WebWave: Globally Load Balanced Fully Distributed Caching of Hot Published Documents

Document publication service over such a large network as the Internet challenges us to harness available server and network resources to meet fast growing demand. In this paper, we show that large-scale dynamic caching can be employed to globally minimize server idle time, and hence maximize the aggregate server throughput of the whole service. To be efficient, scalable and robust, a successful caching mechanism must have three properties: (1) maximize the global throughput of the system, (2) find cache copies without recourse to a directory service, or to a discovery protocol, and (3) be completely distributed in the sense of operating only on the basis of local information. In this paper, we develop a precise definition, which we call tree load-balance (TLB), of what it means for a mechanism to satisfy these three goals. We present an algorithm that computes TLB off-line, and a distributed protocol that induces a load distribution that converges quickly to a TLB one. Both algorithms place cache copies of immutable documents, on the routing tree that connects the cached document's home server to its clients, thus enabling requests to stumble on cache copies en route to the home server.Harvard University; The Saudi Cultural Mission to the U.S.A

Coherence in Large-Scale Networks: Dimension-Dependent Limitations of Local Feedback

We consider distributed consensus and vehicular formation control problems. Specifically we address the question of whether local feedback is sufficient to maintain coherence in large-scale networks subject to stochastic disturbances. We define macroscopic performance measures which are global quantities that capture the notion of coherence; a notion of global order that quantifies how closely the formation resembles a solid object. We consider how these measures scale asymptotically with network size in the topologies of regular lattices in 1, 2 and higher dimensions, with vehicular platoons corresponding to the 1 dimensional case. A common phenomenon appears where a higher spatial dimension implies a more favorable scaling of coherence measures, with a dimensions of 3 being necessary to achieve coherence in consensus and vehicular formations under certain conditions. In particular, we show that it is impossible to have large coherent one dimensional vehicular platoons with only local feedback. We analyze these effects in terms of the underlying energetic modes of motion, showing that they take the form of large temporal and spatial scales resulting in an accordion-like motion of formations. A conclusion can be drawn that in low spatial dimensions, local feedback is unable to regulate large-scale disturbances, but it can in higher spatial dimensions. This phenomenon is distinct from, and unrelated to string instability issues which are commonly encountered in control problems for automated highways.Comment: To appear in IEEE Trans. Automat. Control; 15 pages, 2 figure