Autonomous Vehicles and Traffic Physics: Framing

Autonomous Vehicles and Traffic Physics: Framing the Questions Hani Mahmassani Northwestern University

Outline Ø  Motivation: Autonomous Vehicles, Connected Systems Ø  Flow Implications: Freeways §  Research Questions §  Simulation Approach: Traffic, Wireless Communication §  Stability Analysis: §  § 

Analytical Approach Simulation Results Trajectory Processor for particle-based simulators

§  Throughput Analysis: Simulation Results §  Lane Changing in Connected Environment: Game Theory

Ø  Flow Implications: Arterials and Urban Street Junctions Ø  Flow Implications: Networks §  NFD §  Fleet Routing – Objective functions, Moving towards SO using empty returns

Ø  Are we there yet?

2

Connectivity Connected systems (internet of everything)

Smart Highways Cooperative Driving

Ad-‐hoc networks

Coordinated

Peer-‐to-‐Peer (Neighbor) Receive only Isolated

-‐  Optimized flow -‐  Routing -‐  Speed harmonization

Connected

-‐  Real-‐time info -‐  Asset tracking -‐  Electronic tolling

Fully manual Level 0

Autonomous Vehicles

INTELLIGENCE RESIDES ENTIRELY IN VEHICLE

Fully automated Level 4

Automation

Questions Traffic Flow Implications: Freeways •  What are the implications of connectivity and/or automated functions on how we model driver behavior and traffic interactions? •  How do we model the communications aspects (of connected systems) jointly with the traffic flow (e.g. to support operational control design)? •  What are the implications of automation vs. connectivity on traffic system performance in terms of

SAFETY THROUGHPUT (“Capacity”) STABILITY ( ! Safety) FLOW BREAKDOWN (Reliability) SUSTAINABILITY (Greenhouse gases, energy)

•  What kinds of collective effects could we expect? Are fundamental diagrams still useful for this purpose? •  What is the sensitivity to relative market penetration on impact on mixed traffic performance? •  What kinds of controls should agencies be contemplating?

Work in collaboration with recent PhD graduate Alireza Talebpour Currently Assistant Professor at Texas A&M University

Accelera'on Framework No Automa'on Not Connected

No Automa'on Connected

Self-‐Driving Not Connected

Accelera'on Framework Self-‐Driving Not Connected


No Automa'on Not Connected

• 

AcceleraKon Behavior:

ProbabilisKc

• 

PercepKon of Surrounding Traffic CondiKon:

SubjecKve

• 

ReacKon Time:

High

• 

Safe Spacing:

High

• 

High-‐Risk maneuvers:

Possible

•  The car-‐following model of Talebpour, Hamdar, and Mahmassani (2011) is used. • 

Probabilistic

• 

Recognizes two different driving regimes: •  Congested •  Uncongested

• 

Consider crashes endogenously




Ac've V2V Communica'ons

InacKve V2V CommunicaKons

AcKve V2I CommunicaKons

InacKve V2I CommunicaKons

• 

AcceleraKon Behavior:

DeterminisKc

• 

PercepKon of Surrounding Traffic CondiKon:

Accurate

• 

ReacKon Time:

Low

• 

Safe Spacing:

Low

• 

High-‐Risk maneuvers:

Very Unlikely

•  The Intelligent Driver Model (Treiber, Hennecke, and Helbing, 2000) is used.




AcKve V2V CommunicaKons

Inac've V2V Communica'ons



•  Sources of informaKon: drivers’ percepKon and road signs •  Behavior is modeled similarly to the “No AutomaKon Not Connected”.






Ac've V2I Communica'ons


•  TMC can detect individual vehicle trajectories •  Speed harmonizaKon •  Queue warning

•  Depending on the availability of V2V CommunicaKons:

•  AcKve V2V CommunicaKons: IDM •  InacKve V2V CommunicaKons: Talebpour, Hamdar, and Mahmassani.







Inac've V2I Communica'ons

•  No communicaKon between vehicle and TMC •  Depending on the availability of V2V CommunicaKons:

•  AcKve V2V CommunicaKons: IDM •  InacKve V2V CommunicaKons: Talebpour , Hamdar, and Mahmassani



•  On-‐board sensors are simulated:


•  SMS AutomaKon Radars (UMRR-‐00 Type 30) with 90m±2.5% detecKon range and ±35 degrees horizontal Field of View (FOV).




