A Dynamic Macroscopic model integrated into Dynamic Traffic Assignment: advantages and

disadvantages

Martijn Breen & Jordi Casas

Overview

• Motivation• Model description• Isolated examples• Case study• Conclusion

Motivation

• Travel Demand models require O/D travel times• Current static models do not capture

congestion/queues spillback• Vehicle-based dynamic models are more complex

Where does it stand?

Model – Link model

• Continuous flow model

• Conservation equation:

• Flux rate function:

Model – link model (ii)

Forward Wave Backward Wave

U ( t − Lγ )=V (t ) U ( t )−V (t − Lω )=KL

Mark P.H. Raadsen, Michiel C.J. Bliemer, Michael G.H. Bell, An efficient and exact event-based algorithm for solving simplified first order dynamic network loading problems in continuous time

Node model

• Generic• Maximizing flows w.r.t

constraints.• Conservation of turn

fractions• Invariance principle.

Tampère C.M.J., Corthout R., Cattrysse D., Immers, L.H. (2011). A Generic Class of First Order Node Models for Dynamic Macroscopic Simulation of Traffic Flows. Transportation Research Part B: methodological. Volume 45B issue 1, 2011, pp289-309

Path propagation (integration with DTA)

MACRO

MESO

MICRO

Static assignment

Dynamic userequilibrium

or

Stochastic route choice

OD Matrix

Network data base

Path

s an

dpa

th fl

ows

data

bas

e

Traffic flow representationTraffic assignment

HYBRID

Integration in Dynamic Traffic Assignment

S

Network input / calibration parameters

• Geometry• Section

– Free flow speed– Capacity– Jam density

• Turn– Capacity

• Traffic lights control plan

Isolated examples - spillback

Isolated examples – traffic lights

Isolated examples – Give-way node

Case Study – M4 model

• 476 zones• 1500 km section

length• 5:00 – 10:00 am• 600.000 vehicles

Case study – Travel Times

OD Travel TimeMeso vs Macro Dynamic 6:00 – 7:00

OD Travel TimeMeso vs Macro Dynamic 7:00 – 8:00

Case study – Travel TimesOD Travel Time

Meso vs Macro Static 6:00 – 8:00

Case study – Flows

Computational performanceSimulator Link actualization

threshold [%]Network Loading [seconds]

Mesoscopic n/a 362

Macro dynamic 5 144

Macro dynamic 10 133

Macro dynamic 20 123

Density view mode

Conclusions

• Dynamic Macroscopic model integrated in Dynamic Traffic Assignment

• Travel times comparable under free flow and congested situations

• O/D travel times are more sensitive to errors for coarse (higher threshold) simulation

• Dynamic Macroscopic model is easily calibrated due to few calibration parameters

• Dynamic Macroscopic doesn’t replace the Mesoscopic

Future developments

• Improve traffic signal treatment• Improve computation speed• Add actions like:

– Metering– Force turn– Capacity reduction