Rate conservation for stationary processes

Abstract

We derive a rate conservation law for distribution densities which extends a result of Brill and Posner. Based on this conservation law, we obtain a generalized Takács equation for the G/G/m/B queueing system that only requires the existence of a stochastic intensity for the arrival process and the residual service time distribution density for the G/GI/1/B queue. Finally, we solve Takács' equation for the N/GI/1/∞ queueing system.