In this work, we present a new approach based on a discrete event formalism to model and simulate micro-scale urban traffic systems. The formalism is a coupling between the P-DEVS (Parallel-Discrete Event System Specification) formalism and UML (Unified Modeling Language) state machines. A system is represented by a set of coupled components. Each component supports the dynamics and logic of a system element. The models presented include the streets, intersections and traffic signs, all of which can be synchronized together through specific mechanisms. These models can be applied to real-world OpenStreetMap networks. A discrete event-driven adaptation of the simplified Gipps car-following model is introduced, and subsequently compared to its discrete time counterpart. The results show that our discrete event model follows dynamics which are similar to those of a discrete time model with a low update time step of 0.1s, despite not taking certain non-linearities of the latter into account. In terms of vehicle state changes and computation time, our approach outperforms the discrete time one with an update time step of 1s, both on a simple case study and on a real network.