A two heterogeneous server queue with one being unreliable server has been considered in this paper. The arrival process and the number service completion process are different Poisson processes. The unreliable server encounters two types of breakdown. The number of breakdowns and the number of repairs are also follows different Poisson processes. During breakdown, the new arrivals become discouraged and may fail to join queue. Also, during busy state, the customers may balk from the system. This model is analysed using matrix geometric method and some performance measures are derived. Numerical examples are provided to show the effort of parameters on the performance measures.

Working vacation; State dependent arrival rate; Matrix-Geometric method