Traffic Flow Control in a Connected Environment Petros Ioannou Center for Advanced Transportation Technologies METRANS University Transportation Center University of Southern California Los Angeles, CA, USA 1 7/10/2019 NSF Workshop June 8-9, 2019
Brief History • Automated Highway System Program started in the 80’s ended with 1997 Demo. Platooning plus other technologies • Replaced with IV initiative with vehicle safety as priority • 2004, 2005, 2007 DARPA Challenge Competition • Current: Autonomous Vehicles, 5 levels of Autonomy (Google Cars, Tesla, Uber etc) • Efforts are to get rid of the driver when vehicles is the cause of congestion NSF Workshop June 8-9, 2019 2 7/10/2019
Vehicle Control Safety and Platooning 𝑊 𝑊 ΔV 2 2 1 𝑇 Drag reduction: Fuel savings, lower at collision 𝛦𝑊 = 𝑊 1 − 𝑊 2 pollution Spacing 𝑇 P A M P : Platoon spacing ( 1 meter) 1 A : Automated M : Manual; Capacity ∝ 𝑇 Safety Objective: No vehicle should be put in a position it cannot handle NSF Workshop June 8-9, 2019 3 7/10/2019
WHAT IS THE MAIN TRANSPORTATION PROBLEM? This is what we usually see and experience Image from Wikipedia Image from www.msnbc.com NSF Workshop June 8-9, 2019 4 7/10/2019
Transportation System for Moving Goods and People is far more complex RAIL OCEAN ROAD PORT 5 7/10/2019 NSF Workshop June 8-9, 2019
CURRENT TRANSPORTATION SYSTEM • Nonlinear Dynamical System of interconnected systems • Open Loop Most of the Time • Limited ineffective feedback • Lack of sensor data and connectivity Consequences • Congestion • Inefficient utilization of infrastructure • Safety • Pollution • Long travel times, High cost • Unbalanced in time and space 7/10/2019 6 NSF Workshop June 8-9, 2019
Connectivity will Revolutionize Transportation • Open loop operations will become more stable and robust via active feedback • Information/data are crucial in optimizing processes and movements of people and goods • Enhance coordination • Vehicle to Infrastructure Connectivity is Proven Technology • Private sector is moving faster to satisfy user needs NSF Workshop June 8-9, 2019 7 7/10/2019
Traffic Management Control (TMC) System TMC System T 2 Data Control Traffic T 1 Inputs Acquisition Controller & Processing T 0 Traffic System Output:Traffic Data NSF Workshop June 8-9, 2019 8 7/10/2019
Closing the loop with the Highway System Speed, TMC Location, OD, Optimum status (incident Beacons speed limits, report) Lane Change, VSL Routing, Pricing Ramp metering Ramp commands Metering NSF Workshop June 8-9, 2019 9 7/10/2019
MANETs For Lane Change Control and Collision Avoidance NSF Workshop June 8-9, 2019 10 7/10/2019
Control of traffic at incidents and bottlenecks • Highway congestions at bottlenecks is detrimental to traffic mobility, safety and environment • Upstream drivers lack of information of bottleneck therefore blindly change lanes when traffic slows down • Forced lane changes performed at vicinity of bottlenecks introduce capacity drop , which further harm the flow rate • Appearance of trucks exacerbate the congestion condition NSF Workshop June 8-9, 2019 11 7/10/2019
NO CONTROL NO CONNECTIVITY
Modeling of Highway Bottleneck Capacity drop 𝑤 𝑔 𝜍 , 𝜍 ≤ 𝜍 𝑒,𝑑 𝑟 𝑐 = ൝ ሺ1 − 𝜗)𝐷 𝑐 , 𝜍 > 𝜍 𝑒,𝑑 Capacity will drop when 𝜍 • > 𝜍 𝑒,𝑑 . Difficult to maintain maximum flow rate by controlling just the speed • NSF Workshop June 8-9, 2019 13 7/10/2019
Design of Lane Change Controller to prevent last minute forced lane changes Two Parts: ❖ Design of lane change control distance How far from incident should start recommending lane changes? ❖ Design of lane change control pattern What lane change recommendation should give in each lane? Not a traditional control problem as the key variable is not time but space. NSF Workshop June 8-9, 2019 14 7/10/2019
Design of Lane Change Controller based on an empirical model developed using simulation tests Length of LC Control Segment: 𝑒 𝑀𝐷 = 𝜊 ⋅ 𝑜 n : number of lanes closed 𝜊 : design parameter based on the demand and capacity NSF Workshop June 8-9, 2019 15 7/10/2019
Effect of Lane Change Control NSF Workshop June 8-9, 2019 16 7/10/2019
Effect of Lane Change Control Without LC Control: With LC Control: Data points for 𝜍 𝑒 ≤ 𝜍 𝑒,𝑑 fits the linear No obvious capacity drop • • relation very well; 𝜍 𝑒 at 𝜍 𝑒 > 𝜍 𝑒,𝑑 is approximately linear • Significant capacity drop occurs, 𝜗 ≈ 0.16 with a negative • Data points concentrate in high density Most data points scatter close to 𝜍 𝑒 > • • area 𝜍 𝑒,𝑑 NSF Workshop June 8-9, 2019 17 7/10/2019
