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首页> 外文期刊>Applied Mathematical Modelling >Investigation of the BMAP/G/1 → ·/PH/1/M tandem queue with retrials and losses
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Investigation of the BMAP/G/1 → ·/PH/1/M tandem queue with retrials and losses

机译：BMAP / G / 1→·/ PH / 1 / M串联队列的重试和丢失研究

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摘要

Tandem queues are good models for different fragments of communication systems and networks, so their investigation is interesting for theory and applications. Retrial tandem queues did not get enough attention in literature. In the present paper, the analytic analysis of tandem retrial queue is implemented under general assumptions about the system parameters. Possible correlation and group arrivals are taken into account by means of considering the Batch Markovian Arrival Process (BMAP) as input stream to the system. The service time at the first phase is assumed to be generally distributed and be different for primary and repeated customers. The service time distribution at the second phase is assumed to be of PH (PHase) type. General assumptions about the form of the total retrial intensity are made. The loss of customers, which meet the second phase of the system be full at the service completion at the first phase, is assumed. Markov chain embedded at service completion epochs at the first service phase and the process of system states at arbitrary time are investigated. Probability of immediate access to the first phase of the service and probability of a loss at the second stage are calculated. Numerical illustrations are presented. They illustrate the feasibility of the proposed algorithms and importance of exact account of a nature of the arrival and service processes.
机译：串联队列是通信系统和网络的不同片段的良好模型，因此它们的研究对于理论和应用都很有趣。重审串联队列在文献中没有得到足够的重视。本文在关于系统参数的一般假设下进行了串联重试队列的分析。通过将批马尔可夫到达过程（BMAP）视为系统的输入流，可以考虑可能的相关性和组到达。假定第一阶段的服务时间通常是分布式的，并且对于主要客户和重复客户而言是不同的。假设第二阶段的服务时间分配为PH（PHase）类型。对总重审强度的形式做出一般假设。假定在第一阶段的服务完成时满足系统第二阶段需求的客户流失了。研究了在第一服务阶段在服务完成时期嵌入的马尔可夫链以及任意时间的系统状态过程。计算立即访问服务的第一阶段的可能性和在第二阶段丢失的可能性。给出了数字插图。它们说明了所提出算法的可行性以及准确说明到达和服务过程的性质的重要性。

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  • 来源
    《Applied Mathematical Modelling》 |2010年第10期|p.2926-2940|共15页
  • 作者

    Che Soong Kim; Seog Ha Park; Alexander Dudin; Valentina Klimenok; Gennady Tsarenkov;

  • 作者单位

    Department of Industrial Engineering, Sangji University, Wonju, Kangwon 220-702, Republic of Korea;

    rnDepartment of Industrial Engineering, Sangji University, Wonju, Kangwon 220-702, Republic of Korea;

    rnDepartment of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus;

    rnDepartment of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus;

    rnDepartment of Applied Mathematics and Computer Science, Belarusian State University, 4, Nezavisimosti Ave., 220030 Minsk, Belarus;

  • 收录信息 美国《科学引文索引》(SCI);美国《工程索引》(EI);
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    data-loss queueing networks; batch Markovian arrival process; phase type service; tandem queue; retrial queue;

    机译：数据丢失排队网络;批马尔可夫到达过程;阶段式服务;串联队列;再审队列;

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