Guido Cantelmo Prof. Francesco Viti. Practical methods for Dynamic Demand Estimation in congested Networks

Transcription

1 Guido Cantelmo Prof. Francesco Viti MobiLab Transport Research Group Faculty of Sciences, Technology and Communication, Practical methods for Dynamic Demand Estimation in congested Networks University of Luxembourg June 1-2, Workshop on Smart Mobility - Bourglinster, Luxembourg

2 Presentation Outline Introduction: The OD estimation at a glance; The Two-Step Approach; Dynamic Demand Estimation Part I: Motorways and Simple Networks; Solution Methods; Results with real data; Dynamic Demand Estimation Part II: Urban and Heterogeneous networks; Explorative analysis on big sixed networks; Preliminary results: Luxembourg city;

3 Introduction 1: The OD estimation at a glance The current state of the practice for managing Transportation Systems: Demand Model Supply Model OD estimation uses traffic information and Big Data to calibrate the demand model Traffic state estimation

4 Introduction 2: The OD estimation at a glance Traffic Zone A 1 Simulation Traffic Zone C Traffic Zone B Observations Where are these vehicles coming from? Are we interest in estimation or prediction?

5 Introduction 3: The OD estimation at a glance The mathematical formulation of the Demand Estimation problem: Demand Data Link Data Node Data Route Data Other Data x = argmin x z 1 d, x w 1 + z 2 l o, l s w 2 + z 2 n o, n s w 2 + z 2 r o, r s w 2 + z 2 D o, D s w 2 S.t. f s = Ax = BPx DTA Dynamic Traffic Assignment Network Loading and Behavioral model Frederix 2012 points out the relevant of the Starting Matrix Issues: Few data vs Too many different data; Models need to be sufficiently accurate; Highly combinatorial and non linear; Choose the correct starting point

6 Introduction 4: The Two-Step Approach Two Steps Demand Estimation: First Step: Broad Exploration of the Solution Space X = argmin G z 2 f o, f s w 2 Second Step: Finding the right OD flows GF ODflows = argmin x z 1 d, x w 1 +z 2 f o, f s w 2 f s = A c x = B c x GoalFunction New GoalFunction Local Minimum Global Minimum Demand

7 Dynamic Demand Estimation Part I: Motorways and Simple Networks Why motorways? No/Limited route choice; Easy to model; Homogeneous travel behavior;

8 Space Km Dynamic Demand Estimation Part I: Motorways and Simple Networks Why motorways? No/Limited route choice; Easy to model; Homogeneous travel behavior; Speed Inner ring Antwerp, Belgium 39 Nodes; 56 Links; Simulated Period: 5:30-10:30 Traffic Data every 5 minutes; 966 time dependent OD pairs; Total starting demand Trips; Time Minutes Experiment setup: Only Link Flow within the Objective Function Speeds are used to verify the quality of the result

9 SPSA: Simultaneous Perturbation Stochastic Approximation Dynamic Demand Estimation Part I: Solution Methods SBODE: Sensitivity Based OD estimation Frederix [1] 1 x J J J θ G F t t i ˆ r k k k i k k i i i k c z c z Δ Δ Δ θ Δ θ θ g Grad_rep ˆ _ 1 rep Grad k k k i i i θ g θ g θ G FDSA: Finite Difference Stochastic Approximation r k k k i k k i i i i c z c z θ θ G

10 Dynamic Demand Estimation Part I: Solution Methods Data-Based Two-Step Approach Network-Based Two-Step Approach Generation-Based Two-Step Approach OD pairs with the maximum error OD pairs on the main Bottleneck Generated Demand Flows FDSA All Variables All Variables All Variables SPSA SBODE Research question: Can we do better? Can we improve efficiency? Can we provide more robust results?

11 Space Km Space Km Space Km Dynamic Demand Estimation Part I: Results with Real Data OBSERVATIONS Real Data Speed SBODE Speed SPSA Speed Time Minutes Time Minutes Error reduction 97 % Time Minutes Error reduction 84 % Computational time Computational time 12 days 4 days

12 Space Km Space Km Space Km Dynamic Demand Estimation Part I: Results with Real Data OBSERVATIONS Real Data Speed SBODE Speed SPSA Speed Time Minutes Time Minutes Error reduction 96 % Time Minutes Error reduction 78 % Computational time Computational time 4 days 4 days

13 Space Km Space Km Space Km Dynamic Demand Estimation Part I: Results with Real Data OBSERVATIONS Real Data Speed SBODE Speed SPSA Speed Time Minutes Time Minutes Error reduction 98 % Time Minutes Error reduction 78 % Computational time Computational time 14 days 24* days

