Rate Conservation Laws for Multidimensional Processes of Bounded Variation with Applications to Priority Queueing Systems

In this paper we derive a multidimensional version of the rate conservation law (RCL) for càdlàg processes of bounded variation. These results are then used to analyze queueing models which have a natural multidimensional characterization, such as priority queues. In particular the RCL is used to establish certain conservation laws between the idle probabilities for such queues. We use the relations to provide a detailed analysis of preemptive resume priority queues with M/G inputs. Special attention is paid to the validity of the so-called reduced service rate approximation.