The space requirement of local forwarding on acyclic networks

We consider packet forwarding in acyclic networks with bounded adversarial packet injections. We focus on the model of adversarial queuing theory, where each packet is injected into the network with a prescribed path to its destination, and both the long-range average rate and the short-range burst size are bounded. Each edge has an associated buffer that stores packets while they wait to cross the edge. Our goal is to minimize the buffer space required to avoid overflows. Previous results for local forwarding protocols required buffers of size Ω(n). In the case of single destination trees, it is known that for centralized protocols, buffers of size O(1) are sufficient. We show that for local protocols, buffers of size Θ(log n) are necessary and sufficient for single destination trees. The upper bound is achieved by a novel protocol which we call Odd-Even Downhill forwarding (OED). We also show that even slightly more general networks - such as path graphs with multiple destinations, or DAGs with a single destination - require buffers of size Ω(n) to avoid overflows, even if forwarding is done by centralized, offline protocols.