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Real time traffic management - challenges and solutions

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Presentation from NORTHMOST - a new biannual series of meetings on the topic of mathematical modelling in transport.

Hosted at its.leeds.ac.uk, NORTHMOST 01 focussed on academic research, to encourage networking and collaboration between academics interested in the methodological development of mathematical modelling applied to transport.

The focus of the meetings will alternate; NORTHMOST 02 - planned for Spring 2017 - will be led by practitioners who are modelling experts. Practitioners will give presentations, with academic researchers in the audience. In addition to giving a forum for expert practitioners to meet and share best practice, a key aim of the series is to close the gap between research and practice, establishing a feedback loop to communicate the needs of practitioners to those working in university research.

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Real time traffic management - challenges and solutions

  1. 1. Real-Time Traffic Management: Challenges and Solutions Ke Han Lecturer (Assistant Professor) Center for Transport Studies Department of Civil and Environmental Engineering, Imperial College London k.han@imperial.ac.uk www.imperial.ac.uk/people/k.han
  2. 2. Outline 1. Overview 2. The CARBOTRAF Project 3. Decision Rule Approach for Real-Time Operation
  3. 3. Real-Time Traffic Management v Challenges Ø Timeliness of decisions Ø Nonlinear and nonconvex objective Ø Multiple objectives Ø Insufficient telecom capacity (centralized vs. distributed) Ø Uncertainties and insufficient data coverage v New Opportunities (more challenges?) Ø Multi-source and heterogeneous data (e.g. mobile data, social media) Ø New collection/communication methods (e.g. crowd sourcing) Ø Need for more robust and fundamentally new theories and methods
  4. 4. Outline 1. Overview 2. The CARBOTRAF Project 3. Decision Rule Approach for Real-Time Operation
  5. 5. The CARBOTRAF Project “A Decision Support System for reduced emissions of CO2 and Black Carbon through Adaptive Traffic Management” Ø Scenario evaluation using traffic and environmental modelling tools Ø Online status updates and decision support Ø Ambient monitoring for evaluation, feedback and learning Ø Two “Pilot Cities” (Glasgow and Graz) Ø Decision Support System with GUI for Traffic Operators
  6. 6. Work Flow of The CARBOTRAF Project Offline modelling & simulation Decision Support System Online Database Interfacetoreal-timedata Real-time traffic data ITS actions Catalogue of ITS actions Traffic simulation Emission models Air quality models Look-up table & database of traffic and emission scenarios Real-time pollutant concentration Real-time air quality data Real-time meteorology data Offline module Online module
  7. 7. Off-Line Modeling Microsimulation Emission Model Dispersion Model • Network model • Traffic flows • Signal plans • Vehicle composition • Vehicle dynamics • Vehicle emission categories • Road elevation • Weather data • Building heights S-Paramics, VISSIM AIRE IFDM
  8. 8. Test Site in West Glasgow Key Performance Indicators v Traffic Ø Travel time Ø Speed Ø Delay v Environment Ø Black Carbon Ø CO2 Ø Nox v Spatial references Ø Network wide Ø Corridor Ø Junction Great W estern Rd. KelvinWay University Av. VMS TSC city center
  9. 9. The CARBOTRAF Project
  10. 10. Reduction of BC Concentration with ITS Actions BC conc (µg/m3) ITS – Base Scenario Boundary condition 1 BC conc (µg/m3) ITS – Base Scenario Boundary condition 2
  11. 11. Managerial Insights Gained from Offline Modeling & Simulation v The effectiveness of ITS actions depends on many factors, which need to be determined and telecommunicated in real time Ø Dynamic demand profile Ø Weather condition Ø Fleet composition v Benefits of the ITS actions are more pronounced at the local level Ø Network level: below 3% Ø Corridor/junction level: 5-30% v In an urban environment, emission is closely related to Ø Traffic flow dynamics (not merely “flow” or “volume”) Ø Fleet composition (bus/LGV/HGV)
  12. 12. Decision Support System v The DSS combines streaming data and the off-line LUT to rank different candidate ITS actions v Input: Ø Current ITS action deployed Ø Probability distributions of KPIs for the complete set of alternative actions (LUT) Ø Operational constraints on the set of ITS actions v Minimization problem (in real time): v Potential issues: Ø Resolution of the Look-Up Table Ø Expectation highly susceptible to outliers and errors Ø Computationally expensive, with additional lags -- Traffic Prediction Tool (Min and Wynter, 2011)
  13. 13. Outline 1. Overview 2. The CARBOTRAF Project 3. Decision Rule Approach for Real-Time Operation
  14. 14. Analytical/ closed-form transformation Decision Rule Approach for Real-Time Traffic Management v Real-time control: Challenges - Timeliness - Nonlinear and nonconvex objective - Distributed vs. centralized control - Uncertainties v Heuristic (genetic algorithm, fuzzy logic), inexact and sub-optimal v Decision Rule (DR) approach for real-time traffic management ü Historical and real-time data ü Within-day and day-to-day variations ü Distributionally Robust Optimization (DRO) to ensure performance in the most adversarial situation ü Efficient on-line operation ü Compatible with analytical computations and microsimulation Real-time system state Control parameters Not optimal? Decision rule
