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Retrial queue with discipline of adaptive permanent pooling

机译：具有自适应永久池规则的重试队列

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摘要

A novel customer service discipline for a single-server retrial queue is proposed and analysed. Arriving customers are accumulated in a pool of finite capacity. Customers arriving when the pool is full go into orbit and attempt to access the service later. It is assumed that customers access the service as a group. The size of the group is defined by the number of customers in the pool at the instant the service commences. All customers within a group finish receiving the service simultaneously. If the pool is full at the point the service finishes, a new service begins immediately and all customers from the pool begin to be served. Otherwise, the customer admission period starts. The duration of this period is random and depends on the number of customers in the pool when the admission period begins. However, if the pool becomes full before the admission period expires, this period is terminated and a new service begins. The system behaviour is described by a multi-dimensional Markov chain. The generator and the condition of ergodicity of this Markov chain are derived, and an algorithm for computing the stationary probability distribution of the states of the Markov chain is given. Formulas for computing various performance measures of the system are presented, and the results of numerical experiments show that these measures essentially depend on the capacity of the pool and the distribution of the duration of the admission period. The advantages of the proposed customer service discipline over the classical discipline and the discipline in which customers cannot enter the pool during the service period are illustrated numerically.
机译：提出并分析了一种针对单服务器重试队列的新颖的客户服务准则。到达的客户积累在有限的容量池中。池满时到达的客户进入轨道，并稍后尝试访问该服务。假定客户以组的形式访问服务。组的大小由服务开始时池中的客户数量定义。组中的所有客户同时完成接收服务。如果池在服务结束时已满，则将立即开始一项新服务，并开始为池中的所有客户提供服务。否则，客户进入期开始。该时间段的持续时间是随机的，并且取决于入场时间开始时池中的客户数量。但是，如果在准入期限到期之前池已满，则该期限将终止并开始新的服务。系统行为由多维马尔可夫链描述。推导了该马尔可夫链的生成器和遍历条件，并给出了计算马尔可夫链状态平稳概率分布的算法。给出了计算系统各种性能指标的公式，数值实验结果表明，这些指标基本上取决于池的容量和准入期持续时间的分布。用数字方式说明了拟议的客户服务学科相对于经典学科以及客户在服务期间无法进入池中的学科的优势。

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  • 来源
    《Applied Mathematical Modelling》 |2017年第10期|1-16|共16页
  • 作者

    Brugno Arianna; Dudin A. N.; Manzo Rosanna;

  • 作者单位

    Department of Information Engineering, Electrical Engineering and Applied Mathematics, University of Salerno, Via Giovanni Paolo II, 132, Fisciano, SA, Italy;

    Belarusian State University, 4, Nezavisimosti Ave., Minsk, Belarus,Peoples Friendship University of Russia, 6, Miklukho-Maklaya st., Moscow, Russian Federation;

    Department of Information Engineering, Electrical Engineering and Applied Mathematics, University of Salerno, Via Giovanni Paolo II, 132, Fisciano, SA, Italy;

  • 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

    Group service; Optimization; Permanent pooling; Retrial queueing system; Stationary distribution;

    机译：团体服务;优化;永久池;重试排队系统;固定分配;

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