We analyze an M2/G2/1 retrial queuing system with two types of customers and linear retrial policy. If any arriving customer finds the server idle, then it begins his service immediately. Blocked customers from the first flow are queued in order to be served; whereas blocked customers from the second flow leave the service area, but after some random amount of time they repeat an attempt to get service. After essential service completion, a customer either may abandon the system forever or may immediately ask for a second service. The essential and optional service times are arbitrarily and exponentially distributed respectively. We study the ergodicity of the embedded Markov chain, its stationary distribution function and the joint generating function of the number of customers in both groups in the steady-state regime.
