BMAP Two Phase Retrial Queue with Feedback

This paper is concerned with the analysis of a single server batch arrival retrial queue with general retrial times. The server provides two phases of service essential and optional. A customer after receiving essential service may leave the system or rejoin the orbit and begin requesting service again. The model for the system is derived and the joint distribution of the server state and the orbit length in steady state is obtained. Numerical examples are presented to illustrate the effect of the parameters on several performance measures.