Study on time-dependent departure process in a finite-buffer queueing model with BMAP-type input stream

Transient departure process of outgoing packets in a finite-buffer queueing model with the BMAP-type input stream and generally distributed processing times is investigated. Applying the paradigm of embedded Markov chain and the total probability law, a system of integral equations for the distribution function of the number of packets successfully processed up to fixed time t; conditioned by the initial level of buffer saturation and the state of the underlying Markov chain, is obtained. The solution of the corresponding system written for the mixed double transforms is found in a compact form by utilizing the approach based on linear and matrix algebra. Remarks on numerical treatment of analytical results and computational example are attached as well.