M/G/1 queueing system with feedback

Abstract

Memoryless property of a Bernoulli feedback makes the mathematical analysis easy in an M/G/1 queueing system with Bernoulli feedback but we have many difficulties in the study on a queueing system with feedback when the feedback is not Bernoulli. In this thesis we deal with two queueing systems with feedback which are not Bernoulli. First we study on the M/G/1 queueing system with feedback. We obtain a system of functional equations related to the Laplace Stieltjes transform of the waiting time and the probability generating function of the queue length and calculate the moments of the waiting time and the queue length. In the second model, we deal with an M/M/1 queueing system with delayed feedback. We obtain the distributions of the waiting time and the queue length.