The authors consider an M2/G2/1 type queueing system which serves two types of calls. In the case of blocking the first type customers can be queued whereas the second type customers must leave the service area but return after some random period of time to try their luck again. This jodel is a natural generalization of the classic M2/G2/1 priority queue with the head-of-the-line priority discipline and the classic M/G/1 retrial queue. The authors carry out an extensive analysis of the system, including existence of the stationary regime, embedded Markov chain, stochastic decomposition, limit theorems under high and low rates of retrials and heavy traffic analysis.
