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Single-server Poisson queueing system with splitting and delayed-feedback: Part I

Author

Listed:
  • Aliakbar Montazer Haghighi
  • Stefanka S. Chukova
  • Dimitar P. Mishev

Abstract

M/M/1 queueing models with immediate feedback and splitting have been considered in the literature. However, with the advancement of communication technologies and increased complexity of the service processes, there is a need to take into account situations where a feedback with delays is required. In this paper, a Poisson arrival with exponential single-processor model with splitter, feedback and three buffers is considered. Feedback occurs exponentially with delay and in bounded random batch size (in this case with size 1). The steady-state system of differential-difference equations is solved analytically that reduces to a functional equation. The mean queue length at each station is found.

Suggested Citation

  • Aliakbar Montazer Haghighi & Stefanka S. Chukova & Dimitar P. Mishev, 2011. "Single-server Poisson queueing system with splitting and delayed-feedback: Part I," International Journal of Mathematics in Operational Research, Inderscience Enterprises Ltd, vol. 3(1), pages 1-21.
    • Handle: RePEc:ids:ijmore:v:3:y:2011:i:1:p:1-21
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