A controllable hybrid queueing system consists of a system controller and two
nodes in tandem of the type M/M/ni. Customers arrive to the controller who allocates
them between the nodes. After service completion at node 2 the controller can allocate
the customer waiting at node 1 to node 2. With probability p after a service completion
at node 1 a failure occurs. In this case the customer from node 1 joins node 2. With
complement probability 1 − p the service completion at node 1 is successful. For the
given cost structure we formulate an optimal allocation problem to minimize the longrun
average cost per unit of time. Using dynamic-programming approach we show
the existents of thresholds which divides the state-space into two contiguous regions
where the optimal decision is to allocate the customers to node 1 or to node 2. Some
monotonicity properties of the dynamic-programming value function are established.