# Globally Optimal Departure Rates for Several Groups of Drivers

## TL;DR

This paper investigates optimal departure rates for multiple driver groups on a road using conservation law traffic models, deriving conditions and algorithms for globally optimal solutions and Nash equilibria.

## Contribution

It introduces a practical algorithm for computing globally optimal departure rates for different driver groups on a single road, expanding traffic flow optimization methods.

## Key findings

- Derived necessary conditions for optimal departure rates.
- Developed a practical algorithm for computing optimal solutions.
- Reviewed solutions for Nash equilibrium and global optimality.

## Abstract

The first part of this paper contains a brief introduction to conservation law models of traffic flow on a network of roads. Globally optimal solutions and Nash equilibrium solutions are reviewed, with several groups of drivers sharing different cost functions. In the second part we consider a globally optimal set of departure rates, for different groups of drivers but on a single road. Necessary conditions are proved, which lead to a practical algorithm for computing the optimal solution.