A finite-buffer M/G/1-type queueing model is considered in which the level of saturation of the buffer is controlled by a dropping function. A direct analytical method to the study of the transient queue-size distribution is proposed. Applying the embedded Markov chain paradigm and the formula of total probability a specific-type system of integral equations for the transient queue-size distributions, conditioned by the number of packets present in the system at the opening, is derived. The corresponding system of linear equations built for the Laplace transforms is written in a matrix form and solved directly. The M/M/1/1-type system is analyzed as a special case separately. Numerical utility of the approach is illustrated as well.
M. Kempa, Wojciech
"A Direct Approach to Transient Queue-Size Distribution in a Finite-Buffer Queue with AQM,"
Applied Mathematics & Information Sciences: Vol. 07:
3, Article 8.
Available at: https://digitalcommons.aaru.edu.jo/amis/vol07/iss3/8