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Heavy traffic limits for queues with non-stationary path-dependent arrival processes
In this paper, we develop a diffusion approximation for the transient distribution of the workload process in a standard single-server queue with a non-stationary Polya arrival process, which is a path-dependent Markov point process. The path-dependent arrival process model is useful because it has...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2022
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8923602/ https://www.ncbi.nlm.nih.gov/pubmed/35310891 http://dx.doi.org/10.1007/s11134-021-09728-5 |
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author | Fendick, Kerry Whitt, Ward |
author_facet | Fendick, Kerry Whitt, Ward |
author_sort | Fendick, Kerry |
collection | PubMed |
description | In this paper, we develop a diffusion approximation for the transient distribution of the workload process in a standard single-server queue with a non-stationary Polya arrival process, which is a path-dependent Markov point process. The path-dependent arrival process model is useful because it has the arrival rate depending on the history of the arrival process, thus capturing a self-reinforcing property that one might expect in some applications. The workload approximation is based on heavy-traffic limits for (i) a sequence of Polya processes, in which the limit is a Gaussian–Markov process, and (ii) a sequence of P/GI/1 queues in which the arrival rate function approaches a constant service rate uniformly over compact intervals. |
format | Online Article Text |
id | pubmed-8923602 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2022 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-89236022022-03-16 Heavy traffic limits for queues with non-stationary path-dependent arrival processes Fendick, Kerry Whitt, Ward Queueing Syst Article In this paper, we develop a diffusion approximation for the transient distribution of the workload process in a standard single-server queue with a non-stationary Polya arrival process, which is a path-dependent Markov point process. The path-dependent arrival process model is useful because it has the arrival rate depending on the history of the arrival process, thus capturing a self-reinforcing property that one might expect in some applications. The workload approximation is based on heavy-traffic limits for (i) a sequence of Polya processes, in which the limit is a Gaussian–Markov process, and (ii) a sequence of P/GI/1 queues in which the arrival rate function approaches a constant service rate uniformly over compact intervals. Springer US 2022-03-15 2022 /pmc/articles/PMC8923602/ /pubmed/35310891 http://dx.doi.org/10.1007/s11134-021-09728-5 Text en © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2022 This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic. |
spellingShingle | Article Fendick, Kerry Whitt, Ward Heavy traffic limits for queues with non-stationary path-dependent arrival processes |
title | Heavy traffic limits for queues with non-stationary path-dependent arrival processes |
title_full | Heavy traffic limits for queues with non-stationary path-dependent arrival processes |
title_fullStr | Heavy traffic limits for queues with non-stationary path-dependent arrival processes |
title_full_unstemmed | Heavy traffic limits for queues with non-stationary path-dependent arrival processes |
title_short | Heavy traffic limits for queues with non-stationary path-dependent arrival processes |
title_sort | heavy traffic limits for queues with non-stationary path-dependent arrival processes |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8923602/ https://www.ncbi.nlm.nih.gov/pubmed/35310891 http://dx.doi.org/10.1007/s11134-021-09728-5 |
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