New throughput bounds for closed networks

An approach to obtaining performance bounds in closed reentrant lines based on an inequality relaxation of the average cost equation is presented. The approach consists of choosing certain simple functions to serve as a surrogate for the differential cost function. Appealing to the transition invariance of a Markov chain modeling the line one can deduce linear programs which provide performance bounds. Functional bounds and an efficiency test are obtained by proposing a functional form for the surrogate of the differential cost function. We develop the linear program bounds for the class of buffer priority policies.