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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (4): 507-516.doi: 10.3969/j.issn.1005-3085.2015.04.004

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基于非强占型优先权的MAP$_{1}$, MAP$_{2}/M/c/N$重试排队模型

周宗好1,   周甄川1,   朱翼隽2,   石志岩2   

  1. 1- 黄山学院数学与统计学院，安徽 黄山 245041
    2- 江苏大学理学院，江苏 镇江 212013
  • 收稿日期:2014-01-17 接受日期:2014-07-03 出版日期:2015-08-15 发布日期:2015-10-15
  • 基金资助:
    国家自然科学基金 (11226210)；安徽省高校优秀青年人才基金重点项目 (2013SQRL087ZD)；黄山学院科研启动项目 (2014xkjq006).

MAP$_{1}$, MAP$_{2}/M/c/N$ Retrial Queueing Model with Non-preemptive Priority

ZHOU Zong-hao1,   ZHOU Zhen-chuan1,   ZHU Yi-jun2,   SHI Zhi-yan2   

  1. 1- School of Mathematics and Statistics, Huangshan University, Huangshan, Anhui 245041
    2- Faculty of Science, Jiangsu University, Zhenjiang, Jiangsu 212013
  • Received:2014-01-17 Accepted:2014-07-03 Online:2015-08-15 Published:2015-10-15
  • Supported by:
    The National Natural Science Foundation of China (11226210); the Key Project of Anhui Province College Fund for Outstanding Young Talent (2013SQRL087ZD); the Fundamental Research Funds for the Huangshan University (2014xkjq006).

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摘要： 为了研究优先权排队策略和不同类型的顾客到达流对广泛应用于通信网络的重试排队模型的排队指标的影响，本文建立了具有非强型优先权顾客的重试排队模型，研究了普通顾客和优先权顾客的到达过程是不同到达率的Markov到达过程．利用拟生灭过程和矩阵分析法求出了系统稳态的充要条件及模型的各项排队指标．通过数值模拟发现Markov到达流相比较Poison流更容易引起系统的拥塞，优先权顾客的到达率增加相比较普通顾客更容易引起系统拥塞等结论．

关键词: 排队模型, 重试, 非强占型优先权, 排队指标

Abstract:

In order to study the influence of the priority queueing policy and different types of input flows on the retrial queueing model indexes in communication networks, this paper constructs a retrial queueing model with non-preemptive priority in which arrival processes of ordinary and priority customers are different arrival rate Markov processes. The main queueing indexes and system steady state condition of the system are derived by the quasi birth-and-death process and matrix analysis. By means of numerical simulation, we found that Markov arrival input flows are more likely to lead to congestion of the system than Poison input flows do, and the priory customer arrival rate is more likely to lead to congestion of the system than the ordinary customers do.

Key words: queueing model, retrial, non-preemptive priority, queueing indexes

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