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

Aliakbar Montazer Haghighi, Stefanka S. Chukova and Dimitar P. Mishev

International Journal of Mathematics in Operational Research, 2011, vol. 3, issue 1, 1-21

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.

Keywords: single-server Poisson queueing; delayed feedback; splitting; functional equations; queueing models; mean queue length. (search for similar items in EconPapers)
Date: 2011
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