Optimal Dynamic Pricing Strategies for High Occupancy/Toll (HOT) Lanes
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1 Opimal Dynami Priing Sraegies for High Oupany/oll HO Lanes Yingyan Lou, Yafeng Yin and Jorge A. Laval Deparmen of Civil and Coasal Engineering, Universiy of Florida Shool of Civil and Environmenal Engineering, Georgia Insiue of ehnology
2 Ouline Inroduion eaive Self-Learning Approah Calibraion of willingness-o-pay olling horizon framework for oll opimizaion Simulaion Sudy Model Exensions Alernaive HO lane design Proaive self-learning approah Demand prediion Conlusion and Disussion
3 Congesion Priing Inroduion Firs proposed in 90 s e.g., Pigou,90 and Knigh, 94 HO Lanes One form of ongesion priing Convered from HOV lanes Allows lower-oupany vehiles o pay o gain aess, bu free for high-oupany vehiles Firs implemened in U.S. in 995 S9 in CA, and now five in operaion I-95 in Florida oming soon hp:// Objeives of HO Lanes o provide a superior unongesed raffi servie on he HO lanes while maximizing he hroughpu rae of he freeway
4 Inroduion Con d. Dynami Priing for HO Lanes One way o ahieve he objeives of HO lanes effiienly Need o know Curren raffi ondiion and inoming flow Willingness-o-pay demand of HO lane raffi evoluion afer mooriss rea o he oll Curren praie I-5 in California I-394 in Minnesoa $3.50 $3.00 $.50 $.00 $.50 $.00 $0.50 $0.00 7:09 AM 7: AM 7:5 AM 7:8 AM 7: AM 7:4 AM 7:7 AM 7:33 AM 7:36 AM 7:4 AM 7:48 AM 7:5 AM 7:54 AM 8:00 AM 8:03 AM 8:06 AM 8:09 AM 8: AM 8:5 AM 8:8 AM 8: AM 8:4 AM oll rae ime of day
5 Inroduion Con d. Limiaions of Exising Mehods Praie: heurisi heoreial sudies: ideal siuaions assumed e.g., Arno e al., 998; Chu 995; Liu and MDonald 999; Yang and Huang 997 and Kuwahara 00 esearh Objeive o explore possibiliies of making dynami priing more effeive and more araive o boh ransporaion auhoriies and mooriss
6 Self-Learning Approah o une he demand funion! Calibrae Mooriss Willingness o Pay Based on he raffi dynamis! Opimize raffi Daa from Sensors oll ae
7 Calibraion of Willingness o Pay Conrol uni HOV egular Logi Model λ μ μ μ μ Loop deeors = + exp λ λ oll ag reader α + α β + γ Sysem/Observaion Equaion HO egular μ ln = α λ μ + α β + γ Downsream Bolenek
8 Calibraion of Willingness o Pay Esimaion Algorihm eursive Leas Squares Kalman Filering [ ] = + = + = ˆ ˆ ˆ ln ˆ ˆ ˆ ˆ ˆ ˆ P G I P P P G G y β σ β β β γ α α β μ λ μ γ α α γ α α
9 Opimal oll Deerminaion raffi Dynamis Muli-lane hybrid raffi flow model Laval and Daganzo, 006 o expliily desribe he effe of lane-hanging behaviors Cell HOV/HO egular l m n Downsream Bolenek q q, k =ψ α, α, γ, β, μ, μ m, n l
10 Opimal oll Deerminaion Con d. oll Opimizaion olling Horizon Framework Opimizaion horizon a inerval + + +N N+ Opimizaion horizon a inerval + + N + N ~ max [ qm j + qn j ] + θ min k k β j= + N j= + s.. 0 β β max l j, 0
11 Simulaion Sudy Parameer Calibraion Opimal oll aes.5 α Calibraed Value Aual Value ime Inerval min α.5 Calibraed Value Aual Value ime Inerval min γ 0.5 oll ae $ Calibraed Value Aual Value ime Inerval min ime Inerval min
12 Simulaion Sudy Con d. HO hroughpu HO Densiy HO hroughpu vph Op. oll HOV only No oll Maximum densiy along HO vpmpl Op. oll HOV only Criial Densiy No oll ime Inerval min ime Inerval min Average hroughpu: 49.6/800 vphpl Average Densiy: 30.3 vplpm
13 Model Exensions Alernaive HO Lane Slip amp Configuraion Lane-hanging behavior is largely affeed by he physial onfiguraion of he HO aess design hree ypial designs of HO lane slip ramp HOV/HO egular Downsream Bolenek Average hroughpu: 750.8/800 vphpl Average Densiy: vplpm
14 Model Exensions Con d. Proaive Self-Learning Approah Fluuaing olls may ause safey issues in realiy Predi shor-erm fuure inflows o adjus oll raes in a smooher manner oll ae $ Sheme A Sheme B ime Inerval min Sheme A: eaive Average hroughpu: 08.8/800 vphpl Average Densiy: 6.98 vplpm Sheme B: Proaive Average hroughpu: 075.8/800 vphpl Average Densiy: vplpm
15 Model Exensions Con d. Demand Prediion Assume raffi arrival follows Poisson proess whose average rae is unknown Updaing he disribuion by Bayesian inferene
16 Conluding emarks Self-Learning Approah for HO Lane Operaions Sep : reursive alibraion of mooriss willingness o pay Sep : rolling-horizon oll opimizaion Muli-lane hybrid raffi model for modeling raffi dynamis Exensions More realisi ell represenaions of HO lane slip ramp Proaive approah oordinaion in ime Demand prediion Fuure esearh Coordinaion in spae Loalized v.s. sysem-wide / equiy Issue Heerogeneous users
17 hank You! QUESIONS?
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