Abstract: In this paper, we study the performance of the strong
stability method of the univariate classical risk model. We interest to
the stability bounds established using two approaches. The first based
on the strong stability method developed for a general Markov chains.
The second approach based on the regenerative processes theory . By
adopting an algorithmic procedure, we study the performance of the
stability method in the case of exponential distribution claim amounts.
After presenting numerically and graphically the stability bounds, an
interpretation and comparison of the results have been done.
Abstract: We present a new numerical method for the computation of the steady-state solution of Markov chains. Theoretical analyses show that the proposed method, with a contraction factor α, converges to the one-dimensional null space of singular linear systems of the form Ax = 0. Numerical experiments are used to illustrate the effectiveness of the proposed method, with applications to a class of interesting models in the domain of tandem queueing networks.
Abstract: In the queueing theory, it is assumed that customer
arrivals correspond to a Poisson process and service time has the
exponential distribution. Using these assumptions, the behaviour of
the queueing system can be described by means of Markov chains
and it is possible to derive the characteristics of the system. In the
paper, these theoretical approaches are presented on several types of
systems and it is also shown how to compute the characteristics in a
situation when these assumptions are not satisfied