Protecting the Network NSF Workshop June 8-9, 2019 18 7/10/2019
Variable Speed Limit Control • If demand increases to the point that exceeds capacity of bottleneck then congestion will kick in. Need a control mechanism to protect the network • Provide speed recommendations upstream the bottleneck or incident in order to slow down the traffic flow to become close to the throughput of the bottleneck. • Approach is implemented at various highways in Europe and US but in an adhoc way NSF Workshop June 8-9, 2019 19 7/10/2019
1.Carlos F Daganzo. The cell transmission model: A dynamic representation of highway track consistent with the hydrodynamic theory. Transportation Research Part B: Methodological , 28(4):269-287, 1994. NSF Workshop June 8-9, 2019 20 7/10/2019
Traffic Flow Model and Stability Analysis Let 𝐽 = ሺ𝐷 𝑒 , 𝐷, 𝑒) be the state of the network and Ω be the set of feasible values of 𝐽 with 𝑒 ≥ 0, 𝐷 𝑒 > 0, 𝐷 > 0 . All possible relationships between 𝐷 𝑒 , 𝐷 and 𝑒 are described by the tree diagram below: Capacity Drop No Capacity Drop NSF Workshop June 8-9, 2019 21 7/10/2019
ሶ Equilibrium Points when Inflow = Outflow i.e. 𝑟 1 = 𝑟 2 𝜍 = 0 NSF Workshop June 8-9, 2019 22 7/10/2019
Variable Speed Limit Control NSF Workshop June 8-9, 2019 23 7/10/2019
Variable Speed Limit (VSL) Control NSF Workshop June 8-9, 2019 24 7/10/2019
Density Model VSL Controller NSF Workshop June 8-9, 2019 25 7/10/2019
Main Theorem The proposed VSL Controller guarantees that densities converge exponentially to a single equilibrium point 𝜍 ∗ = min[𝑒,𝐷 𝑒 ] 𝑤 𝑔 that corresponds to maximum possible flow and speed under any demand and capacity constraints. Proof: based on simple Lyapunov stability arguments NSF Workshop June 8-9, 2019 26 7/10/2019
𝑒 < 1 − 𝜁 0 ∗ 𝐷 𝑒 NSF Workshop June 8-9, 2019 27 7/10/2019
𝑒 = 1 − 𝜁 0 ∗ 𝐷 𝑒 NSF Workshop June 8-9, 2019 28 7/10/2019
1 − 𝜁 0 ∗ 𝐷 𝑒 < 𝑒 ≤ 𝐷 𝑒 NSF Workshop June 8-9, 2019 29 7/10/2019
𝐷 𝑒 < 𝑒 < 𝐷 NSF Workshop June 8-9, 2019 30 7/10/2019
Why it Works: Less for More https://www.youtube.com/watch?v=9QwPfe-_T7s NSF Workshop June 8-9, 2019 31 7/10/2019
Multiple Sections NSF Workshop June 8-9, 2019 32 7/10/2019
Numerical Simulation 1. Simulation Network: Simulation Setup: 16km-long southbound segment of I-710 freeway in California, whose normal capacity without an accident is about 6800 veh/h. 2. Incident Scenarios: We construct accident scenarios with different accident durations 3. Monte Carlo Simulation 10 sets of Monte Carlo simulation for each scenario in microscopic simulations. NSF Workshop June 8-9, 2019 33 7/10/2019
Fundamental Diagram under Control • Traffic states can be stabilized in a small region for different demand levels • Density stops increasing when demand higher than the capacity • Flow speed decreases when density close to the critical value NSF Workshop June 8-9, 2019 34 7/10/2019
Performance Criteria Control Improvements for considered scenarios Total Time Spent in Network 10-15%. Number of Stops 80-90% Number of Lane Changes 6-10% NOx 6-7% CO2 7-8% Fuel 7-8% PM25 4-7% NSF Workshop June 8-9, 2019 35 7/10/2019
Coordination and connectivity in multimodal: Co-Simulation Optimization Control Approach Final Decision Stopping Controller Criteria Transportation Network Network states Network Network Data Optimization Simulation Models NSF CPS Synergy: Cyber Physical Regional Freight Transportation System NSF Workshop June 8-9, 2019 36 7/10/2019
Conclusions • Connectivity (V to V and V to I) is a key technology in achieving transportation efficiency • Connectivity will generate vital information and provide missing data that are necessary for effective control and optimization designs • Vehicle automation, self driving vehicles will face the major challenge of Safety • The main causes of congestion are too many vehicles. Getting rid of the driver and keeping the vehicle is unlikely to reduce congestion • Congestion is a system level problem. The system is dynamical and feedback control and optimization are important tools to make it stable, robust and efficient NSF Workshop June 8-9, 2019 37 7/10/2019
THANK YOU NSF Workshop June 8-9, 2019 38 7/10/2019
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