Mathematical Modelling of Travel Behavior: Theory and Advanced Applications

A comprehensive seminar on the mathematical foundations of travel behavior modeling, covering theory and advanced applications in transportation network analysis.

Theory

User Equilibrium (UE)

• Wardrop's First Principle: Journey times on all used routes are equal and minimal
• Mathematical formulation as an optimization problem
• Link performance functions and congestion modeling

Stochastic User Equilibrium (SUE)

• Utility-based choice models
• Logit model for route choice probability
• Integration of random error terms in behavioral modeling

Applications

Network Design

• Bilevel programming formulation
• Leader-follower framework (Planner vs Travelers)
• Infrastructure planning under user equilibrium constraints

Solution Algorithms

1. Exact Methods: Rigorous mathematical optimization
2. Heuristics & Metaheuristics: Adaptive Large Neighborhood Search (ALNS), Matheuristics
3. Machine Learning: Data-driven approaches for complex networks

Key Insight

"There's no art to find the mind's construction in the face." - William Shakespeare

We are building that missing art through mathematical modelling—creating tools to understand and predict human travel behavior in complex urban mobility systems.