We consider a two-channel Markov queueing system with unreliable heterogeneous
servers and a common queue. The claims are distributed among the servers with a threshold
control policy. According to this policy, a server with the smaller average usage cost must be
busy if the system itself is not empty, and the other server is used if the number of customers
in the queue exceeds a certain threshold. We analyze the system in stationary mode. We
present a method for computing the probabilities of system states and expressions for average
performance and reliability characteristics. For the problem of minimizing average losses per
unit of time, we obtain a heuristic formula that approximately computes the optimal threshold
policy and proposes a method for computing the stationary distribution of the claim waiting
time in the system.