•  Speed should be low enough so that the vehicle can react to any event outside of the sensor range (v max ) (Reece and Shafer, 1993 and Arem, Driel, Visser, 2006).

Connected Vehicles Technology Communication

•  It is essential to consider the V2V/V2I communications when modeling a connected environment. •  Connectivity through the vehicular ad hoc network (VANET) is a key element. •  Several studies focused on connectivity in a VANET, • 

Jin et al. (2011)

• 

Ajeer et al. (2011)

• 

Durrani et al. (2010)

14

Connected Vehicles Technology Communication

•  Most of these studies, • 

Assume homogenous Poisson distribution for vehicles along a road segment.

• 

Consider road segments as one-‐dimensional objects.

• 

Assume normal distribution for speed.

•  It is essential to study the connectivity of VANET by considering • 

Non-‐homogenous distribution for vehicles along a road segment.

• 

Road segments as two-‐dimensional objects.

•  Existence of a communication link between two nodes depends on, • 

Wireless technology

• 

Transmission power and rate

• 

Distance and geographical location

• 

Signal propagation and interference

15

Communication Network Dynamic Nature of Vehicular Movements

t = 0 Sec

t = 100 Sec

t = 500 Sec

t = 1000 Sec Based on NGSIM Data

16

Communication Network Percolation

•  There are many instances in which a fluid spreads through a medium, a disease spreads among people, information spreads in social networks, and a liquid penetrates into a porous material.

•  Broadbent and Hammersley (1957) introduced the “percolation theory” to model these instances. •  There are two models, Discrete Percolation and Continuum Percolation

•  Design question: how to form clusters of communicating vehicles, with a “leader” communicating with the infrastructure (V2I) and other groups, and transmitting information within the group?

17

Clustering Algorithm What i s a c luster? •  Each cluster consists of, o  One cluster head o  Several cluster members

•  Assumption: cluster members can only communicate with the cluster head (1-‐hop communication between cluster members). •  A cluster head can communicate with cluster members and other cluster heads from other clusters.

Having stable clusters is the key to reducing signal interference. This study incorporated driving history and driver heterogeneity, in addition to the usual distance and speed measures into VANET clustering algorithms.

V2V Communica'ons Model Clustering

V2V Communica'ons Model NS3 Implementa'on

Network Simulator 3 (NS3) is a discrete-‐event communicaKon network simulator. Dedicated Short-‐Range CommunicaKon (DSRC) Protocol is the standard protocol for V2V communicaKons. DSRC in 5.9GHz spectrum. DSRC interface uses 7 non-‐overlapping channels (Xu et al., 2012): •  A control channel with 1000m range. •  Six service channels with 30-‐400m range.

DSRC uses

•  The control channel to send safety packets. •  Service channels to send non-‐safety packets (e.g. Clustering informaKon)

V2V Communica'ons Model

NS3 Implementa'on – Clustering Frequency Packet size = 50 byte: LocaKon, speed, acceleraKon Packet Forwarding Overhead = 10 ms (Koizumi et al., 2012)

Communication Network

Connectivity: C onstant Transmission Power

Communication network at t = 0 Sec

EffecKve Transmission range = 5m Biggest Cluster Size = 8 EffecKve Transmission range = 10m Biggest Cluster Size = 93

DSRC in 5.9GHz spectrum. EffecKve Transmission range = 20m Biggest Cluster Size = 216

22

V2V Communica'ons Model

NS3 Implementa'on – Packet Delivery






24

Stability Analysis •  Local Stability vs. String Stability Stability String Local Stability

Wilson, R. E., and J. A. Ward. (2010) Car-‐following models: fifty years of linear stability analysis – a mathematical perspective. Transportation Planning and Technology

Stability Analysis A car-‐following model can be formulated as: Empirical observaKons suggest that there exists an equilibrium speed-‐spacing relaKonship: f ( s * ,0, V ( s * )) = 0, ∀s * > 0 A platoon of infinite vehicles is string stable if a perturbaKon from equilibrium decays as it propagates upstream.

