A Single-server Discrete-time Retrial G-queue with Server Breakdowns and Repairs  

作　　者：Jin-ting Wang Peng Zhang 

机构地区：[1]Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China [2]Qingdao Branch, The Bank of Communication, Qingdao 266001, China

出　　处：《Acta Mathematicae Applicatae Sinica》2009年第4期675-684,共10页应用数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(No.10871020)

摘　　要：This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals. The arrival of a negative customer causes one positive customer to be killed if any is present, and simultaneously breaks the server down. The server is sent to repair immediately and after repair it is as good as new. The negative customer also causes the server breakdown if the server is found idle, but has no effect on the system if the server is under repair. We analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating function of the number of customers in the orbit and in the system are also obtained, along with the marginal distributions of the orbit size when the server is idle, busy or down. Finally, we present some numerical examples to illustrate the influence of the parameters on several performance characteristics of the system.This paper concerns a discrete-time Geo/Geo/1 retrial queue with both positive and negative customers where the server is subject to breakdowns and repairs due to negative arrivals. The arrival of a negative customer causes one positive customer to be killed if any is present, and simultaneously breaks the server down. The server is sent to repair immediately and after repair it is as good as new. The negative customer also causes the server breakdown if the server is found idle, but has no effect on the system if the server is under repair. We analyze the Markov chain underlying the queueing system and obtain its ergodicity condition. The generating function of the number of customers in the orbit and in the system are also obtained, along with the marginal distributions of the orbit size when the server is idle, busy or down. Finally, we present some numerical examples to illustrate the influence of the parameters on several performance characteristics of the system.

关 键 词：Discrete-time retrial queue G-queue Markov chain unreliable server 

分 类 号：TP271.8[自动化与计算机技术—检测技术与自动化装置] TP368.5[自动化与计算机技术—控制科学与工程]