Optimal control of a queueing system with heterogeneous servers and setup costs

This paper considers a queueing model with batch Poisson input and two hete rogeneous servers, where the service times are exponentially distributed. T he faster server is always on, but the slower server is only used when the queue length exceeds a certain level. Activating the slower server involves fixed set-up costs. Also there are linear operating costs and linear holdi ng costs. The class of two-level hysteretic control rules is considered. Ra ther than proving the overall average cost optimality of a hysteretic rule, the purpose of this paper is to develop a tailor-made policy-iteration alg orithm for computing the optimal switch-an and switch-off levels for the sl ower server. An embedding method is used that is generally applicable to st ructured Markovian control problems with an infinitely large state space.