On transient departure process in a finite-buffer queueing model with probabilistic packet dropping

Probabilistic packet dropping in dependence on the instantaneous buffer queue level at the pre-arrival epoch is one of Active Queue Management (AQM) mechanisms, used in IP routers for avoiding the risk of buffer overflow and for stabilizing the intensity of the input stream of packets. In the paper transient behavior of departure process h(t), counting packets which leave the service station before the fixed time t, is investigated in the GI/M/1/N queueing model with AQM-type probabilistic packet dropping. Using the approach based on the paradigm of embedded Markov chain and the total probability law, a system of Volterra integral equations for the distribution of h(t), conditioned by the number of packets present in the system initially, is obtained. The solution of the corresponding system written for 2-fold transforms of conditional distributions of h(t) is derived using the linear algebra approach. Illustrative numerical examples are attached as well.