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      • Department of Electrical and Electronics Engineering
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      The workload-dependent MAP/PH/1 queue with infinite/finite workload capacity

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      Author
      Yazici, M. A.
      Akar, N.
      Date
      2013
      Source Title
      Performance Evaluation
      Print ISSN
      0166-5316
      Publisher
      Elsevier
      Volume
      70
      Issue
      12
      Pages
      1047 - 1058
      Language
      English
      Type
      Article
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      Abstract
      We propose a numerical algorithm for finding the steady-state queue occupancy distribution for a workload-dependent MAP/PH/1 queue in which the arrival process and the service rate depend continuously on the instantaneous workload in the system. Both infinite and finite queue capacity scenarios are considered, including partial rejection and complete rejection policies for the latter. Using discretization, this system is approximately described by a multi-regime Markov fluid queue for which numerical algorithms are available. The computational complexity of the proposed method is linear in the number of regimes used for discretization. We provide numerical examples to validate the proposed approach.
      Keywords
      Block-LU factorization
      Markov fluid queues
      Markovian arrival process
      Phase-type distribution
      Workload-dependent queues
      Arrival process
      Discretizations
      Markov fluid queues
      Markovian arrival process
      Numerical algorithms
      Phase type distributions
      Service rates
      Workload-dependent queues
      Algorithms
      Markov processes
      Queueing theory
      Permalink
      http://hdl.handle.net/11693/20720
      Published Version (Please cite this version)
      http://dx.doi.org/10.1016/j.peva.2013.09.002
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      • Department of Electrical and Electronics Engineering 3524
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