Heterogeneous servers which can differ in service speed and reliability are getting more popular in modeling of modern communication systems. For a two-server queueing system with unreliable servers the allocation of customers between the servers is performed via a threshold control policy which prescribes to use the fastest server whenever it is free and the slower one only if the number of waiting customers exceeds some threshold level depending on the state of faster server. The main task of the paper consists in reliability analysis of the proposed system including evaluation of the stationary availability and reliability function. The effects of different parameters on introduced reliability characteristics are analyzed numerically. © Springer International Publishing AG 2017.