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暂时的GI/MSP/1/N队列

Andrzej Chydzinski¹

¹Department of Computer Networks and Systems, Silesian University of Technology, Akademicka 16, 44-100 Gliwice, Poland.

Entropy (Basel, Switzerland)

|September 27, 2024

概括

本研究分析了使用马科维服务过程 (MSP) 相关服务时间的系统中的队列长度. 我们为队列长度分布和随时间推移的平均队列长度提供定理和示例.

科学领域:

运营研究运营研究
应用概率学应用概率学

背景情况:

现实世界排队系统通常在服务时间中表现出非零的相关性.
马科维服务过程 (MSP) 是一种可操作的模型,用于关联的服务时间,提供强大的装配能力.

研究的目的:

在排队模型中对队列长度进行过渡性分析,使用MSP服务和一般到达间隔时间.
证明有关队列长度分布和在任意时间t.的平均队列长度的定理.
为了说明在不同条件下队列长度指标的动态行为.

主要方法:

开发结合马科维亚服务流程的排队模型.
对队列长度分布和平均队列长度的定理的分析推导.
数字模拟来证明短暂的队列长度行为.

主要成果:

建立了两个定理:一个用于时间 t 的队列长度分布,另一个用于时间 t 的平均队列长度.
数字示例展示了平均队列长度,标准偏差和完整分布的演变.
服务相关性强度,初始条件和到达间时间差异对队列动态的影响得到说明.

结论:

该研究提供了理论框架和对与服务时间相关联的排队系统的实际见解.
这些发现适用于优化各种排队场景中的性能,其服务时间非指数.
马科夫服务过程证明有效地分析了短暂的队列长度动态.

关键词:

在GI/MSP/1/N队列中马尔科维亚服务流程相关的服务时间与服务时间相关.排队的平均长度是队列长度分布队列长度分布单个服务器排队过渡性分析是一种过渡性分析.

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