Discriminatory processor sharing queues and the DREB method

Z. LIAN*, X. LIU, L. LIU

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)

2 Citations (Scopus)

Abstract

We study a discriminatory processor-sharing (DPS) queue with a Markovian arrival process (MAP) and K classes of customers. This system can be modeled into a K-dimensional quasi-birth-and death (QBD) process by the standard matrix-analytical approach, but such a process is computationally difficult to handle. We present a different formulation by which the K-dimensional QBD process is reduced to a single-dimensional level-dependent QBD process with expanding blocks. We derive analytical expressions and use them to compute the sojourn time and joint queue length distributions efficiently. This method allows us to study numerically a wide range of important open queueing problems that are common in computer and communication systems, such as various priority queues, queueing networks, and other dependent queues.

Original languageEnglish
Pages (from-to)19-40
Number of pages22
JournalStochastic Models
Volume24
Issue number1
DOIs
Publication statusPublished - 2008
Externally publishedYes

Fingerprint

Quasi-birth-and-death Process
Processor Sharing
Queueing networks
Queue
Communication systems
Computer systems
Markovian Arrival Process
Queue Length Distribution
Priority Queue
Sojourn Time
Queueing Networks
Dependent
Queueing
Joint Distribution
Communication Systems
Customers
Formulation
Range of data

Keywords

  • Dimensions reduction
  • Discriminatory processor sharing
  • DREB method
  • Joint queue length
  • Level-dependent
  • Multi-dimensional QBD
  • Priority queues
  • Sojourn time

Cite this

LIAN, Z. ; LIU, X. ; LIU, L. / Discriminatory processor sharing queues and the DREB method. In: Stochastic Models. 2008 ; Vol. 24, No. 1. pp. 19-40.
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Discriminatory processor sharing queues and the DREB method. / LIAN, Z.; LIU, X.; LIU, L.

In: Stochastic Models, Vol. 24, No. 1, 2008, p. 19-40.

Research output: Journal PublicationsJournal Article (refereed)

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AU - LIU, X.

AU - LIU, L.

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N2 - We study a discriminatory processor-sharing (DPS) queue with a Markovian arrival process (MAP) and K classes of customers. This system can be modeled into a K-dimensional quasi-birth-and death (QBD) process by the standard matrix-analytical approach, but such a process is computationally difficult to handle. We present a different formulation by which the K-dimensional QBD process is reduced to a single-dimensional level-dependent QBD process with expanding blocks. We derive analytical expressions and use them to compute the sojourn time and joint queue length distributions efficiently. This method allows us to study numerically a wide range of important open queueing problems that are common in computer and communication systems, such as various priority queues, queueing networks, and other dependent queues.

AB - We study a discriminatory processor-sharing (DPS) queue with a Markovian arrival process (MAP) and K classes of customers. This system can be modeled into a K-dimensional quasi-birth-and death (QBD) process by the standard matrix-analytical approach, but such a process is computationally difficult to handle. We present a different formulation by which the K-dimensional QBD process is reduced to a single-dimensional level-dependent QBD process with expanding blocks. We derive analytical expressions and use them to compute the sojourn time and joint queue length distributions efficiently. This method allows us to study numerically a wide range of important open queueing problems that are common in computer and communication systems, such as various priority queues, queueing networks, and other dependent queues.

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