A single-server discrete-time queue with correlated positive and negative customer arrivals

被引：15

作者：

Wang, Jinting ^{[1
]}

Huang, Yunbo ^{[1
]}

Tien Van Do ^{[2
,3
]}

机构：

[1] Beijing Jiaotong Univ, Dept Math, Beijing 100044, Peoples R China

[2] Budapest Univ Technol & Econ, Dept Networked Syst & Serv, MTA BME Informat Syst Res Grp, H-117 Budapest, Hungary

[3] Budapest Univ Technol & Econ, Interuniv Ctr Telecommun & Informat, H-4028 Debrecen, Hungary

来源：

APPLIED MATHEMATICAL MODELLING | 2013年 / 37卷 / 09期

基金：

中国国家自然科学基金;

关键词：

Discrete-time queue; Correlated arrivals; MMBP; Negative customers; Generating function; G-NETWORKS; GEO/GEO/1; QUEUE; SIGNALS;

D O I：

10.1016/j.apm.2012.12.021

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

An MMBP/Geo/1 queue with correlated positive and negative customer arrivals is studied. In the infinite-capacity queueing system, positive customers and negative customers are generated by a Bernoulli bursty source with two correlated geometrically distributed periods. I.e., positive and negative customers arrive to the system according to two different geometrical arrival processes. Under the late arrival scheme (LAS), two removal disciplines caused by negative customers are investigated in the paper. In individual removal scheme, a negative customer removes a positive customer in service if any, while in disaster model, a negative customer removes all positive customers in the system if any. The negative customer arrival has no effect on the system if it finds the system empty. We analyze the Markov chains underlying the queueing systems and evaluate the performance of two systems based on generating functions technique. Some explicit solutions of the system, such as the average buffer content and the stationary probabilities are obtained. Finally, the effect of several parameters on the system performance is shown numerically. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：6212 / 6224

页数：13

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