Single-server Poisson queueing system with splitting and delayed-feedback: Part I. (12th February 2015)

• Record Type: Journal Article
• Authors: Haghighi, Aliakbar Montazer; Chukova, Stefanka S.; Mishev, Dimitar P.
• Is Part Of: International journal of mathematics in operational research. Volume 3:Number 1(2011)
• Page Start: 1
• Page End: 21
• Publication Date: 2015-02-12
• Subjects: queue -- Poisson -- delayed-feedback -- splitting -- functional equation; Operations research -- Mathematical models -- Periodicals; Operations research -- Mathematics -- Periodicals; Decision making -- Mathematical models -- Periodicals; 658.4033
• Languages: English
• ISSNs: 1757-5850

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.