Stability Conditions of a Multiclass System with NBU Retrials

We consider a multiclass multiserver retrial queuing system with classical retrial discipline: the customers, meeting server busy, are blocked on the corresponding (virtual) orbit and then retry to occupy server independently. The retrial times have general class-dependent distributions. The input process is renewal and a new arrival is class-i customer with a given probability \(p_i\). We exploit a regenerative structure of a basic process describing the dynamics of the system to establish stability conditions. More exactly, we show that, provided the retrial times belong to the New-Better-Than-Used class, the convenient requirement that the mean load (traffic intensity) is less than the number of servers, is the stability criterion of the model. A few numerical results are included which, in particular, show that this condition ensures stability of the system with the New-Worse-Than-Used Weibull retrial times as well.