An ad hoc distributed simulation is a collection of online simulators embedded in a sensor network that communicate and synchronize among themselves. Each simulator is driven by sensor data and state predictions from other simulators. Previous work has examined this approach in transportation systems and queueing networks. Ad hoc distributed simulations have the potential to offer greater resilience to failures, but also raise a variety of statistical issues including: (a) rapid and effective estimation of the input processes at modeling boundaries; (b) estimation of system-wide performance measures from individual simulator outputs; and (c) correction mechanisms responding to unexpected events or inaccuracies of the model itself. This paper formalizes these problems and discusses relevant statistical methodologies that allow ad hoc distributed simulations to realize their full potential. To illustrate one aspect of these methodologies, an example concerning rollback threshold parameter selection is presented in the context of managing surface transportation systems.