Current results and problems analysing road pricing policies - MATSim

On the analysis of multi-agent transport 

simulations: Current results and problems 

analysing road pricing policies 

Dominik Grether 

www.matsim.org 

Transport Systems Planning and Transport Telematics 

Technical University Berlin 

09.09.2008 

Dominik Grether (TU Berlin) On the analysis of MATSim 09.09.2008 1 / 22

Introduction 

What we intended to do 

• Simulation of time–dependent road–pricing policies 

• Analysis: 

• Car– and non–car traffic 

• Benefits of system 

• Winner / Loser 

• Speed up computation by “better” initial plans 


Outline 

• Current road–pricing resuts 

• Problems on analysis 

• Initial plans 


Scenario Zurich, Switzerland 


Agents on Route 


Average Speed 


Winner / Loser 


Mode Reactions 


Mode Reactions No Toll 


Mode Reactions Comparision 


Relative Traffic Deviation 


Benefits 


Daganzo’s Theory of Multiple Equilibria 

Introduction 

Daganzo, C. (1998), Queue spillovers in transportation networks with a 

route choice. Transportation Science 32(1): 3–11: 

1 DTA problem in dynamic network: Increased capacity of a link can 

lead to oversaturation 

2 Over- and Undersaturated states in static network 

3 Initial conditions and temporary perturbations (endogenous and 

exogenous) which can lead to 2 


Physical Queues & Transitions toward a Final Static 

State 

Variables 

• Q total flow 

• q i flow on link i 

• τ i freespeed tt on link i 

• c i capacity of link i 

• n i number of vehicles on link i 

• ˆn i storage capacity of link i 

• t i travel time in equilibrium on link i 



Network & Model 

• Link 2 shorter than Link 1 but has 

bottleneck with capacity c 2 

⇒ τ 2 < τ 1 

• No flow limitation on Link 1 

⇒ Traveltime is constant τ 1 

• Wardropian model of driver behavior 

⇒ Number of vehicles on link 2 n 2 

determined by capacity of link 2 c 2 

and freespeed travel time on link 1 τ 1 : 

n 2 = τ 1 c 2 



Oversaturated Equilibrium 

• Link 2 has a storage capacity of ˆn 2 

• Spillback emerges if c 2 > c 2crit = ˆn 2 /τ 1 

and traffic inflow greater than the 

bottleneck capacity ⇒ τ 1 > ˆn 2 /c 2 

⇒ No traffic on Link 1 

⇒ System oversaturated 



Undersaturated Equilibrium 

• Undersaturated Equilibrium exisits if 

c 2crit τ 1 ≤ ˆn 2 

• As n 2 = τ 1 c 2 

⇒ q 2 = c 2 

⇒ q 1 = Q − c 2 , 

⇒ t 1 = t 2 = τ 1 



Static network 

• Traffic on link 2 has to yield right of 

way 

⇒ c 2 nonincreasing function of q 1 : 

c 2 = c 2 (q 1 ) 

• Oversaturated state: Q > c 2 (0) > c 2crit 

• Undersaturated state: 

q 2 > c 2 (q 1 ) < c 2crit 


Occurrence in MATSim 

Importance of initial plans 

• Multiple equilibria in MATSim 

• How to choose initial plans 

• Need of a simple test–network 

⇒ Daganzo’s theory in the MATSim model 

• Problem: No right of way, no adaptive traffic lights 

• But: Multiple equilibria occur anyway 


Daganzo’s theory in the MATSim Model 

Network & Model 


MATSim network 

Network with multiple equilibria 

Show demo... 


Summary 

• Need for better run management 

• Need for better analysis methods 

• Need for more methodology before growing too fast

Current results and problems analysing road pricing policies - MATSim

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