�Classifications and Generalizations of �Traffic Flow Models in Statistical Mechanics
Department of Physics, Chuo University, Tokyo
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Mini-Symposium with Prof. Gregory Schehr at Chuo University
Aug 18th, 2023
Saori MORIMOTO
Outline
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Outline
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Introduction
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▶︎ Problem
▶︎ Purpose
: Physicists have suggested too many distinct models.
: Interpolate the models and discuss how to reduce traffic jam.
Outline
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Modeling Method
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▶︎ Using Models
▶︎ Boundary Condition
▶︎ Update Rule
: Cellular Automaton Models
: Periodic Boundary Condition
: Parallel Update
Rule-184 CA model
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t+1 steps later
If the front cell is empty, the car moves forward.
But if the front cell is occupied by another car, the car stops.
This is the simplest model and almost all models are its extensions.
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Quick-Start model
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The drivers can anticipate the next time step.
Even though the front cell is occupied by another car, if that preceding car is able to move at the next step, then the car moves.
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expected
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Slow-to-Start model
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When the front cell is empty, the car postpones to move for one time-step.
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t+3 steps later
Outline
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Fundamental diagram
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density
Flow
Fundamental diagram of empirical data for the CHUO express way in Japan, inbound, Near Sagami Lake
https://www.jstage.jst.go.jp/article/isciesci/63/7/63_271/_pdf/-char/ja
The fundamental diagram is the graph showing the flow of cars versus the density of cars.
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Fundamental diagram
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density
Flow
Fundamental diagram of empirical data for the CHUO express way in Japan, inbound, Near Sagami Lake
https://www.jstage.jst.go.jp/article/isciesci/63/7/63_271/_pdf/-char/ja
Fundamental diagram
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density
Flow
Free-flow phase
Fundamental diagram of empirical data for the CHUO express way in Japan, inbound, Near Sagami Lake
https://www.jstage.jst.go.jp/article/isciesci/63/7/63_271/_pdf/-char/ja
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Fundamental diagram
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density
Flow
Jamming phase
Fundamental diagram of empirical data for the CHUO express way in Japan, inbound, Near Sagami Lake
https://www.jstage.jst.go.jp/article/isciesci/63/7/63_271/_pdf/-char/ja
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Fundamental diagram
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density
Flow
Metastable states
Fundamental diagram of empirical data for the CHUO express way in Japan, inbound, Near Sagami Lake
https://www.jstage.jst.go.jp/article/isciesci/63/7/63_271/_pdf/-char/ja
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Three parts of the fundamental diagram
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density
Flow
▶︎ The free-flow phase
▶︎ The jamming phase
▶︎ The metastable states
The flow in this phase turns to decrease as the density increases.
The flow in this phase is proportional to the density.
Free-flow phase
Jamming phase
Metastable states
Fundamental diagram of empirical data for the CHUO EXPWY in Japan, inbound, Near Sagami Lake
https://www.jstage.jst.go.jp/article/isciesci/63/7/63_271/_pdf/-char/ja
Fundamental diagram for Rule-184
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Number of Cells is L = 100, Initial states is 10 pattern, Time steps is t = 250 ~ 300
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Fundamental diagram for Quick-Start model
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Number of Cells is L = 100, Initial states is 10 pattern, Time steps is t = 250 ~ 300
Fundamental diagram for Slow-to-Start model
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Number of Cells is L = 100, Initial states is 10 pattern, Time steps is t = 250 ~ 300
Outline
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Two types of new stochastic models
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Rule-184
SlS
QS
I introduce a stochastic rule interpolating the Rule-184 and the QS model.
Two types of new stochastic models
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Rule-184
SlS
QS
I introduce a stochastic rule interpolating the Rule-184 and the SlS model.
I introduce a stochastic rule :
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Number of Cells is L = 100, Initial states is 10 pattern, Time steps is t = 250 ~ 300
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I introduce a stochastic rule :
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Number of Cells is L = 100, Initial states is 10 pattern, Time steps is t = 250 ~ 300
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Sizes of metastable states
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Number of Cells is L = 100, Initial states taken average is 1000 pattern, Time steps is t = 250 ~ 300
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I calculated the excess of the maximum flow over the flow at the critical density.
maximum flow
flow at the critical density
Summary
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Outline
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Future Problems
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Drivers’ Individual effects
Environmental effects
They include car performances, how to drive, etc.
They include road structures, surrounding facilities, etc.
▶︎ QS model
( It deals with the driver’s anticipation effect. )
▶︎ SlS model
( It deals with the inertia effect of cars. )
▶︎ TASEP [ Totally Asymmetric Simple Exclusion Process ]
( It deals with the random braking effect. )
▶︎ two-lane model
( It deals with the lane change effect. )
I want to propose two categories of effects acting on cars
I wish to understand essential mechanism of traffic jam and obtain mathematical expressions with focusing on this classification.
Thank you very much !
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