# Optimal distance- and time-dependent area-based pricing with the Network Fundamental Diagram

## TL;DR

This paper develops and evaluates distance- and time-dependent area-based toll models using the Network Fundamental Diagram to optimize traffic flow and congestion in large-scale networks through simulation-based methods.

## Contribution

It introduces novel joint distance-time and distance-delay toll models and a simulation-based optimization framework for dynamic traffic pricing in large networks.

## Key findings

- Distance toll prevents congestion but causes uneven path congestion.
- Joint tolls reduce hysteresis loop size in the NFD.
- Framework can be extended to time-dependent pricing.

## Abstract

Given the efficiency and equity concerns of a cordon toll, this paper proposes a few alternative distance-dependent area-based pricing models for a large-scale dynamic traffic network. We use the Network Fundamental Diagram (NFD) to monitor the network traffic state over time and consider different trip lengths in the toll calculation. The first model is a distance toll that is linearly related to the distance traveled within the cordon. The second model is an improved joint distance and time toll (JDTT) whereby users are charged jointly in proportion to the distance traveled and time spent within the cordon. The third model is a further improved joint distance and delay toll (JDDT) which replaces the time toll in the JDTT with a delay toll component. To solve the optimal toll level problem, we develop a simulation-based optimization (SBO) framework. Specifically, we propose a simultaneous approach and a sequential approach, respectively, based on the proportional-integral (PI) feedback controller to iteratively adjust the JDTT and JDDT, and use a calibrated large-scale simulation-based dynamic traffic assignment (DTA) model of Melbourne, Australia to evaluate the network performance under different pricing scenarios. While the framework is developed for static pricing, we show that it can be easily extended to solve time-dependent pricing by using multiple PI controllers. Results show that although the distance toll keeps the network from entering the congested regime of the NFD, it naturally drives users into the shortest paths within the cordon resulting in an uneven distribution of congestion. This is reflected by a large clockwise hysteresis loop in the NFD. In contrast, both the JDTT and JDDT reduce the size of the hysteresis loop while achieving the same control objective.

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Source: https://tomesphere.com/paper/1904.11746