Time-dependent Queue-size Distribution in the Finite Gi/m/1 Model with Aqm-type Dropping

A GI/M/1-type queueing system with finite buffer capacity and AQM-type packet dropping is investigated. Even when the buffer is not saturated an incoming packet can be dropped (lost) with probability dependent on the instanteneous queue size. The system of integral equations for time-dependent queue-size distribution conditioned by the number of packets present in the system initially is built using the embedded Markov chain approach. The solution of the corresponding system written for Laplace transforms is found using the linear algebra. Numerical examples, in which different-type dropping functions are investigated in some network-motivated traffic scenarios, are attached as well.