Burst reduction properties of rate-control throttles: Departure process

In this paper the authors 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, they analyze the effect that parameters such as the token buffer capacity and token generation rate have on the vector of interdeparture times. In the transient case, the authors establish the monotonicity of the burst reduction in the sense of the majorization. In the case that the departure process converges in coupling to a stationary and ergodic process, the transient comparison results allow them to establish the monotonicity of the stationary interdeparture times in the sense of the convex ordering. Comparisons between the two flow control schemes are also established when appropriate.