Introduction to stochastic models of transportation flows. Part I

TL;DR

This paper introduces probabilistic models of transportation flows focusing on intuitive, visually simple representations of car movements, covering short-term dynamics, individual trajectories, and complex network interactions.

Contribution

It presents a structured overview of stochastic transportation models emphasizing visual simplicity and rigorous formulation across different time scales and network complexities.

Findings

Models capture driver behavior variations.

Framework unifies short-term and long-term flow analysis.

Applicable to complex transport network analysis.

Abstract

We consider here probabilistic models of transportation flows. The main goal of this introduction is rather not to present various techniques for problem solving but to present some intuition to invent adequate and natural models having visual simplicity and simple (but rigorous) formulation, the main objects being cars not abstract flows. The papers consists of three parts. First part considers mainly linear flows on short time scale - dynamics of the flow due to changing driver behavior. Second part studies linear flow on longer time scales - individual car trajectory from entry to exit from the road. Part three considers collective car movement in complex transport networks.