Rate conservation laws for multidimensional processes of bounded variation with applications to priority queueing systems
The paper establishes the rate conservation law (RCL) as well as Fokker-Planck equation for multidimensional stochastic processes of bounded variation. Multidimensional RCL is applied to the M/G/1 queue with preemptive resume priority. Special attention is paid in the analysis of queueing systems to the validity of the so-called reduced service rate approximation, which is often used to approximate the behaviour of the low priority queue. This approximation specifically states that everything happens as if the service rate of the low priority queue were reduced up to the offered traffic of the high priority stream. The paper is concluded with an application of the RCL to derive the buffer content distributions for generalized processor sharing queues.
scientific article; zbMATH DE number 2085804