Stability of retrial queueing system with constant retrial rate

Abstract

We study the stability of a single-server retrial queueing system with constant retrial rate and general input and service processes. In such system the external (primary) arrivals follow a renewal input with rate $\lambda$. The system also has service times with rate $\mu$. If a new customer finds all servers busy and the buffer full, it joins an infinite-capacity virtual buffer (or \textit{orbit}). An orbital (secondary) customer attempts to rejoin the primary queue after an exponentially distributed time with rate $\mu_0$