Let us consider a queueing system M/G/1 with Poisson arrival process, which is independent of the generally distributed service time, and instantaneous Bernoulli feedback, that is, after completing a service the customer may return to the queue with probability p or may depart with probability \(q=1-p\). The time-stationary distribution of the queue length and virtual waiting time at an arbitrary point at time are investigated.
Moreover, the authors determine the queue length and waiting time at arrival epochs of the Poisson process, at the feedback epochs (at which a customer whose service is terminated returns to the queue), at times an arbitrary customer enters the queue, at the output epochs (at which the service is terminated) and at the departure epochs. Finally, as an example the M/M/1 queue with instantaneous Bernoulli feedback is considered.