Convergence of a Packet Routing Model to Flows over Time

The mathematical approaches for modeling dynamic traffic can roughly be divided into two categories: discrete packet routing models and continuous flow over time models. Despite very vital research activities on in both categories, the connection between these was poorly understood so far. In this work we build by specifying a (competitive) model, which is terms of time, proving its convergence to intensively studied model flows with deterministic queuing. More precisely, prove that limit process, when decreasing size step length constitutes multiple commodities. addition, show result implies existence approximate equilibria competitive version model. This significant interest as exact pure Nash equilibria, similar almost all other models, cannot guaranteed multi-commodity setting. Moreover, introduced queuing application-oriented it based network loading module agent-based transport simulation MATSim. As present first formalization simulation, provides theoretical foundation an environment provable statements