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In the past few years, overlay networks have received much attention but there has been little study on the "interaction" of multiple, co-existing overlays on top of a physical network. In addition to previously introduced concept of overlay routing strategy such as selfish routing, we introduce a new strategy called "overlay optimal routing". Under this routing policy, the overlay seeks to minimize its weighted average delay by splitting its traffic onto multiple paths. We establish that (i)doi:10.1016/j.peva.2005.07.005 fatcat:6wjlr2v5tbgznjspsnta5jtxxu