Verification of Stability Condition in 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 ith class customer joins the ‘end’ of a virtual ith class 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 and Markov Chain approach we derive stability conditions of this system relying on analysis for less-complicated model with reliable server. Obtained conditions are verified by simulation. Additionally, we analyze a controllable variant of the main model operating under a cμ-rule. For that case the system becomes less stable comparing to the non-controllable counterpart.