Car-Following Model - MATLAB Implementation with Optimal Velocity Model (OVM)

Application Background This program implements a typical traffic flow car-following model based on the Optimal Velocity Model (OVM), allowing simulation condition modifications through parameter adjustments for sensitivity and headway distance. It serves as an educational resource for beginners studying optimal velocity models. The implementation includes key algorithmic components: velocity update functions with delay differential equations, headway distance calculations, and acceleration/deceleration constraints. Technical Features - Traffic Flow OVM Model: Implements the fundamental optimal velocity function V(Δx) = v_max[tanh(Δx - h_c) + tanh(h_c)] where Δx represents headway distance - Driver Reaction Delay Time: Incorporates time-delayed differential equations using delay differential equation solvers or fixed-time step implementations - Delayed Feedback: Implements feedback control systems with configurable delay parameters through circular buffer or history array structures - Multi-Vehicle Tracking: Features vehicle chain management with predecessor-follower relationships using object-oriented or array-based implementations - Single-Lane Simulation: Provides 1D traffic flow modeling with periodic boundary conditions or open boundary implementations Enhanced Functionalities - Traffic Congestion Simulation: Includes jam formation algorithms with density-wave propagation and bottleneck scenarios - Inter-Lane Traffic Flow: Extends to multi-lane simulations with lane-changing logic using gap acceptance models - Vehicle Acceleration Patterns: Implements realistic acceleration profiles through calibrated OVM parameters and kinematic constraints The enhanced features enable better understanding of practical traffic flow applications while improving simulation accuracy and complexity through robust numerical integration methods and parameter calibration techniques.