Prof. Fatihcan Atay of the Department of Mathematics has co-authored a new book, “Deterministic Car-Following Traffic Models: Delay Effects and Linear Stability,” published by Springer. The work, written in collaboration with Rifat Sipahi and Silviu-Iulian Niculescu, provides an in-depth exploration of how time delays impact traffic flow stability and vehicle interactions.
The dynamical instabilities in traffic give rise to several common nuisances, such as stop-and-go waves, and driver reaction delays are among the main causes of accidents. The book examines car-following models with delays from human reaction times, mechanical lag and vehicular motion. Using mathematical tools, it analyzes traffic stability and oscillatory behavior. Focusing on microscopic flow models, the study categorizes delays into discrete, distributed and time-varying types, emphasizing constant and distributed delays. The publication contributes theoretical insights and practical applications for improving traffic flow and stability, with implications for smarter transportation networks.