, for the mean of additive functionals, that reeect dependence on the initial state of ...

The purpose of this paper is to solve the seventh-order functional equation as follows:  --------------------------- Next, we study the stability of this type of functional equation. Clearly, the function ----------  holds in this type functional equation. Also, we prove Hyers-Ulam stability for this type functional equation in the β-Gaussian Banach space.