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Strategic timing of arrivals to a finite queue multi-server loss system

机译:到达有限队列多服务器损失系统的战略时机

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摘要

We provide Game-theoretic analysis of the arrival process to a multi-server system with a limited queue buffer, which admits customers only during a finite time interval. A customer who arrives at a full system is blocked and does not receive service. Customers can choose their arrival times with the goal of minimizing their probability of being blocked. We characterise the unique symmetric Nash equilibrium arrival distribution and present a method for computing it. This distribution is comprised of an atom at time zero, an interval with no arrivals (a gap), and a continuous distribution until the closing time. We further present a fluid approximation for the equilibrium behaviour when the population is large, where the fluid solution also admits an atom at zero, no gap, and a uniform distribution throughout the arrival interval. In doing so, we provide an approximation model for the equilibrium behaviour that does not require a numerical solution for a set of differential equations, as is required in the discrete case. For the corresponding problem of social optimization, we provide explicit analysis of some special cases and numerical analysis of the general model. An upper bound is established for the price of anarchy (PoA). The PoA is shown to be not monotone with respect to population size.
机译:我们向具有有限队列缓冲区的多服务器系统提供到达过程的博弈论分析,该系统仅在有限的时间间隔内允许客户进入。到达完整系统的客户被阻止,无法获得服务。客户可以选择到达时间,以最大程度地降低被阻止的可能性。我们表征了唯一的对称纳什均衡到达分布,并提出了一种计算方法。该分布由时间为零的原子,无到达间隔(间隔)和直到关闭时间的连续分布组成。当总体较大时,我们进一步给出了平衡行为的流体近似,其中流体溶液还允许原子为零,无间隙且在整个到达间隔内分布均匀。这样,我们提供了一种平衡行为的近似模型,该模型不需要离散方程组所需的一组微分方程的数值解。对于相应的社会优化问题,我们提供了一些特殊情况的显式分析和通用模型的数值分析。建立了无政府状态价格(PoA)的上限。关于人口规模,证明PoA不是单调的。

著录项

  • 来源
    《Queueing systems》 |2015年第1期|71-96|共26页
  • 作者

    Moshe Haviv; Liron Ravner;

  • 作者单位

    Department of Statistics and the Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem, Jerusalem, Israel;

    Department of Statistics and the Federmann Center for the Study of Rationality, The Hebrew University of Jerusalem, Jerusalem, Israel;

  • 收录信息
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    Queueing games; Loss queues; Transient queues; Strategic arrival times;

    机译:排队游戏;损失队列;临时队列;战略到达时间;

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