Analysis of queueing system with discrete autoregressive arrivals having DML as marginal distribution
In this paper we analyze DAR(1)/D/s Queue with Discrete Mittag-Leffler [DML(α)] as marginal distribution. Simulation study of the sample path of the arrival process is conducted. For this queueing system, the stationary distribution of the system size and the waiting time distribution of an arbitrar...
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ftdoajarticles:oai:doaj.org/article:13c7a775620c41d899abd390484b8822 2023-05-15T16:01:21+02:00 Analysis of queueing system with discrete autoregressive arrivals having DML as marginal distribution Bindu Abraham Kanichukattu Korakutty Jose 2014-05-01T00:00:00Z https://doi.org/10.6092/issn.1973-2201/4327 https://doaj.org/article/13c7a775620c41d899abd390484b8822 EN eng University of Bologna http://rivista-statistica.unibo.it/article/view/4327 https://doaj.org/toc/0390-590X https://doaj.org/toc/1973-2201 0390-590X 1973-2201 doi:10.6092/issn.1973-2201/4327 https://doaj.org/article/13c7a775620c41d899abd390484b8822 Statistica, Vol 73, Iss 3, Pp 317-339 (2014) Discrete Autoregressive process of order 1[DAR(1)] Discrete Mittag-Leer distribution (DML) multiserver queue ATM multiplexer Matrix analytic methods Statistics HA1-4737 article 2014 ftdoajarticles https://doi.org/10.6092/issn.1973-2201/4327 2022-12-31T09:20:17Z In this paper we analyze DAR(1)/D/s Queue with Discrete Mittag-Leffler [DML(α)] as marginal distribution. Simulation study of the sample path of the arrival process is conducted. For this queueing system, the stationary distribution of the system size and the waiting time distribution of an arbitrary packet is obtained with the help of matrix analytic methods and Markov regenerative theory. The quantitative effect of the stationary distribution on system size, waiting time and the autocorrelation function as well as the parameters of the input traffic is illustrated empirically. The model is applied to a real data on the passenger arrivals at a subway bus terminal in Santiago de Chile and is established that the model well suits this data. Article in Journal/Newspaper DML Directory of Open Access Journals: DOAJ Articles |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Discrete Autoregressive process of order 1[DAR(1)] Discrete Mittag-Leer distribution (DML) multiserver queue ATM multiplexer Matrix analytic methods Statistics HA1-4737 |
spellingShingle |
Discrete Autoregressive process of order 1[DAR(1)] Discrete Mittag-Leer distribution (DML) multiserver queue ATM multiplexer Matrix analytic methods Statistics HA1-4737 Bindu Abraham Kanichukattu Korakutty Jose Analysis of queueing system with discrete autoregressive arrivals having DML as marginal distribution |
topic_facet |
Discrete Autoregressive process of order 1[DAR(1)] Discrete Mittag-Leer distribution (DML) multiserver queue ATM multiplexer Matrix analytic methods Statistics HA1-4737 |
description |
In this paper we analyze DAR(1)/D/s Queue with Discrete Mittag-Leffler [DML(α)] as marginal distribution. Simulation study of the sample path of the arrival process is conducted. For this queueing system, the stationary distribution of the system size and the waiting time distribution of an arbitrary packet is obtained with the help of matrix analytic methods and Markov regenerative theory. The quantitative effect of the stationary distribution on system size, waiting time and the autocorrelation function as well as the parameters of the input traffic is illustrated empirically. The model is applied to a real data on the passenger arrivals at a subway bus terminal in Santiago de Chile and is established that the model well suits this data. |
format |
Article in Journal/Newspaper |
author |
Bindu Abraham Kanichukattu Korakutty Jose |
author_facet |
Bindu Abraham Kanichukattu Korakutty Jose |
author_sort |
Bindu Abraham |
title |
Analysis of queueing system with discrete autoregressive arrivals having DML as marginal distribution |
title_short |
Analysis of queueing system with discrete autoregressive arrivals having DML as marginal distribution |
title_full |
Analysis of queueing system with discrete autoregressive arrivals having DML as marginal distribution |
title_fullStr |
Analysis of queueing system with discrete autoregressive arrivals having DML as marginal distribution |
title_full_unstemmed |
Analysis of queueing system with discrete autoregressive arrivals having DML as marginal distribution |
title_sort |
analysis of queueing system with discrete autoregressive arrivals having dml as marginal distribution |
publisher |
University of Bologna |
publishDate |
2014 |
url |
https://doi.org/10.6092/issn.1973-2201/4327 https://doaj.org/article/13c7a775620c41d899abd390484b8822 |
genre |
DML |
genre_facet |
DML |
op_source |
Statistica, Vol 73, Iss 3, Pp 317-339 (2014) |
op_relation |
http://rivista-statistica.unibo.it/article/view/4327 https://doaj.org/toc/0390-590X https://doaj.org/toc/1973-2201 0390-590X 1973-2201 doi:10.6092/issn.1973-2201/4327 https://doaj.org/article/13c7a775620c41d899abd390484b8822 |
op_doi |
https://doi.org/10.6092/issn.1973-2201/4327 |
_version_ |
1766397255232782336 |