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带有丢弃功能的队列稳定性研究。

On the stability of queues with the dropping function.

机构信息

Department of Computer Networks and Systems, Silesian University of Technology, Gliwice, Poland.

出版信息

PLoS One. 2021 Nov 3;16(11):e0259186. doi: 10.1371/journal.pone.0259186. eCollection 2021.

DOI:10.1371/journal.pone.0259186
PMID:34731189
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8565781/
Abstract

In this paper, the stability of the queueing system with the dropping function is studied. In such system, every incoming job may be dropped randomly, with the probability being a function of the queue length. The main objective of the work is to find an easy to use condition, sufficient for the instability of the system, under assumption of Poisson arrivals and general service time distribution. Such condition is found and proven using a boundary for the dropping function and analysis of the embedded Markov chain. Applicability of the proven condition is demonstrated on several examples of dropping functions. Additionally, its correctness is confirmed using a discrete-event simulator.

摘要

本文研究了具有丢弃功能的排队系统的稳定性。在这种系统中，每个到达的作业都可能随机丢弃，丢弃的概率是队列长度的函数。这项工作的主要目的是在泊松到达和一般服务时间分布的假设下，找到一个易于使用的条件，足以保证系统的不稳定性。通过丢弃函数的边界和嵌入式马尔可夫链的分析，找到了并证明了这个条件。对几个丢弃函数的例子进行了证明条件的适用性的演示。此外，还使用离散事件模拟器确认了其正确性。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7c4a/8565781/d71d490812a8/pone.0259186.g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7c4a/8565781/5e00e5d0bf76/pone.0259186.g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7c4a/8565781/70be3728431d/pone.0259186.g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7c4a/8565781/4826f7ab3158/pone.0259186.g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7c4a/8565781/d71d490812a8/pone.0259186.g004.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7c4a/8565781/5e00e5d0bf76/pone.0259186.g001.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7c4a/8565781/70be3728431d/pone.0259186.g002.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7c4a/8565781/4826f7ab3158/pone.0259186.g003.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/7c4a/8565781/d71d490812a8/pone.0259186.g004.jpg

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本文引用的文献

1
Queues with the dropping function and general service time.带有降服务时间功能的队列。
PLoS One. 2019 Jul 17;14(7):e0219444. doi: 10.1371/journal.pone.0219444. eCollection 2019.
2
Queues with Dropping Functions and General Arrival Processes.具有丢弃功能和一般到达过程的队列
PLoS One. 2016 Mar 4;11(3):e0150702. doi: 10.1371/journal.pone.0150702. eCollection 2016.