Delft University of Technology
Transport & Planning
www.victorknoop.eu/research
Abstract
The Macroscopic or Network Fundamental Diagram (NFD) describes the network performance as a
function of the number of vehicles. Even if the network has the same roadway length, type of roads, number of intersections and traffic light setting strategy, the
shape of the NFD changes. Therefore, the NFD needs to be calculated or simulated separately for each
network.
Victor Knoop David de Jong Serge Hoogendoorn
Traffic and Granular Flow 2013
Network Fundamental Diagrams
and their Dependence on Network Topology
Victor L. Knoop, PhD
TRAIL Research School
Delft University of Technology Transport & Planning
v.l.knoop@tudelft.nl
5. Conclusions and outlook
The NFDs for different networks have different capacities and critical accumula-tions. So NFDs are not only dependent on the general network properties men-tioned above, but also on the exact network layout (e.g., which link connects to which link) and/or origin/destination pattern. As a consequence, the NFD needs to be determined for each network separately (e.g., by microsimulation) and can-not be derived from these general properties alone.
1. Network generation tool
Randomly created networks (Matlab implemented) Standardised intersection design
(including nr of lanes per direction) Similar:
• Number of intersections
• Length of signalised multi-lane arterial roads • Lengths of single-lane urban roads
• Traffic light strategy
0 5 10 15 20 25 30 0 50 100 150 200 Accumulation (veh/km/lane) Production (veh/h/lane)
Network Fundamental Diagrams
Network 1 Network 2 Network 3 −500 0 500 1000 1500 2000 2500 3000 3500 −500 0 500 1000 1500 2000 2500 3000 3500 Network 2 x−coordinate (m) y−coordinate (m) −500 0 500 1000 1500 2000 2500 3000 3500 −500 0 500 1000 1500 2000 2500 3000 3500 Network 3 x−coordinate (m) y−coordinate (m) −500 0 500 1000 1500 2000 2500 3000 3500 −500 0 500 1000 1500 2000 2500 3000 3500 Network 1 x−coordinate (m) y−coordinate (m)
4. Results
• Capacity differs up to 15%.• Variation in the pattern differs • Jam accumulation differs less
2. Simulate
• Vissim microsimulation tool • Different demand levels
(OD proportional scaling)
3. Construct NFD
The Network Fundamental Diagram
relates average density (accumulation A) to average flow (production P)
Total travel distance in a time step
[veh/h/lane] Duration of time step x Network length
P =
Nr of vehicles in the network
[veh/km/lane] Network length
