Capacity allocation in a transient queue

We consider an optimal capacity allocation problem of a two-period queueing model, being in steady-state in the first time interval, but changing parameters at the instance of the new period. The error in the objective function made by disregarding the transient phase before reaching stationarity in this second interval is quantified and approximated. Furthermore, we analyze the consequence of staffing the system according to its steady-state behavior and propose a corrected staffing rule