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Some embodiments establish for an entity a virtual network over several public clouds of several public cloud providers and/or in several regions. In some embodiments, the virtual network is an overlay network that spans across several public clouds to interconnect one or more private networks (eg, networks within branches, divisions, departments of the entity or their associated datacenters), mobile users, and SaaS (Software as a Service) provider machines, and other web applications of the entity. The virtual network in some embodiments can be configured to optimize the routing of the entity's data messages to their destinations for best end-to-end performance, reliability and security, while trying to minimize the routing of this traffic through the Internet. Also, the virtual network in some embodiments can be configured to optimize the layer 4 processing of the data message flows passing through the network.