Dynamic allocation of reconfigurable resources in a two-stage tandem queueing system with reliability considerations

Consider a two stage tandem queueing system, with dedicated machines in each stage. Additional reconfigurable resources can be assigned to one of these two stations without setup cost and time. In a clearing system (without external arrivals) both with and without machine failures, we show the existence of an optimal monotone policy. Moreover, when all of the machines are reliable, the switching curve defined by this policy has slope greater than or equal to-1. This continues to hold true when the holding cost rate is higher at the first stage and machine failures are considered. I