1. A method of administering a plurality of virtual machines (‘VMs’) in a distributed computing environment, the distributed computing environment comprising a plurality of hosts, one or more of the hosts executing a virtual machine monitor (‘VMM’), each VMM supporting execution of one or more VMs, the method comprising: assigning, by a VMM manager, the VMMs of the distributed computing environment to a logical tree topology, including assigning one of the VMMs as a root VMM of the tree topology, wherein assigning the VMMs of the distributed computing environment to a logical tree topology comprises assigning at least two VMMs as a parent-child pair based on a physical proximity of a network coupling between hosts executing the at least two VMMs; and executing, in dependence upon an execution policy and responsive to an occurrence of one or more events specified in the execution policy, amongst the VMMs of the tree topology, a broadcast operation, including: pausing, by the root VMM, execution of one or more VMs supported by the root VMM; sending, by the root VMM, to other VMMs in the tree topology, a message indicating a pending transfer of the paused VMs; and transferring the paused VMs from the root VMM to the other VMMs, wherein transferring the paused VMs from the root VMM to the other VMMs comprises transferring the paused VMs using multiple data communications messages sent between the VMMs of the tree topology; wherein the execution policy specifies one or more actions to take upon the occurrence of the one or more events including duplicating all the one or more VMs of the root VMM on all the other VMMs if a workload executing within the one or more VMs of the root VMM has not completed within particular amount of time.