Scheduling in a random environment: stability and asymptotic optimality

Autores
Ayesta, U.; Erauskin, M.; Jonckheere, Matthieu Thimothy Samson; Verloop, M.
Año de publicación
2013
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We investigate the scheduling of a common resource between several concurrent users when the feasible transmission rate of each user varies randomly over time. Time is slotted and users arrive and depart upon service completion. This may model for example the flow-level behavior of end-users in a narrowband HDR wireless channel (CDMA 1xEV-DO). As performance criteria we consider the stability of the system and the mean delay experienced by the users. Given the complexity of the problem we investigate the fluid-scaled system, which allows to obtain important results and insights for the original system: (1) We characterize for a large class of scheduling policies the stability conditions and identify a set of maximum stable policies, giving in each time slot preference to users being in their best possible channel condition. We find in particular that many opportunistic scheduling policies like Score-Based [8], Proportionally Best [1] or Potential Improvement [4] are stable under the maximum stability conditions, whereas the opportunistic scheduler Relative-Best [9] or the c-rule are not. (2) We show that choosing the right tie-breaking rule is crucial for the performance (e.g. average delay) as perceived by a user. We prove that a policy is asymptotically optimal if it is maximum stable and the tie-breaking rule gives priority to the user with the highest departure probability. We will refer to such tiebreaking rule as myopic. (3) We derive the growth rates of the number of users in the system in overload settings under various policies, which give additional insights on the performance. (4) We conclude that simple priority-index policies with the myopic tie-breaking rule, are stable and asymptotically optimal. All our findings are validated with extensive numerical experiments.
Fil: Ayesta, U.. Basque Center for Applied Mathematics; España
Fil: Erauskin, M.. Basque Center for Applied Mathematics; España. Basque Foundation for Science; España. Universidad del Pais Vasco; España
Fil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina
Fil: Verloop, M.. Basque Center for Applied Mathematics; España
Materia
Fluid limits
Performance evaluation
Stability analysis
Cellular ireless systems
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/14846
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/14846
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Scheduling in a random environment: stability and asymptotic optimalityAyesta, U.Erauskin, M.Jonckheere, Matthieu Thimothy SamsonVerloop, M.Fluid limitsPerformance evaluationStability analysisCellular ireless systemshttps://purl.org/becyt/ford/1.1https://purl.org/becyt/ford/1We investigate the scheduling of a common resource between several concurrent users when the feasible transmission rate of each user varies randomly over time. Time is slotted and users arrive and depart upon service completion. This may model for example the flow-level behavior of end-users in a narrowband HDR wireless channel (CDMA 1xEV-DO). As performance criteria we consider the stability of the system and the mean delay experienced by the users. Given the complexity of the problem we investigate the fluid-scaled system, which allows to obtain important results and insights for the original system: (1) We characterize for a large class of scheduling policies the stability conditions and identify a set of maximum stable policies, giving in each time slot preference to users being in their best possible channel condition. We find in particular that many opportunistic scheduling policies like Score-Based [8], Proportionally Best [1] or Potential Improvement [4] are stable under the maximum stability conditions, whereas the opportunistic scheduler Relative-Best [9] or the c-rule are not. (2) We show that choosing the right tie-breaking rule is crucial for the performance (e.g. average delay) as perceived by a user. We prove that a policy is asymptotically optimal if it is maximum stable and the tie-breaking rule gives priority to the user with the highest departure probability. We will refer to such tiebreaking rule as myopic. (3) We derive the growth rates of the number of users in the system in overload settings under various policies, which give additional insights on the performance. (4) We conclude that simple priority-index policies with the myopic tie-breaking rule, are stable and asymptotically optimal. All our findings are validated with extensive numerical experiments.Fil: Ayesta, U.. Basque Center for Applied Mathematics; EspañaFil: Erauskin, M.. Basque Center for Applied Mathematics; España. Basque Foundation for Science; España. Universidad del Pais Vasco; EspañaFil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; ArgentinaFil: Verloop, M.. Basque Center for Applied Mathematics; EspañaInstitute Of Electrical And Electronics Engineers2013-02info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/14846Ayesta, U.; Erauskin, M.; Jonckheere, Matthieu Thimothy Samson; Verloop, M.; Scheduling in a random environment: stability and asymptotic optimality; Institute Of Electrical And Electronics Engineers; Ieee-acm Transactions On Networking; 21; 1; 2-2013; 258-2711063-6692enginfo:eu-repo/semantics/altIdentifier/doi/10.1109/TNET.2012.2199764info:eu-repo/semantics/altIdentifier/url/http://ieeexplore.ieee.org/document/6209453/info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:34:30Zoai:ri.conicet.gov.ar:11336/14846instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:34:30.523CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Scheduling in a random environment: stability and asymptotic optimality
title Scheduling in a random environment: stability and asymptotic optimality
spellingShingle Scheduling in a random environment: stability and asymptotic optimality
Ayesta, U.
