Séminaire Mathématique de Béjaia
Volume 16, Numéro 1, Pages 82-82
2018-12-31
Queuing System Equivalent To The Two-dimensional Classical Risk Model: Numerical Approach
Authors : Hocine Safia . Benouaret Zina . Aïssani Djamil .
Abstract
The general concept of stability for the stochastic models has been proposed by V. Zolotarev. By using this concept, several problems of queuing theory and characterization of distributions of probability have been solved. The stability method allows to delineate the domain in which the ideal model can be used as a good approximation of the real system. Among the methods developed on the stability of stochastic models we can find the strong stability method, also named the operators method of stability theory. It was introduced in the early eighties. This method is applicable to all stochastic models that can be governed by a homogeneous Markov chain. The strong stability method has a very wide field of application in queuing theory, in risk theory this method is recently used especially in the case of a two-dimensional risk model. Compared to other approaches, the strong stability method re- quires that the disruption of the transition kernel be small compared to a certain operator norm. In other words, a small deviation of the model parameters leads to a small deviation of its characteristics. This condition, which is much stricter than the usual conditions, makes it possible to obtain essentially a good approximation for perturbed stationary distribution. Moreover, on the basis of this method (strong stability), it is possible to obtain an asymptotic decomposition for the stationary characteristics of the disturbed chains. In this work, we study the interaction between two-dimensional risk model and a specific queuing system. The aim of this study is to determine the strong stability inequalities for the stationary distribution of the wait time by using the interaction between risk theory and queuing system theory. In other words, the aim is to trans- late the strong stability inequalities obtained in a two-dimensional risk model in order to estimate the deviation of the stationary distribution of the waiting time.
Keywords
Markov chain; Queuing system; Risk models; Ruin probability; Stationary distribution; Strong stability.
Les articles similaires
Cheniguel A
.
pages 19-24.
A. Brezini
.
M. Sebbani
.
pages 52-55.
A. Brezini
.
M. Sebbani
.
pages 56-61.
Taibi Boumedyen
.
Tahi Abderrahmane
.
Djebouri Mohamed
.
pages 1-15.
