1. Extending the Link Transmission Model with general concave fundamental diagrams and capacity drops
Jeroen van der Gun
Adam Pel
Bart van Arem
Rijkswaterstaat / Joop van Houdt

2. Solving kinematic wave theory
Lighthill & Whitham (1955), Richards (1956)
Formulation of kinematic wave theory
Godunov (1956), Daganzo (1994)
Numerical solution through Cell Transmission Model
Newell (1993), Yperman et al. (2006), Yperman (2007), Gentile (2010)
Alternative numerical solution through Link Transmission Model
Daganzo (2005), Jin (2015), Han et al. (2015)
Proofs using variational theory that LTM converges for triangular fundamental diagrams as Δt↓0

3. Triangular fundamental diagrams
Constant speed in subcritical traffic
Constant travel times in light traffic
Identical capacity in free-flow and congestion
No capacity drop
No benefit of metering
Rijkswaterstaat / DVK-RWS

4. Contents Overview of LTM structure
Link model for continuous concave FD
LWR theory with capacity drop
Link model with capacity drop
Node model with capacity drop
Numerical examples

5. Overview of LTM structure

6. LTM structure (discrete time version)

7. Link model for continuous concave FD

8. Continuous concave FD

9. Sending flow as solution network

10. LWR theory with capacity drop

11. FD with capacity drop

12. Example with separating shock

13. Link model with capacity drop

14. Link algorithm modifications
Sending flow
Add queue discharge rate constraint in congestion
Receiving flow
Apply backward paths only in case link outflow was congested
Track separating shock implicitly by adding extra paths
New dissolution procedure

15. Node model with capacity drop

16. Node algorithm modifications
Capacity drop invariance
First time step after breakdown same flow as later time steps
Standing queues with capacity drop
Congested transition flows never exceed discharge rate
Receiving flow reduced to discharge rate if exceeded
No memory effect

17. Numerical examples

18. Model features

19. A13 motorway corridor network

20. Conclusions

21. Conclusions LTM extended with continuous concave FDs
LWR and LTM extended with capacity drop
Models acceleration fans
Models both onset and propagation of both standing and moving queues, including stop-and-go waves
Computationally-efficient first-order network model with small numerical error