Burst reduction properties of rate-based flow control schemes : downstream queue behavior

In this paper we considerer rate-based flow control throttles feeding a sequence of single server infinite capacity queues. Specifically, we consider two types of throttles, the token bank and the leaky bucket. We show that the cell waiting times at the downstream queues are increasing functions of the token buffer capacity. These results are established when the rate-based throttles have finite capacity data buffers as well as infinite capacity buffers. In the case that the data buffer has finite capacity, we require that the sum of the capacities of the data buffer and token buffer be a constant. Last, we establish similar results for the process of number of losses at the last downstream queue in the case that the waiting buffer has finite capacity