Stochastic interpretation for a single server retrial queue with Bernoulli feedback and negative customers  

作　　者：Mohamed Boualem Amina Angelika Bouchentouf Aicha Bareche Mouloud Cherfaoui 

机构地区：[1]Research Unit LaMOS(Modeling and Optimization of Systems),Faculty of Technology,University of Bejaia,06000 Bejaia,Algeria [2]Laboratory of Mathematics,Djillali Liabes University of Sidi Bel Abbes,B.P.89,Sidi Bel Abbes 22000,Algeria [3]Research Unit LaMOS(Modeling and Optimization of Systems),University of Bejaia,06000 Bejaia,Algeria

出　　处：《Applied Mathematics(A Journal of Chinese Universities)》2025年第1期1-19,共19页高校应用数学学报(英文版)(B辑)

摘　　要：In this paper,we introduce a qualitative analysis in order to study the monotonicity and comparability properties of a single-server retrial queueing model with Bernoulli feedback and negative customers,relative to stochastic orderings.Performance measures of such a system are available explicitly,while their forms are cumbersome(these formulas include integrals of Laplace transform,solutions of functional equations,etc.).Therefore,they are not exploitable from the application point of view.To overcome these difficulties,we present stochastic comparison methods in order to get qualitative estimates of these measures.In particular,we prove the monotonicity of the transition operator of the embedded Markov chain.In addition,we establish conditions for which transition operators as well as stationary probabilities,associated with two embedded Markov chains,having the same structure but with different parameters,are comparable relative to the given stochastic orderings.Further,numerical examples are carried out to illustrate the theoretical results.

关 键 词：retrial queueing models negative arrivals stochastic orderings MONOTONICITY SIMULATION 

分 类 号：O17[理学—数学]