Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue

This paper compares two discrete-time single-server queueing models with two queues. In both models, the server is available to a queue with probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for the joint moments is not feasible, we rely on a heavy-traffic lim...

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Autores principales:	Arnaud Devos, Joris Walraevens, Dieter Fiems, Herwig Bruneel
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	queueing theory discrete-time server-sharing scheduling heavy-traffic boundary value problems Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/351d964fe4ae492fa0d61fa5998bf363
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spelling	oai:doaj.org-article:351d964fe4ae492fa0d61fa5998bf3632021-11-11T18:16:40ZHeavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue10.3390/math92127232227-7390https://doaj.org/article/351d964fe4ae492fa0d61fa5998bf3632021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2723https://doaj.org/toc/2227-7390This paper compares two discrete-time single-server queueing models with two queues. In both models, the server is available to a queue with probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for the joint moments is not feasible, we rely on a heavy-traffic limit approach. The correlation coefficient of the queue-contents is computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a hyperbola. In most server-sharing models, it is assumed that the system is work-conserving in the sense that if one of the queues is empty, a customer of the other queue is served with probability 1. In our second model, we omit this work-conserving rule such that the server can be idle in case of a non-empty queue. Contrary to what we would expect, the resulting heavy-traffic approximations reveal that both models remain different for critically loaded queues.Arnaud DevosJoris WalraevensDieter FiemsHerwig BruneelMDPI AGarticlequeueing theorydiscrete-timeserver-sharingschedulingheavy-trafficboundary value problemsMathematicsQA1-939ENMathematics, Vol 9, Iss 2723, p 2723 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	queueing theory discrete-time server-sharing scheduling heavy-traffic boundary value problems Mathematics QA1-939
spellingShingle	queueing theory discrete-time server-sharing scheduling heavy-traffic boundary value problems Mathematics QA1-939 Arnaud Devos Joris Walraevens Dieter Fiems Herwig Bruneel Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue
description	This paper compares two discrete-time single-server queueing models with two queues. In both models, the server is available to a queue with probability 1/2 at each service opportunity. Since obtaining easy-to-evaluate expressions for the joint moments is not feasible, we rely on a heavy-traffic limit approach. The correlation coefficient of the queue-contents is computed via the solution of a two-dimensional functional equation obtained by reducing it to a boundary value problem on a hyperbola. In most server-sharing models, it is assumed that the system is work-conserving in the sense that if one of the queues is empty, a customer of the other queue is served with probability 1. In our second model, we omit this work-conserving rule such that the server can be idle in case of a non-empty queue. Contrary to what we would expect, the resulting heavy-traffic approximations reveal that both models remain different for critically loaded queues.
format	article
author	Arnaud Devos Joris Walraevens Dieter Fiems Herwig Bruneel
author_facet	Arnaud Devos Joris Walraevens Dieter Fiems Herwig Bruneel
author_sort	Arnaud Devos
title	Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue
title_short	Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue
title_full	Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue
title_fullStr	Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue
title_full_unstemmed	Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue
title_sort	heavy-traffic comparison of a discrete-time generalized processor sharing queue and a pure randomly alternating service queue
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/351d964fe4ae492fa0d61fa5998bf363
work_keys_str_mv	AT arnauddevos heavytrafficcomparisonofadiscretetimegeneralizedprocessorsharingqueueandapurerandomlyalternatingservicequeue AT joriswalraevens heavytrafficcomparisonofadiscretetimegeneralizedprocessorsharingqueueandapurerandomlyalternatingservicequeue AT dieterfiems heavytrafficcomparisonofadiscretetimegeneralizedprocessorsharingqueueandapurerandomlyalternatingservicequeue AT herwigbruneel heavytrafficcomparisonofadiscretetimegeneralizedprocessorsharingqueueandapurerandomlyalternatingservicequeue
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Heavy-Traffic Comparison of a Discrete-Time Generalized Processor Sharing Queue and a Pure Randomly Alternating Service Queue

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