Open AccessOn 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 , queueing theory , computer science , function (biology) , stability (learning theory) , probability generating function , event (particle physics) , discrete event simulation , mathematics , boundary (topology) , probability distribution , mathematical optimization , probability mass function , simulation , algorithm , 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.