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This paper presents an analysis on performance of logarithmic degree structured P2P (peer-to-peer) overlay networks. P2P network consist of highly transient peers, where peers join and leave the network randomly also known as dynamic environment. It is, therefore difficult to measure the performance of the parameters in real environment. The design of structured overlay networks is fragmented and due to various designs few simulations have been conducted to compare the protocols in dynamic environment. The outcome of the analysis helps the decision in choosing and designing better structured overlay protocol for P2P network. In order to evaluate the routing performance, this work simulates logarithmic-hop overlays - Chord, Pastry and Kademlia. The result shows that among Chord, Pastry and Kademlia protocols, performance of Kademlia is better than Chord and Pastry with 94.2-99% routing efficiency. Hence, Kademlia architecture is better choice to implement structured P2P network.