On the stability of queues with the dropping function.
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 ins...
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Public Library of Science (PLoS)
2021
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oai:doaj.org-article:c24a93aa7cb64173964e3edaa97c05a52021-12-02T20:04:29ZOn the stability of queues with the dropping function.1932-620310.1371/journal.pone.0259186https://doaj.org/article/c24a93aa7cb64173964e3edaa97c05a52021-01-01T00:00:00Zhttps://doi.org/10.1371/journal.pone.0259186https://doaj.org/toc/1932-6203In 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.Andrzej ChydzinskiPublic Library of Science (PLoS)articleMedicineRScienceQENPLoS ONE, Vol 16, Iss 11, p e0259186 (2021) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
Medicine R Science Q |
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Medicine R Science Q Andrzej Chydzinski On the stability of queues with the dropping function. |
| description |
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. |
| format |
article |
| author |
Andrzej Chydzinski |
| author_facet |
Andrzej Chydzinski |
| author_sort |
Andrzej Chydzinski |
| title |
On the stability of queues with the dropping function. |
| title_short |
On the stability of queues with the dropping function. |
| title_full |
On the stability of queues with the dropping function. |
| title_fullStr |
On the stability of queues with the dropping function. |
| title_full_unstemmed |
On the stability of queues with the dropping function. |
| title_sort |
on the stability of queues with the dropping function. |
| publisher |
Public Library of Science (PLoS) |
| publishDate |
2021 |
| url |
https://doaj.org/article/c24a93aa7cb64173964e3edaa97c05a5 |
| work_keys_str_mv |
AT andrzejchydzinski onthestabilityofqueueswiththedroppingfunction |
| _version_ |
1718375566866907136 |