A Single Server Markovian General Service Retrial- Encouraged arrival queuing system with Persistent Retrial Technique under the Transitory Behaviour

In this paper, the objective of this research is to analyse the behaviour and performance of a single server retrial-encouraged arrival queuing system. Specifically, it aims to derive the steady-state distributions for the system using the transitory technique. To calculate the performance metrics such as the average number of consumers in the orbit, and probabilities of the server being busy and idle. Hereafter conduct the numerical illustration for various service time distributions like (Exponential and Erlang) to understand the impact of different system performances on parameters. This research helps in understanding how the system performs under different conditions and can be useful for optimizing queue management in different applications.