  15. 15. Decision Rule: Concept Off-line module On-line module Analytical/ closed-form transformation Real-time traffic state Real-time decision Decision rule Offline training Real-time traffic state Historical traffic state Look-up table Traffic prediction tool Real-time decision Historical traffic state Offline simulation Decision rule approach CARBOTRAF approach Stochastic optimization Offline simulation
  16. 16. -- real-time information (flow, count, speed, queue) -- Analytical transformation with undetermined coefficients x -- Projection onto feasible control set -- Network performance measure (minimize) (congestion, emission, fuel consumption) Real-time Information q Control u Decision Rule Network performance measure (simulation) Φ(q,u) f (x,q) u = PΩ[ f (x,q)] Decision Rule: Deterministic Formulation q Deterministic Formulation Given real-time information q, find the best decision rule (x): u = PΩ[ f (x,q)]
  17. 17. Linear Decision Rule Time Location/ data type past T observations REAL-TIME DATA CONTROL COEFFICIENT
  18. 18. Nonlinear Decision Rule (Artificial Neural Network) REAL-TIME DATA CONTROL ANN . . . . . . Artificial Neural Network v : a neural network with m hidden layers and n neurons v Activation function pre-determined (e.g. sigmoid functions) v x represents the weights of the connections between neurons
  19. 19. Decision Rule: Stochastic Extension v In reality, q is stochastic, subject to within-day & day-to-day variations v Stochastic programming – exact probability distribution required v Ambiguous information on the distribution with finite samples v Distributionally robust optimization (DRO) Ø Worst-case scenario (‘max’), Ø among all candidate distributions Ø Subsumes stochastic optimization Ø Data-driven calibration of Distributionally Robust Formulation Given stochastic input q, find the best decision rule coefficient x: “Uncertain distributions (DRO) instead of uncertain parameters (RO)”
  20. 20. Advantages of the Decision Rule Approach v Finding the best responsive signal strategy è Finding x v Feasible and efficient on-line operation - Off-line: Distributionally robust optimization (expensive) - On-line: Linear transformation and projection (inexpensive) v Flexible sensor location, data type, and control resolution v User-defined feasible set for signal control parameters v Two solution procedures for the off-line problem: - Mixed integer linear program - Metaheuristic search Distributionally Robust Optimization
  21. 21. v Kolmogorov-Smirnov (K-S) goodness-of-fit test (Massey, 1951; Bertsimas et al., 2013): v Random variable: ,parameterized by v Uncertainty set: ,parameterized by v Fix ,and consider K samples (historical data) v Does a distribution well capture a finite set of sampled data? v Reject H0 at the level α if Data-Driven Calibration of the Uncertainty Set Set of candidate distributions
  22. 22. Formulation of the Uncertainty Set
  23. 23. Evaluating the Objective Function v Random Variable (objective): , parameterized by v Lower and upper bounds of : , partitioned into W intervals v Fix (control), g1Lf Uf g2 gi-1 gi . . . . . . K-S test
  24. 24. Numerical Study, Part 1 Great Western Rd Great Western Rd ByresRd City Center University of Glasgow § West end of Glasgow § 5 signalized intersections § 35 directed links § LWR network model Network Data § Turn-by-turn flow count § 8-9 am, 7 June 2010 § Daily variations are generated synthetically, using a variety of distributions Benchmarks § Fixed signal timing (deterministic & DRO) § Field signal parameters (Glasgow City Council)
  25. 25. Numerical Study: Part 1 Particle Swarm Optimization Great Western Rd Great Western Rd ByresRd City Center University of Glasgow § Zeroth-order information on the objective and constraints § LWR-based network simulation model § Flexible trade-off between solution quality and computational cost § Off-line computational time: 24h § On-line computational time: negligible Criteria Deterministic Fixed timing DRO Fixed timing Field parameter (Glasgow City) LDR-DRO NDR-DRO Objective (maximize) 1.61 3.81 4.14 4.28 4.34 Throughput 1498 (veh) 3382 (veh) 3576 (veh) 3910 (veh) 3951 CPU time (offline/online) 24h/- 24h/- -/- 24h/0.01s 24h/0.03s
  26. 26. Numerical Study: Part 2 v 4-by-4 grid network in S-Paramics v 8 zones, 56 O-D pairs v Dynamic route assignment v Fleet: passenger car, LGV, MGV, HGV, coach v 4-stage signal plan at all four junctions v 30 random seeds for generating samples 72 74 76 78 80 82 1 AverageDelay(s) 3.0% improvement
  27. 27. 210 215 220 225 230 235 240 245 250 0 1 2 3 4 5 6 7 Average Vehicle Delay (s) Count 215 220 225 230 235 240 245 1 2 AverageVehicleDelay(s) Numerical Study: Part 3 v West Glasgow in S-Paramics v 21 zones, 420 O-D pairs v Dynamic route assignment v Fleet: passenger car, LGV, MGV, HGV, coach v 30 random seeds for generating samples v 80 PSO major iterations v Signal optimization at the key junction Byres Rd. & University Ave. NDR-DRO Webster 1.3% improvement
  28. 28. Numerical Study: Part 4 v The decision rule approach combined with metaheuristic methods allow for sufficiently nonlinear and non-analytical objective functions, such as v Emission (hydrocarbon, HC) is calculated based on vehicle speed, density, and acceleration/deceleration derived from the kinematic wave model, and the instantaneous HC emission model (Ahn et al., 2002) f = w× Throughput - (1− w)× Total Emission w ∈ [0,1] Great Western Rd Great Western Rd ByresRd City Center University of Glasgow 3100 3200 3300 3400 3500 3600 3700 3800 3900 4000 3.1 3.15 3.2 3.25 3.3 3.35 3.4 3.45 x 10 7 Throughput (veh) TotalHCEmission(µg) w=0.1 w=1.0 (no emission consideration)
  29. 29. Thank you! k.han@imperial.ac.uk

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