On the stability of queues with the dropping function | Zendy

Andrzej Chydziński | Zendy

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On the stability of queues with the dropping function

Author(s) -

Andrzej Chydziński

Publication year - 2021

Publication title -

plos one

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.99

H-Index - 332

ISSN - 1932-6203

DOI - 10.1371/journal.pone.0259186

Subject(s) - queue , correctness , markov chain , poisson distribution , computer science , queueing theory , function (biology) , stability (learning theory) , probability generating function , discrete event simulation , event (particle physics) , boundary (topology) , mathematics , probability distribution , mathematical optimization , probability mass function , algorithm , simulation , statistics , physics , mathematical analysis , computer network , quantum mechanics , machine learning , evolutionary biology , biology

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.

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