Single-server Poisson queueing system with splitting and delayed-feedback: part I (Q622805)

Summary: \(M/M/1\) 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.