Analysis of a versatile multi-class delay–loss system with a superimposed Markovian arrival process

We analyze the behavior of a multi-class single-server delay–loss system ∑^χi MAPi/PH/l/m with a superposition of independent Markovian Arrival Processes as arrival stream and phase-type distributed service times. Considering the underlying finite Markov chain with its quasi-birth-and-death structure with two boundary sets, we derive a new representation of its steady-state vector by a linear combination of two matrix-geometric terms. Furthermore, we state efficient procedures to calculate the performance characteristics of this delay–loss system.