We consider the M/G/1 queue with instantaneous feedback. The probabilities of feedback are determined by the state of the underlying Markov chain. By using the supplementary variable method, we derive the generating function of the number of customers...
We consider the M/G/1 queue with instantaneous feedback. The probabilities of feedback are determined by the state of the underlying Markov chain. By using the supplementary variable method, we derive the generating function of the number of customers in the system. In the analysis, it is required to calculate the matrix equations. To solve the matrix equations, we use the notion of Extended Laplace Transform.