14 Space Km Space Km Simulation Dynamic Demand Estimation Part I: Results with Real Data OBSERVATIONS Real Data Speed SPSA Speed Link Flows Time Minutes Time Minutes Observation Experiments show that: The OF improves 1%; The solution is more robust: Less variance in the solution; The solution is closer to the Seed Matrix; Different setups, same result;

15 Dynamic Demand Estimation Part I: Conclusions for Simple Networks Two-Step approach has a more reliable solution for DDEP; Introducing a Two-Step procedure, the localism of the DDEP decreases; The variance of the results decreases; Computational time can decrease; Can exploit different models, thus their properties;

16 Dynamic Demand Estimation Part II: Urban and Heterogeneous networks Why so complex? Route choice; Difficult to model; Heterogeneous travel behavior;

17 GF GF Dynamic Demand Estimation Part II: Urban and Heterogeneous networks A more reliable solution Incremental Demand X = α X real Convex Combination X = α X real + 1 α X starting alpha alpha

18 Dynamic Demand Estimation Part II: Explorative analysis on big sized networks Small Network of Luxembourg 17 traffic zones Large number of Variables OD pairs 24 h of Simulation 32 Loop Detectors vs 2744 active Links ~250 links

19 Objective function Dynamic Demand Estimation Part II: Explorative analysis on big sized networks Two-Step vs Single-Step Only Link flows Goal Function Single Step Two Step 0 Iterations Seed Two-Step Single-Step RMSE link Veh/h RMSE Speed Veh/h RMSE OD Veh/h

20 Dynamic Demand Estimation Part II: Explorative analysis on big sized networks Two-Step vs Single-Step Only Link flows SINGLE-STEPS 0 Seed Two-Step Single-Step RMSE link Veh/h RMSE Speed Veh/h RMSE OD Veh/h

21 Dynamic Demand Estimation Part II: Explorative analysis on big sized networks Two-Step vs Single-Step Only Link flows 0 Seed Two-Step Single-Step RMSE link Veh/h RMSE Speed Veh/h RMSE OD Veh/h

22 Dynamic Demand Estimation Part II: Explorative analysis on big sized networks Working with Big Data: Mobile Network Data 2 Clusters of Antennas: External and internal; Generated Flow TO Luxembourg and FROM Luxembourg Handovers have been used to calculate the Generated Demand Demand entering in Luxembourg Demand leaving Luxembourg Data provided by POST Luxembourg

23 % Generated Demand % Generated Demand Dynamic Demand Estimation Part II: Explorative analysis on big sized networks Real data Four-Step Approach Time of the day [h] Time of the day [h] t GenInt GSM t GenExt GSM Data provided by POST Luxembourg

24 Objective function Dynamic Demand Estimation Part II: Explorative analysis on big sized networks GSM data: Faster Optimization; TWO-STEP GSM GSM No GSM No GSM Iterations Two-Steps: More reliable results;

25 Dynamic Demand Estimation Part II: Preliminary results: Luxembourg city Context: OD Estimation In Luxembourg City Small country 2586 km 2 & small population ; jobs in the country; cross border workers: from Belgium; from Germany; from France; Acknowledgments: Francois Sprumont UL

26 Dynamic Demand Estimation Part II: Preliminary results: Luxembourg city The network of Luxembourg: 4056 Links; 1469 Nodes; 2116 ODs variables Ettelbruck Traffic Information: Link Flows -121 Counting Station Every Hour Speeds Probe Vehicles Belgium Arlon Luxembourg City Germany Trier Dynamic Demand: Static data Departure Time choice model Esch sur Alzette France Thionville-Metz

27 Simulated Flows Simulated Flows Dynamic Demand Estimation Part II: Preliminary results: Luxembourg city Results: Link Flows STARTING-POINT TWO-STEP r 2 = 0.08 r 2 = 0.6 Observed Flows Most of the improvement is the first step Observed Flows

28 Speeds Veh/h Speeds Veh/h Dynamic Demand Estimation Part II: Preliminary results: Luxembourg city Results: Congestion Pattern: Motorways Ring Urban roads Luxembourg City Estimation Observation Starting Point Time of the day [h] Time of the day [h] Underestimation of the congestion;

29 Internal External Demand Dynamic Demand Estimation Part II: Preliminary results: Luxembourg city Validation: Mobile Network data Internal VS External Demand Under estimation of the demand Travel Time Time of the day [h] Data provided by POST Luxembourg

30 Conclusions More data are needed when dealing with large and heterogeneous networks; Validation is needed; The proposed framework shows is capability in dealing with small and large networks: Computational time; Quality of the solution; Reducing the localism of the problem; Challenges and future work; Including more data in the OD estimation GSM Exploiting smarter algorithms Adaptive-SPSA, W-SPSA, C-SPSA; Reducing the number of variables PCA; Working on the parameters of the departure time choice model to improve the quality of the seed matrix;

31 Questions?