Discrete event system simulation models provide an alternative methodology for analyzing behavior of certain types of systems where we wish to emphasize the reaction of components within the system to events that occur either within the system or in the system environment. The implementation of discrete event system simulations has been primarily algorithmic rather than computational. Specific non-traditional algebraic structures have been used to provide a mathematical foundation for modeling discrete event systems in a more formal and rigorous setting. In this paper we present a tutorial introduction to the use of so called max-plus algebras formulated in a universal algebraic setting for discrete event system simulation. We make the observation that slightly modified versions of standard feed-forward neural networks can be used to implement discrete event system simulations in the max-plus algebraic setting.