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

HO HOW MANY W MANY SMAR SMART CARS T CARS DOES IT TAKE T DOES IT T AKE TO MAKE O MAKE A SMART TRAFFIC A SMAR T TRAFFIC NETWORK? NETW ORK? C. G . G. Cassand . Cassandras as Division of Systems Engineering Dept. of Electrical and Computer Engineering Center for Information and Systems Engineering Boston University CODES Lab. - Boston University Christos G. Cassandras

WHY CAN’T WE IMPROVE TRAFFIC… … EVEN IF WE KNOW THE ACHIEVABLE OPTIMUM IN A TRAFFIC NETWORK ??? 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, PRICE OF ANARCHY not system-wide (social) optimum (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 THE “INTERNET OF CARS CARS ” NO TRAFFIC LIGHTS, NEVER STOP… Christos G. Cassandras CISE SE - CODES Lab. - Boston University

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 Merge: roundabout Merge and pass: lane change maneuver Merge: on-ramp Intersection: with/without signal Christos G. Cassandras CODES Lab. - Boston University

CONTROL ZONES CONTROL ZONE (CZ): Vehicles can cooperate to achieve desirable performance Minimize Travel Time through CZ Minimize Energy through CZ Maximize Pssenger Comfort Guarantee Safety Christos G. Cassandras CODES Lab. - Boston University

DECENTRALIZED OPTIMAL CONTROL PROBLEM Travel Time Energy Comfort   m t 1 i m 0 2  2 min w ( t - t ) [ w u ( t ) w J ( t )] dt 1 i i 2 i 3 i 2 0 u ( t ) t i i subject to : 1. CAV dynamics 2. Speed/Acceleration constraints 3. Safety constraints 0 0 0 m 4. Given , ( ), ( ), ( ) t x t v t x t i i i i i i i 3    1 , [ 0 , 1 ] w w 5. i i  i 1 …for ANY CZ defined in the traffic network Christos G. Cassandras CODES Lab. - Boston University

THE INTERSECTION MODEL   CAV dynamics: p v ( t ) i i   v u ( t ) i i  0 f [ , ] t t t i i : Enters Control Zone (CZ) 0 t i f : Exits Merging Zone (MZ) t i Speed, Acceleration constraints: Enters CZ Exits MZ   u u ( t ) u min max i    0 v v ( t ) v min i max m Enters MZ at time t i Christos G. Cassandras CISE SE - CODES Lab. - Boston University

CAV i MINIMIZATION PROBLEM m t  1 i    m 0 2 min ( t t ) u ( t ) dt i i i 0 2 u ( t ) t i i subject to : 1. CAV dynamics 2. Speed/Acceleration constraints m  m 3. Order constraints: t t  i i 1 4. Rear-end safety constraint 5. Lateral collision avoidance constraint   0 m 0 0 p ( t ) 0 , p ( t ) L , given : t , v ( t ) i i i i i i i Each CAV minimizes TRAVEL TIME + ENERGY COST FUNCTIONAL Christos G. Cassandras CISE SE - CODES Lab. - Boston University

SOLUTION – NO ACTIVE CONSTRAINTS   1 1 1 *     u ( t ) a t b *  2   * 3 2 v ( t ) a t b t c p ( t ) a t b t c t d i i i i i i i i i i i i 2 6 2 Coefficients and optimal merging time obtained from: THEOREM: *  The optimal control is and monotonically non-increasing u i ( t ) 0 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 + fewer harmful WIN-WIN ! 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 m t  1 i 2     2 min [ ( ) ( ( ) ) ] u t s t dt i i 2 0 u ( t ) t i i 1. CAV dynamics subject to : 2. Speed/Acceleration constraints m m  0 0 0 , ( ) , given : , ( ), ( ) t p t L t p t v t i i i i i i i i 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 x a COST FUNCTION t a ( x a ) Eastern Mass. 13,000 + road segments user USER-CENTRIC (selfish) control - Non-CAVs: is the equilibrium flow x a SYSTEM-CENTRIC (social) control - CAVs: is the equilibrium flow social x a 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) ??? Christos G. Cassandras CISE SE - CODES Lab. - Boston University

CONCLUSIONS, OPEN QUESTIONS 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%...) Christos G. Cassandras CODES Lab. - Boston University