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Car-following behavior is fundamental to traffic flow theory, yet traditional models often fail to capture the stochasticity of naturalistic driving. This paper introduces a new car-following modeling category called the empirical…

Systems and Control · Electrical Eng. & Systems 2026-03-31 Sungyong Chung , Yanlin Zhang , Nachuan Li , Dana Monzer , Alireza Talebpour

Existing studies on the degree correlation of evolving networks typically rely on differential equations and statistical analysis, resulting in only approximate solutions due to inherent randomness. To address this limitation, we propose an…

Computation · Statistics 2024-06-13 Yue Xiao , Xiaojun Zhang

We present a generative model of human mobility in which trajectories arise as realizations of a prescribed, time-dependent Markov dynamics defined on a spatial interaction network. The model constructs a hierarchical routing structure with…

Social and Information Networks · Computer Science 2026-01-12 David A. Meyer , Asif Shakeel

Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce…

Social and Information Networks · Computer Science 2025-02-17 Ziyan Zeng , Minyu Feng , Pengfei Liu , Jurgen Kurths

Dynamic processes in complex networks are crucial for better understanding collective behavior in human societies, biological systems, and the internet. In this paper, we first focus on the continuous Markov-based modeling of evolving…

Social and Information Networks · Computer Science 2025-05-21 Minyu Feng , Ziyan Zeng , Qin Li , Matjaž Perc , Jürgen Kurths

The mean-field limit of a Markovian model describing the interaction of several classes of permanent connections in a network is analyzed. Each of the connections has a self-adaptive behavior in that its transmission rate along its route…

Probability · Mathematics 2009-12-15 Carl Graham , Philippe Robert

We examine adaptive strategies adopted by vehicles for route selection en-route in transportation networks. By studying a model of two-dimensional cellular automata, we model vehicles characterized by a parameter called path-greediness,…

Cellular Automata and Lattice Gases · Physics 2022-04-06 T. S. Tai , C. H. Yeung

Understanding the behavior of road users is of vital importance for the development of trajectory prediction systems. In this context, the latest advances have focused on recurrent structures, establishing the social interaction between the…

Computer Vision and Pattern Recognition · Computer Science 2021-06-09 A. Quintanar , D. Fernández-Llorca , I. Parra , R. Izquierdo , M. A. Sotelo

The replicator-mutator dynamic was originally derived to model the evolution of language, and since the model was derived in such a general manner, it has been applied to the dynamics of social behavior and decision making in multi-agent…

Probability · Mathematics 2020-05-05 Andrew Vlasic

We consider Markov processes, which describe e.g. queueing network processes, in a random environment which influences the network by determining random breakdown of nodes, and the necessity of repair thereafter. Starting from an explicit…

Probability · Mathematics 2015-03-03 H. Daduna , R. Szekli

By analyzing data from a car-following experiment, it is shown that drivers control their car by a simple scheme. The acceleration $a(t)$ is held approximately constant for a certain time interval, followed by a jump to a new acceleration.…

Statistical Mechanics · Physics 2007-05-23 Peter Wagner , Ihor Lubashevsky

Trust management is a critical research pillar in Vehicular Ad Hoc Networks (VANETs), where the reliability of shared data depends entirely on driver integrity. In these networks, a driver's reputation is dynamically constructed based on…

Cryptography and Security · Computer Science 2026-03-10 Rezvi Shahariar

A source traffic model for machine-to-machine communications is presented in this paper. We consider a model in which devices operate in a regular mode until they are triggered into an alarm mode by an alarm event. The positions of devices…

Networking and Internet Architecture · Computer Science 2017-09-05 Henning Thomsen , Carles Navarro Manchón , Bernard Henri Fleury

Dynamic transportation networks have been analyzed for years by means of static graph-based indicators in order to study the temporal evolution of relevant network components, and to reveal complex dependencies that would not be easily…

Machine Learning · Statistics 2022-02-25 Hector Rodriguez-Deniz , Mattias Villani , Augusto Voltes-Dorta

The parameters of a discrete stationary Markov model are transition probabilities between states. Traditionally, data consist in sequences of observed states for a given number of individuals over the whole observation period. In such a…

Computation · Statistics 2012-04-30 Alberto Pasanisi , Shuai Fu , Nicolas Bousquet

In this paper, two-state Markov switching models are proposed to study accident frequencies. These models assume that there are two unobserved states of roadway safety, and that roadway entities (roadway segments) can switch between these…

Applications · Statistics 2009-08-02 Nataliya V. Malyshkina , Fred L. Mannering , Andrew P. Tarko

The ability to predict the future movements of other vehicles is a subconscious and effortless skill for humans and key to safe autonomous driving. Therefore, trajectory prediction for autonomous cars has gained a lot of attention in recent…

Robotics · Computer Science 2021-09-16 Benedikt Mersch , Thomas Höllen , Kun Zhao , Cyrill Stachniss , Ribana Roscher

We present a simple model and algorithm for predicting driver destinations and routes, based on the input of the latest road links visited as part of an ongoing trip. The algorithm may be used to predict any clusters previously observed in…

Physics and Society · Physics 2018-04-11 Yassine Lassoued , Julien Monteil , Yingqi Gu , Giovanni Russo , Robert Shorten , Martin Mevissen

We study how the dynamics of a class of discrete dynamical system models for neuronal networks depends on the connectivity of the network. Specifically, we assume that the network is an Erd\H{o}s-R\'{enyi} random graph and analytically…

Dynamical Systems · Mathematics 2014-04-23 Winfried Just , Sungwoo Ahn

This study examines long-term trends and shifting behavior in the collaboration network of mathematics literature, using a subset of data from Mathematical Reviews spanning 1985-2009. Rather than modeling the network cumulatively, this…