Stability analysis of an unreliable two-class retrial system with constant retrial rates

A two-class single-server retrial system with Poisson inputs is considered. In this system, unlike conventional retrial systems, each new class-i customer joins the ``end'' of a virtual class-i orbit, and the ``oldest'' customer from each orbit is only allowed to make an attempt to occupy server after a class-dependent exponential retrial time. Moreover, the server is assumed to be not reliable, and a customer whose service is interrupted joins the ``top'' of class-i orbit queue. Thus FIFO discipline is applied in both orbits. Using regenerative methodology we derive stability conditions of this system.