Quasi-stationary distribution of virtual waiting time in a retrial queue

We consider a single-server retrial system with constant retrial rate. The input stream is Poisson and retrial times are exponentially distributed. We assume a stable case under a heavy load. Namely we set the system parameters inside the stability zone near to the stability border. For such a model we obtain the asymptotic results for stationary distribution of a virtual waiting time under the condition that the first busy cycle length infinitely grows. The conditioned stationary distribution is called quasi-stationary. The applied approach is based on preliminary results obtained for a regular infinite buffer queuing models with Poisson input.