Discrete-time GGI/GG/1 Retrial Queues with Time-controlled Vacation Policies

作     者：Jin-ting WANG Nan WANG Attahiru S.ALFA 

作者机构：Department of MathematicsBeijing Jiaotong University Department of Electrical and Computer EngineeringUniversity of Manitoba 

出 版 物：《Acta Mathematicae Applicatae Sinica》 (应用数学学报（英文版）)

年 卷 期：2013年第29卷第4期

页      面：689-704页

核心收录：

学科分类：0711[理学-系统科学] 12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 08[工学] 070105[理学-运筹学与控制论] 081101[工学-控制理论与控制工程] 071101[理学-系统理论] 0811[工学-控制科学与工程] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Grant Nos.10871020 and 11171019) Program for New Century Excellent Talents in University(No.NCET-11-0568) the Fundamental Research Funds for the Central Universities(Nos.2011JBZ012 and 2013JBZ019) 

主　　题：discrete queues retrial queues time-controlled vacations early and late arrival systems matrixanalytic method 

摘      要：A discrete-time GI/G/1 retrial queue with Bernoulli retrials and time-controlled vacation policies is investigated in this paper. By representing the inter-arrival, service and vacation tlmes using a Markov-based approach, we are able to analyze this model as a level-dependent quasi-birth-and-death （LDQBD） process which makes the model algorithmically tractable. Several performance measures such as the stationary probability distribution and the expected number of customers in the orbit have been discussed with two different policies： deterministic time-controlled system and random time-controlled system. To give a comparison with the known vacation policy in the literature, we present the exhaustive vacation policy as a contrast between these policies under the early arrival system （EAS） and the late arrival system with delayed access （LAS-DA）. Significant difference between EAS and LAS-DA is illustrated by some numerical examples.