On the representation of time in modeling & simulation

The representation of time plays a key role in the modeling and simulation of dynamic systems. Traditionally, time has been represented by real numbers for continuous and discrete event models, and integer numbers for what is commonly defined as discrete time models. These choices have been found to be insufficient for achieving deterministic models when representing systems subjected to changes in topology or when simultaneous events occur. In this paper we study the advantages of using the set of hyperreal numbers for the time base. For demonstrating the advantages of Hyperreals over the set of reals we use the Hybrid Flow System Specification (HyFlow) formalism. This formalism uses a single hyperreal time base to achieve a unifying representation of sampling and discrete event semantics. We show that a hyperreal time base (HRTB) enables the definition of deterministic, dynamic topology, hybrid systems, while a real time base cannot achieve these fundamental properties.