The present study proposes an extended opportunity-basedage replacement policy where opportunities occur according to a Poissonprocess. When the age, x of the system satisfies x < S for aprespecified value S, a corrective replacement is conducted if theobjective system fails. In case x satisfies S ≤ x < T foranother prespecified value T, we take an opportunity to preventivelyreplace the system by a new one with probability p, and do not takethe opportunity with probability 1 - p. At the moment x reaches T,a preventive replacement is executed independently of opportunities. Thelong-term average cost of the proposed policy is formulated. Theconditions under which optimal values for S and T exist for aprespecified value of T and S, respectively, are then clarified. Numerical examples are also presented to illustrate the theoreticalunderpinnings of the proposed replacement policy formulation.

We consider two parallel M/M/1 queues. The server at one of the queuesis subject to intermittent breakdowns. By the theory of dynamic programming, we determine a threshold optimal policy which consists to transfer, when it is necessary, the customers that arrive at the first queue towards the second queue in order to minimize an instantaneous costdepending of the two queue lengths.