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

Authors: Aliakbar Montazer Haghighi, Stefanka S. Chukova, Dimitar P. Mishev

Addresses: Department of Mathematics, Prairie View A&M University, P.O. Box 519, Mail Stop 2225, Prairie View, Texas 77446-0519, USA. ' Statistics and Operations Research, School of Mathematics, Statistics and Computer Science, Victoria University of Wellington, Private Bag 600, Wellington, New Zealand. ' Department of Mathematics, Prairie View A&M University, P.O. Box 519, Mail Stop 2225, Prairie View, Texas 77446-0519, USA

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.

DOI: 10.1504/IJMOR.2011.037310

International Journal of Mathematics in Operational Research, 2011 Vol.3 No.1, pp.1 - 21

Available online: 03 Dec 2010 *

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