When using multiple models to describe a (software) system, one can use a network of model transformations to keep the models consistent after changes. No strategy exists, however, to orchestrate the execution of transformations if the network has an arbitrary topology. In this paper, we analyse how often and in which order transformations need to be executed. We argue why linear execution bounds are too restrictive to be useful in practice and prove that there is no upper bound for the number of necessary executions. To avoid non-termination, we propose a conservative strategy that makes execution failures easier to understand. These insights help developers and users of transformation networks to understand under which circumstances their networks can terminate. Additionally, the proposed strategy helps them to find the cause when a network cannot restore consistency.