Burst Reduction Properties of Rate-Control Throttles: Departure Process

In this paper we study the departure processes of two rate-control throttles: the token bank and the leaky bucket. Using sample path methods and the notion of majorization, we analyze the eeect that parameters such as the token buuer capacity and token generation period have on the vector of interdeparture times. In the transient case, we establish the monotonicity of the burst reduction in the sense of the majorization. In the case that the departure process is asymptotically mean stationary and ergodic, the transient comparison results allow us to establish the monotonicity of the stationary interdeparture times in the sense of the convex ordering. Comparisons between the two ow control schemes are also established when appropriate.