Stochastic Analysis of a Fault-Tolerant and Bandwidth-Efficient P2P Network

We present the design and analysis of a fault-tolerant and bandwidth-efficient Peer-to-Peer (P2P) scheme (called as WARP). WARP employs a simple and natural fault-tolerant mechanism to manage the dynamic nature of node arrivals and departures by allowing multiple physical nodes to service data mapped to a single node in the overlay. WARP’s overlay network is asymmetric (built using an underlying tree topology) which naturally allows search queries of two different types — centralized and distributed — to be handled in an uniform way. Centralized queries go to specific chosen nodes in the network and are useful in the context of popular data while distributed queries can be directed to any node in the network. We prove via a stochastic analysis that any query, regardless of type, will be successfully serviced with high probability (w.h.p). Specifically, we show that for a network with N nodes on the average, the hop complexity of any search is O(logN) w.h.p., while the degree of each node is bounded by O(log N) w.h.p. When many search queries happen at the same time, it is important to avoid congestion at any one node. WARP achieves this by introducing small-world edges to the overlay which reduces the bandwidth complexity (the worst case expected number of queries that go through any node). We prove that this complexity is bounded by O(log N) w.h.p. We also generalize our results when the P2P network is built using other underlying topologies such as hypercubes or rings. Thus our scheme can be used to “convert” any static topology into a dynamic fault-tolerant network.