1. A computer-implemented method comprising: obtaining, by one or more configured computing devices of an application execution service, information indicating an access policy for use with a first computing node, the indicated access policy specifying one or more criteria regarding communications allowed to be at least one of sent by or received by the first computing node; initiating, by the one or more configured computing devices, execution of the first computing node as a virtual machine hosted by a physical computing system of the application execution service; and configuring, by the one or more configured computing devices, one or more software components executing on the physical computing system to manage at least communications for virtual machines hosted by the physical computing system, the configuring including storing information on the physical computing system about the access policy for use by the one or more software components in managing communications for the first computing node in accordance with the one or more specified criteria.