LCN2 Seminar: A Diffusion-Based Analysis of a Road Traffic Network
- vrijdag 29 november 2019
- Gorlaeus Building
2333 CC Leiden
- Science club
36th LCN2 seminar
Speaker: Michel Mandjes (Universiteit van Amsterdam)
Title: A Diffusion-Based Analysis of a Road Traffic Network
In this talk, I will discuss an important example of complex networks, namely road traffic networks. I start by giving an overview of the existing literature, distinguishing between microscopic models (describing the stochastic evolution of the position of individual vehicles) and macroscopic models (built around deterministic continuous flows, represented as partial differential equations). Then I argue that the “optimal" model is a compromise between these: we aim at a stochastic model with enough aggregation to make sure that explicit limiting analysis can be performed. The underlying dynamics are consistent with the macroscopic fundamental diagram that describes the functional relation between the vehicle density and velocity. Discretizing space, the model can be phrased in terms of a spatial population process, thus allowing the application of a classical scaling approach. More specifically, it follows that under a diffusion scaling, the vehicle density process can be approximated by an appropriate Gaussian process. This Gaussian approximation can be used to evaluate the travel time distribution between a given origin and destination.
Joint work with Jaap Storm (VU).
About the LCN2 seminar
This talk is part of a series of seminars organized within an ongoing scientific initiative called the "Leiden Complex Networks Network" (LCN2), which brings together scientists with a common interest in both theoretical models and empirical analyses of complex networks and random graphs. The LCN2 community shares the approach of using networks for describing real-world complex systems and aims at developing related analytical and numerical methods, while also being open to other research approaches for studying complex systems. The talks are designed for a broad audience, allowing for constructive exchanges of ideas between scientists from different disciplines. During and after the talk, drinks and snacks are provided.