In this research work we are concerned with single unit server queue  queue with Markov Modulated process in Poisson fashion and the service time follow exponential distribution. The system is framed as a state dependent with the arrival process as Markov Modulated input and service is rendered by a single server with variation in service rate based on the intensity of service state of the system. The rate matrix that is essential to compute the stationary probability vector is obtained and various performance measures are computed using matrix method.