Abstract: We consider a single server constant retrial queue, in which a state-dependent service policy are used to control the service rate.Customer arrival follows Poisson process, while service time and retrial time are exponential distribution. Whenever the server is available, it admits the retrial customers into service based on a first-come first-served rule. The service rate adjusts in real-time based on the retrial queue length. An iterative algorithm is proposed to numerically solve the personal optimal problem in the fully observable scenario. Furthermore, we investigate the impact of parameters on the social optimal threshold. The effectiveness of the results are illustrated by two examples.