A novel metamodel-based framework for large-scale dynamic origin-destination demand calibration Takao Dantsuji Institute of Science and Engineering, Kanazawa University (Joint work with Nam H. Hoang, Nan Zheng and Hai L. Vu at Monash University)
2 ・OD demand estimation Estimating general OD matrices for traffic planning and design ・ OD demand calibration Calibrating general OD matrices for a stochastic traffic simulator
• A tool to describe the complex interactions of many traffic components of the demand and supply sides • What is likely to occur quantitatively ・ Useful for policy makers to investigate the performance of the pre-determined policies Zheng, Dantsuji, Wang and Geroliminis 2017, TRR Dantsuji et al. 2021, Transportation 3
The input for simulation (e.g., traffic demand) is a key component . • Reliability of simulations • Calibration ・The general purpose algorithms (e.g., SPSA, GA, Kalman filter) • Applicable to a wide range of problems • The computational efficiency is not a priority • Dynamic OD calibration for large-scale network is challenging • Computational efficiency • Scalability • The lack of quantitatively methods to evaluate the calibration performance at large-scales • How to connect OD matrix with the complex traffic dynamics at aggregated levels SPSA : Stochastic Perturbation Stochastic Approximation
.  A traffic model at the network level The MFD relates the network flow to the network density (Daganzo, 2007) . ・ Some requirements for the well-defined MFD (Geroliminis and Daganzo, 2008) • Homogeneous congestion patter over space • Average trip length is constant over time 5 • Propose a novel OD matrix calibration framework for large-scaled networks •  aggregated traffic flow dynamics ・ metamodel optimization approach • Utilize multiple data sources for deriving the ground-truth values • Demonstrate the scalability, accuracy and efficiency
.  A simulation network is divided into N regions (e.g., Ji and Geroliminis, 2012) Traffic demand from centroids are aggregated to representative regional centroids . • Optimization problem for OD demand calibration min
MSE in the total accumulations Distance between initial and optimized demands D : vector of the regional car OD matrix N, , : ground truth total accumulation in region i at time t nç,(D) : Car accumulation in region i at time t from simulation with demand D n ; ; (D) : Bus accumulation in region ; at time ; from simulation with demand D D ρ (t) : Initial demand generated in region i with final destination j at time t D, ;(t) : demand generated in region i with final destination j at time t δ」：weight factor 7
. Dimension as the size of the problem is I × I × T I,T : number of regions, time steps . ・Even for a small-scale network (e.g. 3 regions, 15 time steps), the dimension is 135 • Calibration of the aggregated OD matrices is still high-dimensional problem • Running multiple replications of the simulation is expensive • An efficient algorithm that require a few iterations has to be developed
・ A model of the models : simpler deterministic approximating function The proposed metamodel optimization .
. The objective function estimate is produced with low computational burden 9
10 . Analytical macroscopic traffic flow model (Zheng and Geroliminis, 2013; Yildirimoglu et al., 2015)
jEJ Number of vehicles
Capaciated inflow Inflow Outflow Regional choices probability Average travel time Average travel speed
• The heterogeneity exists in the trip lengths or congestion patterns over spaces (Buisson and Ladier, 2009; Mazloumian et al., 2010; Sun and Geroliminis, 2011) • Gaps between the simulated and the analytical accumulations . To fill the gaps, the metamodel parameters are adjusted analytical accumulation of sample s adjusting parameter at iteration h sES tamodel parameter at iterati a set of samples Subject to metamodel parameter at next iteration .  Weight wh(D c ) 11

Real datasets
Bluetooth travel speed data Traffic volume data IC card transaction data Calibration datasets Initial profile OD matrix Route choice parameter Bi-modal MFD model Estimation (i.e.  free-flow speed and marginal effects of car and bus accumulations on travel speeds a t , a t and a t in Eq.(11))) - Ground-truth traffic conditions (i.e. car accumulation N ξ in Eq. (3)) Sioux-falls (SF) network
. The performance of the proposed approach and SPSA • A few iterations are needed to understand the direction of parameters’ adjustment • After 5th iteration, the objective function estimated becomes stable over iterations SPSA 14
15 SPSA at 10th iteration The proposed approach at 10th iteration
Sensitivity analysis on weight factor Sensitivity analysis on initial demand Sensitivity analysis on number of regions
17 Ground-truth (dotted) and simulated (solid) accumulations • Data for grand-truth values .  SCATS data •  Bluetooth travel time ・IC smart card (Myki data) Initial (blue) & simulated (red) Obj. function estimated
Conclusions • Developed a computationally efficient metamodel optimization framework for the OD demand calibration of large-scaled networks • Utilized the region-based traffic dynamics as an analytical model of the metamodel . Tested the proposed approach with two case studies Future directions • Extend to other optimization problems such as dynamic congestion pricing