We define a family of execution policies for a programming model called PTIDES (Programming Temporally Integrated Distributed Embedded Systems). A PTIDES application (factory automation, for example) is given as a discrete-event (DE) model of a distributed real-time system that includes sensors and actuators. The time stamps of DE events are bound to physical time at the sensors and actuators, turning the DE model into an executable specification of the system with explicit real-time constraints. This paper first defines a general execution strategy that conforms to the DE semantics, and then specializes this strategy to give practical, implementable and distributed policies. Our policies leverage network time synchronization to eliminate the need for null messages, allow independent events to be processed out of time stamp order, thus increasing concurrency and making more models feasible (w.r.t. real-time constraints), and improve fault isolation in distributed systems. The policies are given in terms of a safe to process predicate on events that depends on the time stamp of the events and the local notion of physical time. In a simple case we show how to statically check whether program execution satisfies timing constraints.