View in EDS PDF Full Text

Towards an Erlang formula for multiclass networks.

Saved in:
Bibliographic Details
Title: Towards an Erlang formula for multiclass networks.
Authors: Jonckheere, Matthieu1 m.t.s.jonckheere@tue.nl, Mairesse, Jean2 Jean.Mairesse@liafa.jussieu.fr
Source: Queueing Systems. Sep2010, Vol. 66 Issue 1, p53-78. 26p. 6 Diagrams, 1 Chart, 3 Graphs.
Subjects: ERLANG (Computer program language), Stochastic analysis, Poisson's equation, Routing (Computer network management), Recursive programming
Abstract: Consider a multiclass stochastic network with state-dependent service rates and arrival rates describing bandwidth-sharing mechanisms as well as admission control and/or load balancing schemes. Given Poisson arrival and exponential service requirements, the number of customers in the network evolves as a multi-dimensional birth-and-death process on a finite subset of ℕ k. We assume that the death (i.e., service) rates and the birth rates depending on the whole state of the system satisfy a local balance condition. This makes the resulting network a Whittle network, and the stochastic process describing the state of the network is reversible with an explicit stationary distribution that is in fact insensitive to the service time distribution. Given routing constraints, we are interested in the optimal performance of such networks. We first construct bounds for generic performance criteria that can be evaluated using recursive procedures, these bounds being attained in the case of a unique arrival process. We then study the case of several arrival processes, focusing in particular on the instance with admission control only. Building on convexity properties, we characterize the optimal policy, and give criteria on the service rates for which our bounds are again attained. [ABSTRACT FROM AUTHOR]
Copyright of Queueing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
FullText Links:
  – Type: pdflink
Text:
  Availability: 0
Header DbId: egs
DbLabel: Engineering Source
An: 52692532
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
PreciseRelevancyScore: 0
IllustrationInfo
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Towards an Erlang formula for multiclass networks.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Jonckheere%2C+Matthieu%22">Jonckheere, Matthieu</searchLink><relatesTo>1</relatesTo><i> m.t.s.jonckheere@tue.nl</i><br /><searchLink fieldCode="AR" term="%22Mairesse%2C+Jean%22">Mairesse, Jean</searchLink><relatesTo>2</relatesTo><i> Jean.Mairesse@liafa.jussieu.fr</i>
– Name: TitleSource
  Label: Source
  Group: Src
  Data: <searchLink fieldCode="JN" term="%22Queueing+Systems%22">Queueing Systems</searchLink>. Sep2010, Vol. 66 Issue 1, p53-78. 26p. 6 Diagrams, 1 Chart, 3 Graphs.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22ERLANG+%28Computer+program+language%29%22">ERLANG (Computer program language)</searchLink><br /><searchLink fieldCode="DE" term="%22Stochastic+analysis%22">Stochastic analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Poisson's+equation%22">Poisson's equation</searchLink><br /><searchLink fieldCode="DE" term="%22Routing+%28Computer+network+management%29%22">Routing (Computer network management)</searchLink><br /><searchLink fieldCode="DE" term="%22Recursive+programming%22">Recursive programming</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: Consider a multiclass stochastic network with state-dependent service rates and arrival rates describing bandwidth-sharing mechanisms as well as admission control and/or load balancing schemes. Given Poisson arrival and exponential service requirements, the number of customers in the network evolves as a multi-dimensional birth-and-death process on a finite subset of ℕ k. We assume that the death (i.e., service) rates and the birth rates depending on the whole state of the system satisfy a local balance condition. This makes the resulting network a Whittle network, and the stochastic process describing the state of the network is reversible with an explicit stationary distribution that is in fact insensitive to the service time distribution. Given routing constraints, we are interested in the optimal performance of such networks. We first construct bounds for generic performance criteria that can be evaluated using recursive procedures, these bounds being attained in the case of a unique arrival process. We then study the case of several arrival processes, focusing in particular on the instance with admission control only. Building on convexity properties, we characterize the optimal policy, and give criteria on the service rates for which our bounds are again attained. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of Queueing Systems is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=52692532
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1007/s11134-010-9185-y
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 26
        StartPage: 53
    Subjects:
      – SubjectFull: ERLANG (Computer program language)
        Type: general
      – SubjectFull: Stochastic analysis
        Type: general
      – SubjectFull: Poisson's equation
        Type: general
      – SubjectFull: Routing (Computer network management)
        Type: general
      – SubjectFull: Recursive programming
        Type: general
    Titles:
      – TitleFull: Towards an Erlang formula for multiclass networks.
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Jonckheere, Matthieu
      – PersonEntity:
          Name:
            NameFull: Mairesse, Jean
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 09
              Text: Sep2010
              Type: published
              Y: 2010
          Identifiers:
            – Type: issn-print
              Value: 02570130
          Numbering:
            – Type: volume
              Value: 66
            – Type: issue
              Value: 1
          Titles:
            – TitleFull: Queueing Systems
              Type: main
ResultId 1