Stability Analysis

String Stable Regime

Unstable Oscillatory Regime

Unstable Collision Regime

Stability Analysis Following the definiKon of string stability, the following criteria guarantees the string stability of a heterogeneous traffic stream (Ward, 2009): 2 ⎡ f n 2 ⎤ ⎡ ⎤ ⎢ v − f Δnv f vn − f sn ⎥ ⎢ f sm ⎥ < 0 2 ⎥⎦ ⎢⎣ m ≠ n ⎥⎦ n ⎢ ⎣ where

∑

∏

Stability Analysis

Heterogeneous Traffic Flow

•  Parameters of regular vehicles are adjusted to create a very unstable traffic flow. •  Low market penetraKon rates of automated vehicles do not result in significant stability improvements. •  At low market penetraKon rates of automated vehicles, Market penetra'on rate of connected vehicles

Automated, Connected, and Regular Vehicles

Stability Analysis

Simulation S egment – R ing Road

•  200 vehicles with 40 meters initial spacing. •  To create perturbation: One vehicle is slowed down to v = 1 m/s with maximum deceleration (-‐8 m/s2). Speed is kept at 1 m/s for 50 s.

Stability Analysis Ring Road A nalysis

No Automation Connected

No Automation Not Connected


Stability Analysis Ring Road A nalysis

No Automation Connected

Market Penetration Rates of Connected Vehicles: 10% 50% 90%


Market Penetration Rates of Autonomous Vehicles: 10% 50% 90%

Stability Analysis Simula'on Results

A one-‐lane highway with an infinite length is simulated. String Stability as a FuncKon of ReacKon Time and Platoon Size is invesKgated.

Regular

Oscilla'on Regime Collision Regime

10% Connected

90% Connected

10% Automated

90% Automated

Stability Analysis Simula'on Results

OscillaKon and collision thresholds increase as platoon size decreases. OscillaKon and collision thresholds increase as market penetraKon rate increases. At high market penetraKon rates, Autonomous vehicles have more posiKve effect on both oscillaKon and collision thresholds compared to connected vehicles. 10% Automated

90% Connected

90% Automated

Stability Analysis Summary

The presented acceleraKon framework is string stable. AnalyKcal invesKgaKons show that string stability can be improved by the addiKon of connected and automated vehicles. • 

Improvements are observed at low market penetraKon rates of connected vehicles (unlike automated vehicles).

• 

At high market penetraKon rates, automated vehicles have more posiKve impact on stability compare to connected vehicles.

SimulaKon results revealed that

• 

OscillaKon and collision thresholds increase as platoon size decreases.

• 

OscillaKon and collision thresholds increase as market penetraKon rate increases.

• 

Automated vehicles have more posiKve impact on stability compare to connected vehicles.






36

THROUGHPUT AND FLOW-DENSITY SIMULATION SEGMENT

The average breakdown flow in a series of simulations is considered as the bottleneck capacity.

THROUGHPUT and SPEED-DENSITY RELATION SENSITIVITY ANALYSIS – MIXED ENVIRONMENT

10% R– 0% C – 90% A

10% R– 50% C – 40% A

10% R– 20% C – 70% A

10% R– 70% C – 20% A

10% R– 40% C – 50% A

10% R– 90% C – 0% A

THROUGHPUT SIMULATION RESULTS •  Low market penetration rates of autonomous and connected vehicles do not result in a significant increase in bottleneck capacity. •  Autonomous vehicles have more positive impact on capacity compare to connected vehicles. •  Capacities over 3000 veh/hr/lane can be achieved by using autonomous vehicles. Autonomous, Connected, and Regular Vehicles

Important Caveat THERE ARE MANY DIFFERENT WAYS OF IMPLEMENTING THE TECHNOLOGIES, ESPECIALLY WITH REGARD TO DRIVING AND FLOW CONTROL. Simulation testbeds can help evaluate alternatives and examine implications.

