Coupling method for asymptotic analysis of queues with regenerative input and unreliable server

First we define a regenerative flow and describe its properties. Then a single-server queueing system with regenerative input flow and an unreliable server are considered. By applying coupling we establish the ergodicity condition and prove the limit theorem in the heavy traffic situation (traffic coefficient $\rho <1, \rho \uparrow 1$ ). The asymptotic analysis of the super-heavy traffic situation ( $\rho \ge 1$ ) is also realized.