Extending the Link Transmission Model with general concave fundamental diagrams and capacity drops Jeroen van der Gun Adam Pel Bart van Arem https://beeldbank.rws.nl, Rijkswaterstaat / Joop van Houdt

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

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 https://beeldbank.rws.nl, Rijkswaterstaat / DVK-RWS

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

Overview of LTM structure

LTM structure (discrete time version)

Link model for continuous concave FD

Continuous concave FD

Sending flow as solution network

LWR theory with capacity drop

FD with capacity drop

Example with separating shock

Link model with capacity drop

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

Node model with capacity drop

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

Numerical examples

Model features

A13 motorway corridor network

Conclusions

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 J.P.T.vanderGun@tudelft.nl