Proofs for draft - ietf - diffserv - ef - supplemental - 01 . txt June 2001

The delay bound in section 3.1 is a corollary of Theorem 10.1, and the fact that the packet-identity-aware definition is stronger than the guaranteed rate clock definition, as shown in the following corollary. We say that a node satisfy the guaranteed rate clock property [1] with rate Ö and latency if the departure time Ò of the Òth packet (numbered by order of arrival) is such that Ò Ò · , where Ò is defined by Theorem 10.1. Consider a guaranteed rate clock node with rate Ö and latency. Assume that the input is constrained by a continuous arrival curve «´¡µ. The node need not be FIFO. The delay for any packet is bounded by ×ÙÔ Øؼ «´Øµ Ö Ø · (2) Note that Equation (2) is the horizontal deviation between the arrival curve « and the rate-latency service curve with rate Ö and latency , which is a known result for FIFO nodes [2]. The new information in the theorem is that it also holds for non FIFO nodes. Proof: Call Ò ¼ Ò ¼ the arrival and departure times, with Ò ½. Packets are numbered in order of arrival. For any fixed Ò, consider the largest Ò such that ½ ; we have: