Stability analysis for retrial queue with collisions and r-persistent customers - Nazarov, Anatoly A. (Information Technologies and Mathematical Modelling. Queueing Theory and Applications : 20th International Conference, ITMM 2021, named after A. F. Terpugov, Tomsk, Russia, December 1–5, 2021 : revised selected papers)
We consider a single server retrial queue with general distribution of service times, collisions and r-persistent customers. The last phenomena describes the behaviour of customers that are leaving the system immediately if the server is busy upon arrival. We consider the system with customers, which leave the system without servicing with constant probability r. We provide the numerical stability analysis in such system using the following approach. First, we build the diffusion limit for the number of customers in the orbit and then analyze its drift coefficient. For different system parameters, we have different stability conditions.