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.