Traffic models and traffic-jam transition in quantum ($N$+1)-level systems

TL;DR

This paper introduces a quantum graph-based model for simulating traffic flow conditions, using Lindbladian dissipators to derive master equations, and validates the approach by comparing with classical traffic models.

Contribution

The paper presents a novel quantum graph model for traffic flow simulation that captures vehicle types and destinations, and demonstrates its effectiveness through classical traffic scenarios.

Findings

Successfully models traffic flow using quantum systems

Accurately reproduces classical traffic model results

Demonstrates versatility in different traffic scenarios

Abstract

We propose a model to implement and simulate different traffic-flow conditions in terms of quantum graphs hosting an ($N$+1)-level dot at each site, which allows us to keep track of the type and of the destination of each vehicle. By implementing proper Lindbladian local dissipators, we derive the master equations that describe the traffic flow in our system. To show the versatility and the reliability of our technique, we employ it to model different types of traffic flow (the symmetric three-way roundabout and the three-road intersection). Eventually, we successfully compare our predictions with results from classical models.