Heterogeneous servers which can differ in service speed and
reliability are becoming more popular in the modelling of modern communication
systems. For a two-server queueing system with one nonreliable
server and constant retrial discipline we formulate an optimal
allocation problem for minimizing a long-run average cost per unit of
time. Using a Markov decision process formulation we prove a number
of monotone properties for the increments of the dynamic-programming
value function. Such properties imply the optimality of a two-level threshold
control policy. This policy prescribes the usage of a less productive
server if the number of customers in the queue becomes higher than a
predefined level which depends on the state of a non-reliable more powerful
server. We provide also a heuristic solution for the optimal threshold
levels in explicit form as a function of system parameters.