Multi-Server Queue with $BMAP$ and $MAP$ Arrivals, Heterogeneous Buffers, and Impatient Customers

This paper investigates a multi-server queueing system with two heterogeneous arrival processes: a Batch Markovian Arrival Process ($BMAP$) and a Markovian Arrival Process ($MAP$). The system architecture includes a two-stage buffering mechanism consisting of an infinite primary buffer (Buffer~1) and a finite auxiliary buffer (Buffer~2). The system dynamics are modeled by a multidimensional continuous-time Markov chain, and the corresponding infinitesimal generator is derived. A comprehensive set of performance measures is obtained, making the results applicable to the optimization of real-time traffic transmission in modern communication networks.