OUR PROPOSAL AGENCY

TELCO No Automa'on Connected

No Automa'on Not Connected

Accel. Choice Lane changing

Comm. Protocols “Rules of engagement”


INTEGRATED TRAFFIC-‐TELECOM SIMULATION PLATFORM

OEM








42

Lane-‐Changing Framework Talebpour, Mahmassani & Hamdar (2015). Modeling lane-‐changing behavior in a connected environment: A game theory approach. Trans. Res. Part C.

Lane-‐Changing Framework

It is assumed that V2V can provide information about the nature of lane-‐ changing maneuvers: Discretionary lane-‐changing vs. Mandatory lane-‐changing A game-‐theoretical approach is adopted with the following pure strategies: •  • 

Lag vehicle: Accelerate, Decelerate, Change Lane Target Vehicle : Change Lane, Do not Change Lane

Lane-‐Changing Framework Inactive V 2V C ommunications

Without information, drivers are uncertain about the nature of other drivers’ lane-‐changing maneuvers. Two-‐person non-‐zero-‐sum non-‐cooperative game under incomplete information. “Harsanyi Transformation” is used to solve the game with incomplete information:

–  “Harsanyi Transformation” transforms the lag vehicle’s incomplete information about the nature of each lane-‐changing maneuver into imperfect information about the move by nature. –  “Nature” as a player chooses the type of each lane-‐changing maneuver. •  Lane-‐changing is mandatory with probability p and discretionary with probability (1-‐p)


Discretionary lane-‐changing game in normal form

Lag Vehicle

ACTION

B1 (Accelerate) B2 (Decelerate) B3 (Change Lane)

Target Vehicle A1 (Change Lane) A2 (Do not Change Lane) ( P11, R11 )

( P12 , R12 )

( P21 , R21 )

( P22 , R22 )

( P31, R31 )

( P32 , R32 )

Mandatory lane-‐changing game in normal form

Lag Vehicle

ACTION


Target Vehicle A1 (Change Lane) A2 (Do not Change Lane) ( P11,Q11 )

( P12 ,Q12 )

( P21,Q21 )

( P22 ,Q22 )

( P31,Q31 )

( P32 ,Q32 )


ACTION

Lag Vehicle

B1 (Accelerate)

A1M A1D

A1M A2D

( P11 ,

(

pQ11 + (1 − p) R11 )

B2

(Decelerate)

( P21 ,

B3

(Change Lane)

( P31 ,

(

pQ21 + (1 − p) R21 ) pQ31 + (1 − p) R31 )

(

Target Vehicle A2M A1D

pP11 + (1 − p) P21 , pQ11 + (1 − p) R21 )

(

pP21 + (1 − p) P22 , pQ21 + (1 − p) R22 )

(

pP31 + (1 − p) P32 , pQ31 + (1 − p) R32 )

(

A2M A2D

pP12 + (1 − p) P11 , pQ12 + (1 − p) R11 )

( P12 ,

pP22 + (1 − p) P21 , pQ22 + (1 − p) R21 )

( P22 ,

pP32 + (1 − p) P31 , pQ32 + (1 − p) R31 )

( P32 ,

pQ12 + (1 − p) R12 )

pQ22 + (1 − p) R22 ) pQ32 + (1 − p) R32 )

Lane-‐Changing Framework Active V 2V C ommunications

With information, drivers are certain about the nature of other drivers’ lane-‐ changing maneuvers.

ACTION Lag Vehicle

Two-‐person non-‐zero-‐sum non-‐cooperaKve game under complete informaKon.


Target Vehicle A1 (Change Lane) A2 (Do not Change Lane) ( P11, Q11orR11 )

( P12 , Q12orR12 )

( P21, Q21orR21 )

( P22 , Q22orR22 )

( P31, Q31orR31 )

( P32 , Q32orR32 )

Lane-‐Changing Framework Payoff F unctions

Payoff matrix of the target vehicle Target Vehicle

ACTION Lag Vehicle


A1 (Change Lane) η1. AccTC arg et + η 2 .ΔV + ε11 η1. AccTCarg et + η 2 .ΔV + ε 21

