TECHNOLOGY CATALOGUE CRS4

Optimal Routes

Digital Platform for Labs

Structure and performance of the fastest routes on networks with interacting self-interested agents

Background

Modern transportation and network systems – such as urban mobility, logistics, and communication networks – are increasingly affected by congestion caused by users who make decisions autonomously and are driven by personal interests.

Traditional models focus on individual network links but fail to describe how the entire route system evolves when collective behavior comes into play.

This limitation is evident in phenomena such as the so-called “price of anarchy,” which measures the inefficiencies generated by uncoordinated user behavior.

What does the Optimal Routes application offer?

The Optimal Routes application introduces an analytical framework to study how the fastest routes in networks change in response to increased congestion caused by the interaction between agents.

To this end, new indicators are introduced to characterize both the geometry of the routes (spatial structure, detours, alternative routes) and mobility performance—that is, the efficiency with which agents reach their destinations.

The developed system has been validated on both synthetic networks and real urban systems, revealing how optimal routes dynamically adapt or collapse as traffic increases.

The fundamental innovation lies in the combination of game theory, network science, and nonlinear dynamics applied to real-world urban network congestion problems to study the inefficiencies arising from decentralized behaviors.

Innovative features

Shift from node-based network analysis to path-based analysis
Introduction of new indicators related to path shape and performance
Identification of critical congestion thresholds at which the system behavior undergoes a sudden change
Identification of nonlinear and asymmetric effects in urban areas
Use of inequality measures (e.g., the Gini coefficient) to assess the uniformity of the deterioration in network performance

Potential users

Urban planners and transportation authorities
Mobility platform providers (route planning, navigation, Mobility-as-a-Service—MaaS)
Logistics and delivery companies
Developers of smart city solutions and researchers in network science and complex systems

Sectors impacted

Smart mobility and transportation systems
Urban planning and infrastructure design
Logistics and supply chain optimization
Digital twins and simulation platforms

The main applications include adaptive dynamic routing, congestion simulation and forecasting, data-driven decision support, and analysis of the resilience and robustness of transportation infrastructure.

Economic and social value

Quantify and predict systemic inefficiencies in congested networks
Improve economic efficiency and reduce costs
Enhance sustainability and quality of life

Additional resources and information

Marco Cogoni, Giovanni Busonera, Enrico Gobbetti. Shape and Performance of Fastest Paths over Networks with Interacting Selfish Agents, Physical Review E, Volume 111, Number 4, page 044318 – april 2025 https://arxiv.org/abs/2412.17665
Marco Cogoni, Giovanni Busonera. Predicting Network Congestion by Extending Betweenness Centrality to Interacting Agents, Physical Review E American Physical Society pages 044302 vol. 109 num. 4 – april 2024 https://link.aps.org/doi/10.1103/PhysRevE.109.044302
Marco Cogoni, Giovanni Busonera. Stability of traffic breakup patterns in urban networks. Phys. Rev. E American Physical Society, pages L012301 vol. 104 num. 5 – july 2021 https://link.aps.org/doi/10.1103/PhysRevE.104.L012301
Marco Cogoni, Giovanni Busonera, Gianluigi Zanetti. Ultrametricity of optimal transport substates for multiple interacting paths over a square lattice network, Phys. Rev. E American Physical Society, pages 030108 vol. 95 num. 5 – march 2017 https://link.aps.org/doi/10.1103/PhysRevE.95.030108

Status

Type of innovation:
incremental, modular

Product type:
software

Emerging technologies adopted:
Computational modeling and Simulation, Advanced metrics, and Data analysis.

Stage of technological development:
TRL 3-4

Intellectual property characteristics: proprietary code

Other partners:
No

Keywords

Route Optimization Algorithms
Network Congestion Management
Multi-agent Systems
Simulation-based Decision Support

Contacts

Marco Cogoni
– industrial collaborations
– pilot projects and demonstrators
– technology transfer (licensing)

For information valorisation@crs4.it

Date

Last update: 25/03/2026