Ordering and replaying of execution traces of distributed systems is a challenging problem. State-of-the-art approaches annotate the traces with logical or physical timestamps. However, both kinds of timestamps have their drawbacks, including increased trace size. We examine the problem of determining consistent orderings of execution traces in the context of model-driven development of reactive distributed systems, that is, systems whose code has been generated from communicating state machine models. By leveraging key concepts of state machines and existing model analysis and transformation techniques, we propose an approach to collecting and reordering execution traces that does not rely on timestamps. We describe a prototype implementation of our approach and an evaluation. The experimental results show that compared to reordering based on logical timestamps using vector time (clocks), our approach reduces the size of the trace information collected by more than half while incurring similar runtime overhead.