η2 .ΔV + ε 31

A2 (Do not Change Lane) 0 + ε 12 0 + ε 22 0 + ε 32

Payoff matrix of the lag vehicle

Lag Vehicle

ACTION


Target Vehicle A1 (Change Lane) A2 (Do not Change Lane) C C η 3 . AccT arg et + δ11 η3 . AccLead + δ12 η 4 . AccTY arg et + δ 21 η4 .AccYLead + δ 22

η1. AccTCarg et ' + η 2 .ΔV + δ 31

AccTCarg et

AccYLead ΔV

: Acceleration to prevent collision for the lag vehicle considering the target vehicle as the leader. : -‐3.05 m/s2 : Speed difference between the old leader and the new leader

Lane-‐Changing Framework

Calibration – M ethod o f S imulated M oments

Lane-‐Changing Framework Calibration Results

The NGSIM US-‐101 dataset from 7:50AM to 8:05AM is used for calibration. Discretionary Lane-changing Parameter Calibrated Value η1 η2 η3 η4

-0.750

β

1.000

Mean Absolute Error (MAE)

0.383

0.875 -0.750 0.125

Mandatory Lane-changing Parameter

Calibrated Value

η1 η2 η3 η4

-0.875

β

1.000

Mean Absolute Error (MAE)

0.059

0.375 -0.625 0.25

Lane-‐Changing Framework Simulation – F ictitious P lay

Lane-‐Changing Framework Simulation S egment

3.5 Miles

Lane-‐Changing Framework Simulation Results

Simulated Period

Loop Detector Data

Gap-Acceptance Model

MOBIL

Game Theory Based Model

Lane-‐Changing Framework Simulation Results

Game Theory

Gap-Acceptance

0% MPR

50% MPR

100% MPR






55

Coordination through connectivity and automation: Continuous-flow at-grade intersections

Traffic Flow/System Implications: Arterials and Urban Road Junctions •  What are the implications of connectivity and/or automated functions on how we model driver behavior and traffic at junctions? •  Will the intersection control systems be as smart as the vehicles and the communication systems would allow them to be? •  New approaches needed to consider local logic vs. corridor and network-‐level coordination (local vs. global intelligence much more relevant) •  What about heterogeneous traffic– bicycles, peds, transit vehicles, delivery vehicles in addition to cars with varying degrees of autonomy and connectivity? •  May need to revise notions of throughput, and performance indicators.

•  What is the sensitivity to relative market penetration on impact on mixed traffic performance?

Traffic Flow/System Implications: Networks •  What is the effect of AV’s and CV’s on Network Fundamental Diagram (NFD) and other network-‐level relations? •  What is an appropriate behavioral notion for network assignment? -  Does UE still make sense? -  Depends on mobility ownership/sharing model: How are AV fleet routed? -  Would seek to minimize traveler’s time in transit when transporting someone. -  What about empty vehicles (repositioned for next ride)? Potential for SO routing

•  Strong interplay between new mobility supply models and modeling network impacts.

•  Sensitivity to relative market penetration not only of fraction of AV’s but of ownership/sharing models.

ARE WE THERE YET? WHO IS READY? 1. Technology is here and now; “Big Tech” and “New Tech” is in the lead– ready to market within 3-5 years.

2.  Automotive players– wide range (“waiting on standards”) •  •  •  • 

Connectivity in vehicles here and now; Driver-assist features already in high-end vehicles; Semi-autonomous in 3~5 yrs. Fully-autonomous: Special uses (freight, internal transit) by 2020

3.  System Integrators: more hype than deployment; not quite there yet. 4.  Insurance, Legal: surprisingly nimble 5.  LEAST READY: Public sector agencies; biggest hurdles on system aspects, public sector side. •  • 

More likely to see autonomous vehicles navigating through conventional infrastructure and control systems Limited evidence that agencies will leverage system benefits by transforming control and management systems.

6.  Many challenges ahead, and many more opportunities

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Acceleration Model Parameters and Their Typical Values for car-‐following model of Talebpour , Mahmassani and Hamdar (2011)

return

Acceleration Model Parameters and Their Typical Values for IDM (Treiber et al. (2000) Parameters Typical Value Free Acceleration Exponent δ=4 Desired Time Gap T=1.5sec Jam Distance s0=2.0m Maximum Acceleration a=1.4m/s2 Desired Deceleration b=-‐2.0m/s2