Simultaneous events, singularity in the space of models and chicken game

Abstract

The discrete event simulation with simultaneous events is discussed. Discrete models are treated as some points in the general space of models. The main topic of this paper is the convergence of sequences of continuous models to the corresponding discrete event model. It is pointed out that the discrete event models may represent some singularities in the space of models. This fact is related to the problem of validity of discrete event simulation. The models presented here are not the topic of the paper. These are known models, used as examples. The model of the “chicken game” and multiple elastic collisions are considered. It is shown that if a discrete event model is some special limit case of a sequence of continuous models with finite event duration, then that limit model is a singularity. It may provide results very different from the expected limit value of the results from the converging sequence of models.