The paper explores an advanced single-server M/G/1 retrial queueing model that employs a push-out service with two unique classes of customers, i.e., transient (priority) customers and recurrent customers. The arrivals of customers are Poisson process. The service time of customers and retrial time of transit customers are follow general probability distributions. The inter-retrial time of the recurrent customer is exponentially distributed. The system also includes feedback behavior of transit customers and probabilistic push-out of repeat customers. Closed-form formulae are obtained expressing steady-state distributions of important system states using supplementary variable technique (SVT) and probability generating functions (PGFs). The impact of parameters is shown with the help of numerical experiments, and the Beetle Antennae Search (BAS) algorithm is used to optimise the performance of the system. These results are useful in designing and optimization of priority-based service systems such as cloud computing systems, communication networks, and real-time task scheduling systems.
Poomalai et al. (Tue,) studied this question.