Fluid limits
Performance evaluation
Stability analysis
Cellular ireless systems
title_short Scheduling in a random environment: stability and asymptotic optimality
title_full Scheduling in a random environment: stability and asymptotic optimality
title_fullStr Scheduling in a random environment: stability and asymptotic optimality
title_full_unstemmed Scheduling in a random environment: stability and asymptotic optimality
title_sort Scheduling in a random environment: stability and asymptotic optimality
dc.creator.none.fl_str_mv Ayesta, U.
Erauskin, M.
Jonckheere, Matthieu Thimothy Samson
Verloop, M.
author Ayesta, U.
author_facet Ayesta, U.
Erauskin, M.
Jonckheere, Matthieu Thimothy Samson
Verloop, M.
author_role author
author2 Erauskin, M.
Jonckheere, Matthieu Thimothy Samson
Verloop, M.
author2_role author
author
author
dc.subject.none.fl_str_mv Fluid limits
Performance evaluation
Stability analysis
Cellular ireless systems
topic Fluid limits
Performance evaluation
Stability analysis
Cellular ireless systems
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.1
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We investigate the scheduling of a common resource between several concurrent users when the feasible transmission rate of each user varies randomly over time. Time is slotted and users arrive and depart upon service completion. This may model for example the flow-level behavior of end-users in a narrowband HDR wireless channel (CDMA 1xEV-DO). As performance criteria we consider the stability of the system and the mean delay experienced by the users. Given the complexity of the problem we investigate the fluid-scaled system, which allows to obtain important results and insights for the original system: (1) We characterize for a large class of scheduling policies the stability conditions and identify a set of maximum stable policies, giving in each time slot preference to users being in their best possible channel condition. We find in particular that many opportunistic scheduling policies like Score-Based [8], Proportionally Best [1] or Potential Improvement [4] are stable under the maximum stability conditions, whereas the opportunistic scheduler Relative-Best [9] or the c-rule are not. (2) We show that choosing the right tie-breaking rule is crucial for the performance (e.g. average delay) as perceived by a user. We prove that a policy is asymptotically optimal if it is maximum stable and the tie-breaking rule gives priority to the user with the highest departure probability. We will refer to such tiebreaking rule as myopic. (3) We derive the growth rates of the number of users in the system in overload settings under various policies, which give additional insights on the performance. (4) We conclude that simple priority-index policies with the myopic tie-breaking rule, are stable and asymptotically optimal. All our findings are validated with extensive numerical experiments.
Fil: Ayesta, U.. Basque Center for Applied Mathematics; España
Fil: Erauskin, M.. Basque Center for Applied Mathematics; España. Basque Foundation for Science; España. Universidad del Pais Vasco; España
Fil: Jonckheere, Matthieu Thimothy Samson. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "luis A. Santaló"; Argentina
Fil: Verloop, M.. Basque Center for Applied Mathematics; España
description We investigate the scheduling of a common resource between several concurrent users when the feasible transmission rate of each user varies randomly over time. Time is slotted and users arrive and depart upon service completion. This may model for example the flow-level behavior of end-users in a narrowband HDR wireless channel (CDMA 1xEV-DO). As performance criteria we consider the stability of the system and the mean delay experienced by the users. Given the complexity of the problem we investigate the fluid-scaled system, which allows to obtain important results and insights for the original system: (1) We characterize for a large class of scheduling policies the stability conditions and identify a set of maximum stable policies, giving in each time slot preference to users being in their best possible channel condition. We find in particular that many opportunistic scheduling policies like Score-Based [8], Proportionally Best [1] or Potential Improvement [4] are stable under the maximum stability conditions, whereas the opportunistic scheduler Relative-Best [9] or the c-rule are not. (2) We show that choosing the right tie-breaking rule is crucial for the performance (e.g. average delay) as perceived by a user. We prove that a policy is asymptotically optimal if it is maximum stable and the tie-breaking rule gives priority to the user with the highest departure probability. We will refer to such tiebreaking rule as myopic. (3) We derive the growth rates of the number of users in the system in overload settings under various policies, which give additional insights on the performance. (4) We conclude that simple priority-index policies with the myopic tie-breaking rule, are stable and asymptotically optimal. All our findings are validated with extensive numerical experiments.
publishDate 2013
dc.date.none.fl_str_mv 2013-02
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/14846
Ayesta, U.; Erauskin, M.; Jonckheere, Matthieu Thimothy Samson; Verloop, M.; Scheduling in a random environment: stability and asymptotic optimality; Institute Of Electrical And Electronics Engineers; Ieee-acm Transactions On Networking; 21; 1; 2-2013; 258-271
1063-6692
url http://hdl.handle.net/11336/14846
identifier_str_mv Ayesta, U.; Erauskin, M.; Jonckheere, Matthieu Thimothy Samson; Verloop, M.; Scheduling in a random environment: stability and asymptotic optimality; Institute Of Electrical And Electronics Engineers; Ieee-acm Transactions On Networking; 21; 1; 2-2013; 258-271
1063-6692
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1109/TNET.2012.2199764
info:eu-repo/semantics/altIdentifier/url/http://ieeexplore.ieee.org/document/6209453/
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv Institute Of Electrical And Electronics Engineers
publisher.none.fl_str_mv Institute Of Electrical And Electronics Engineers
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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