HO HOW MANY W MANY SMAR SMART CARS T CARS DOES IT TAKE T DOES - - PowerPoint PPT Presentation

• C. G

. G. Cassand . Cassandras as

Division of Systems Engineering

• Dept. of Electrical and Computer Engineering

Center for Information and Systems Engineering Boston University

Christos G. Cassandras

CODES Lab. - Boston University

HO HOW MANY W MANY SMAR SMART CARS T CARS DOES IT T DOES IT TAKE T AKE TO MAKE O MAKE A SMAR A SMART TRAFFIC T TRAFFIC NETW NETWORK? ORK?

… EVEN IF WE KNOW THE ACHIEVABLE OPTIMUM IN A TRAFFIC NETWORK ???

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

WHY CAN’T WE IMPROVE TRAFFIC…

Because:

• Not enough controls (traffic lights, tolls, speed fines)

→ No chance to unleash the power of feedback!

• Not knowing other drivers’ behavior leads to poor decisions

(a simple game-theoretic fact)

→ Drivers seek individual (selfish) optimum,

not system-wide (social) optimum

PRICE OF ANARCHY (POA)

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

GAME-CHANGING OPPORTUNITY: CONNECTED AUTONOMOUS VEHICLES (CAVs) FROM (SELFISH) “DRIVER OPTIMAL” TO (SOCIAL) “SYSTEM OPTIMAL” TRAFFIC CONTROL NO TRAFFIC LIGHTS, NEVER STOP…

THE “INTERNET OF CARS CARS”

A DECENTRALIZED A DECENTRALIZED OPTIMAL C OPTIMAL CONTR ONTROL OL FRAMEW FRAMEWORK ORK FOR CA FOR CAVs Vs

NO TRAFFIC LIGHTS, NEVER STOP…

CONFLICT AREAS

• COOPERATIVE CONTROL OPPORTUNITIES

Christos G. Cassandras CODES Lab. - Boston University

Merge: on-ramp Merge: roundabout Intersection:

with/without signal

Merge and pass: lane change maneuver

CONTROL ZONES

Christos G. Cassandras CODES Lab. - Boston University

CONTROL ZONE (CZ):

Vehicles can cooperate to achieve desirable performance

Minimize Travel Time through CZ Minimize Energy through CZ Maximize Pssenger Comfort Guarantee Safety

DECENTRALIZED OPTIMAL CONTROL PROBLEM

Christos G. Cassandras CODES Lab. - Boston University

: subject to )] ( ) ( [ 2 1 )

• (

min

2 3 2 2 1 ) (

dt t J w t u w t t w

i t t i i m i t u

m i i i

  

• 1. CAV dynamics
• 2. Speed/Acceleration constraints
• 3. Safety constraints
• 4. Given

5.

) ( ), ( ), ( ,

m i i i i i i i

t x t v t x t

] 1 , [ , 1

3 1

 



 i i i

w w

…for ANY CZ defined in the traffic network Travel Time Energy Comfort

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

THE INTERSECTION MODEL

CAV dynamics:

] , [ ) ( ) (

f i i i i i i

t t t t u v t v p     

: Enters Control Zone (CZ)

i

t

: Exits Merging Zone (MZ)

f i

t

max min max min

) ( ) ( v t v v u t u u

i i

    

Speed, Acceleration constraints: Enters CZ Exits MZ Enters MZ at time

m i

t

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

CAV i MINIMIZATION PROBLEM

Each CAV minimizes TRAVEL TIME + ENERGY COST FUNCTIONAL : subject to ) ( 2 1 ) ( min

2 ) (

dt t u t t

m i i i

t t i i m i t u



  

• 1. CAV dynamics
• 2. Speed/Acceleration constraints
• 3. Order constraints:
• 4. Rear-end safety constraint
• 5. Lateral collision avoidance constraint

m i m i

t t

1 



) ( , : given , ) ( , ) (

i i i m i i i i

t v t L t p t p  

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

SOLUTION – NO ACTIVE CONSTRAINTS

i i i

b t a t u   ) (

*

i i i i

c t b t a t v   

2 *

2 1 ) (

i i i i i

d t c t b t a t p    

2 3 *

2 1 6 1 ) ( Coefficients and optimal merging time

• btained from:

THEOREM: The optimal control is and monotonically non-increasing ) (

*

 t ui

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

SOLUTION – MULTIPLE CONSTRAINTS ACTIVE When constraints are active: Solution is of the same form and still analytically tractable

• Malikopoulos, Cassandras, and Zhang, Automatica, 2018
• Zhang and Cassandras, Automatica, 2019 (subm.)

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

WHO NEEDS TRAFFIC LIGHTS?

With traffic lights With decentralized control of CAVs

One of the worst-designed double intersections ever… (BU Bridge – Commonwealth Ave, Boston, MA)

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

EXAMPLE

WIN-WIN ! + fewer harmful

emissions

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

WHAT HAPPENS IN MIXED TRAFFIC ?

• CAVs
• Non-CAVs

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

MIXED TRAFFIC - CAV BEHAVIOR

: subject to ] ) ) ( ( ) ( [ 2 1 min

2 2 ) (

dt t s t u

i t t i t u

m i i i

   



• 1. CAV dynamics
• 2. Speed/Acceleration constraints

) ( ), ( , : given , ) ( ,

i i i i i m i i m i

t v t p t L t p t 

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

MIXED TRAFFIC – NON-CAV BEAVIOR

• Car-following behavior: The Wiedemann Model [Wiedemann, 1974]
• Collision avoidance model in MZ through Conflict Areas.

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

ENERGY IMPACT OF CAV PENETRATION

Traffic Flow Rate = 700 veh/(hourlane)

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

ENERGY IMPACT OF CAV PENETRATION

Traffic Light Control

NOTE: Impact depends on Traffic Flow Rate !

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

ENERGY IMPACT OF CAV PENETRATION

NOTE: Impact depends on CAV and Non-CAV behavior models

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

CAV PENETRATION IMPACT IN TRAFFIC ROUTING

LINK a FLOW xa COST FUNCTION ta (xa) USER-CENTRIC (selfish) control - Non-CAVs: is the equilibrium flow SYSTEM-CENTRIC (social) control - CAVs: is the equilibrium flow

user a

x

social a

x

Eastern Mass. 13,000+ road segments

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

DO NON-CAVs BENEFIT FROM CAV PENETRATION? Non-CAVs (selfish users) benefit from the addition of CAVs !

INTUITION: CAVs improve resource allocation for everyone, e.g., they decongest a link so that Non-CAVs still using this link benefit

Christos G. Cassandras CISE SE - CODES Lab. - Boston University

DO NON-CAVs BENEFIT FROM CAV PENETRATION? What incentive does a selfish user have to switch to a cooperative game setting (i.e., get a CAV) ???

CONCLUSIONS, OPEN QUESTIONS

Christos G. Cassandras CODES Lab. - Boston University

• When it is optimal for CAVs to decelerate, Non-CAVs are

induced to act optimally (natural platoons formed)

• When it is optimal for CAVs to accelerate, Non-CAVs

become obstacles inducing sub-optimality

• Incentives for Non-CAVs to convert to CAVs ?
• Is Shared Mobility On-Demand the long-term answer ?

(typical car utilization is 4%...)