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      • Department of Electrical and Electronics Engineering
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      Markov modulated periodic arrival process offered to an ATM multiplexer

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      Author(s)
      Akar, N.
      Arıkan, E.
      Date
      1995-04
      Source Title
      Performance Evaluation
      Print ISSN
      0166-5316
      Electronic ISSN
      1872-745X
      Publisher
      Elsevier BV * North-Holland
      Volume
      22
      Issue
      2
      Pages
      175 - 190
      Language
      English
      Type
      Article
      Item Usage Stats
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      247
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      Abstract
      When a superposition of on/off sources is offered to a deterministic server, we are faced with a particular queueing system, the analysis of which has a significant role in ATM networks. Periodic cell generation during active times is a major feature of these sources. We provide an analytical approach to solve for this queueing system via an approximation to the transient behavior of the nD/D/1 queue. The solution to the queue length distribution is given in terms of a solution to a linear differential equation with variable coefficients. The technique proposed here has close similarities with the fluid flow approximation and is amenable to extension for more complicated queueing systems with such correlated arrival processes. A numerical example for a packetized voice multiplexer is finally given to demonstrate our results.
      Keywords
      ATM networks
      Fluid-flow models
      nD/D/1 queue
      Approximation theory
      Asynchronous transfer mode
      Broadband networks
      Correlation theory
      Differential equations
      Markov processes
      Multiplexing equipment
      Numerical methods
      Packet switching
      Voice/data communication systems
      Linear equation
      Markov modulated periodic arrival process
      Packetized voice multiplexer
      Queueing theory
      Permalink
      http://hdl.handle.net/11693/25906
      Published Version (Please cite this version)
      https://doi.org/10.1016/0166-5316(93)E0058-D
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      • Department of Electrical and Electronics Engineering 4011
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