Toward Unbiased Deterministic Total Orderings Of Parallel Simulations With Simultaneous Events

In the area of discrete event simulation (DES), event simultaneity occurs when any two events are scheduled to happen at the same point in simulated time. Since events in DES are the sole mechanism for state change, ensuring consistent real-time event processing order is crucial to maintaining deterministic execution. This is synonymous with finding a consistent total ordering of events. In this work, we extend the concept of virtual time to utilize an arbitrary-length series of tie-breaking values to preserve determinism in parallel, optimistically executed simulations without imposing additional bias influencing the ordering of otherwise incomparable events. Furthermore, by changing the core pseudo-random number generator seed at initialization, different orderings of simultaneous events can be observed, allowing for deeper statistical analysis. We implement and evaluate this mechanism using the Rensselaer Optimistic Simulation System (ROSS) and discuss the importance of deterministic event ordering given the existence of event ties.