Stability condition for retrial queuing systems with limited service source

In the paper, a retrial queuing system with a limited service source is considered a mathematical model of communication systems where the consumption of the service resource occurs. This paper studies a single-server retrial queue with a Poisson arrival process and exponentially distributed service and delay times. The main feature of the proposed model is that each customer consumes a constant volume of resource during the service. The server has a fixed volume of service source; this means that it needs to go through a recovery period to replenish the source after it reaches a given threshold of the number of serviced customers. The recovery time is assumed to be exponentially distributed. The stability condition of the considered system is derived.