Pareto- -improving Congestion improving Congestion Pareto Pricing - PowerPoint PPT Presentation

Pareto- -improving Congestion improving Congestion Pareto Pricing on Multimodal Pricing on Multimodal Transportation Networks Transportation Networks Wu, Di Wu, Di Civil & Coastal Engineering, Univ. of Florida Civil & Coastal Engineering, Univ. of Florida Yin, Yafeng Yafeng Yin, Civil & Coastal Engineering, Univ. of Florida Civil & Coastal Engineering, Univ. of Florida Lawphongpanich, Lawphongpanich , Siriphong Siriphong ( ( Toi Toi) ) Industrial & System Engineering, Univ. of Florida Industrial & System Engineering, Univ. of Florida CMS Annual Student Conference March 2009

Outline Outline � Background Background � � Pareto Pareto- -Improving Pricing Scheme Improving Pricing Scheme � � Pareto Pareto- -Improving Pricing Problem on Improving Pricing Problem on � Multi- -modal Network modal Network Multi � Mathematical Model Mathematical Model � � Numerical Examples Numerical Examples � � Conclusion Conclusion �

Background Background � Congestion Pricing Congestion Pricing � � Alleviate traffic congestion by charging tolls. Alleviate traffic congestion by charging tolls. � � Current Practice: Current Practice: � � London, UK London, UK � � Singapore Singapore � � Stockholm, Sweden Stockholm, Sweden � � Can successfully reduce congestion, but is still Can successfully reduce congestion, but is still � facing strong objection from the general facing strong objection from the general public. public.

Example Example 2 10v 13 2+ 25v 34 10+ v 32 1 3 10v 24 50+ v 12 4 There are 3.6 travelers for OD pair (1, 3)

Example (Contd.) Example (Contd.) System Optimal User Equilibrium Pareto-I mproving Under Marginal Cost Toll 2 2 2 2 1.3223 2 2 1.1685 1.79 1 1 0.45 3 3 1 1 1 1 3 3 3 3 0.8956 2.2772 1.36 1.5359 4 4 4 4 4 4 2 2 2 2 2 2 35.06 36.00 20.64+ 20.64 22.40 31.21+ 29.21 46.75+ 0.31 12.28 10.89+ 0.90 10.45+ 18.51 1 1 3 3 1 1 3 3 1 1 3 3 51.53+ 1.54 50.00 18.10 22.78 24.32+ 24.32 51.36 4 4 4 4 4 4 Total travel time: 241.17 Total travel time: 227.11 Total travel time: 255.82 1-2-3: 101.70 1-2-3: 69.46 1-2-3: 71.06 1-2-4-3: 101.70 1-2-4-3: 69.46 1-2-4-3: 71.06 1-4-3: 101.70 1-4-3: 69.46

Pareto- -Improving Approach Improving Approach Pareto � By Italian economist By Italian economist Vilfredo Vilfredo Pareto Pareto � � make at least one individual better off make at least one individual better off � without making any other individual worse without making any other individual worse off off

Single Modal Pareto- -Improving Improving Single Modal Pareto Scheme Scheme � Studied by Studied by Lawphongpanich Lawphongpanich and Yin and Yin � (2008) (2008) � Pareto Pareto- -improving condition may be improving condition may be � relatively prevalent relatively prevalent � Exact Pareto Exact Pareto- -improvement may not lead improvement may not lead � to significant travel time reduction. to significant travel time reduction.

Multi- -Modal Pareto Modal Pareto- -Improvement Improvement Multi � Develop a Pareto Develop a Pareto- -improving model improving model for for � multimodal networks. multimodal networks. � Allow cross Allow cross- -subsidy of different travel subsidy of different travel � modes to encourage travelers switch to modes to encourage travelers switch to higher occupancy travel modes in order to higher occupancy travel modes in order to further increase the system efficiency. further increase the system efficiency.

Multi- -Modal Pareto Modal Pareto- -Improvement Improvement Multi (Contd.) (Contd.) � Three travel modes: Three travel modes: � � Single Occupancy Vehicle Single Occupancy Vehicle � � High Occupancy Vehicle High Occupancy Vehicle � � Transit (transit shares highway lanes with auto modes) Transit (transit shares highway lanes with auto modes) � � Three types of transportation facilities: Three types of transportation facilities: � � Regular (Toll) Lanes Regular (Toll) Lanes � � High Occupancy Toll (HOT) Lanes High Occupancy Toll (HOT) Lanes � � Transit services (fixed frequency and capacity) Transit services (fixed frequency and capacity) �

Multi- -Modal Pareto Modal Pareto- -Improvement Improvement Multi (Contd.) (Contd.) � Assumptions Assumptions � � One class of homogenous users One class of homogenous users � � Total O Total O- -D demand is fixed and known. D demand is fixed and known. � � Users Users’ ’ decision on travel decision on travel- -mode choosing mode choosing � follows logit model based on travel cost. follows logit model based on travel cost. � Traffic flow distribution follows user Traffic flow distribution follows user � equilibrium condition within a chosen mode. equilibrium condition within a chosen mode.

Multi- -Modal Pareto Modal Pareto- -Improvement Improvement Multi (Contd.) (Contd.) � Objectives Objectives � � The user utility will not decrease for any The user utility will not decrease for any � traveler. traveler. � Remain in the same travel mode and the travel Remain in the same travel mode and the travel � cost will not increase. cost will not increase. � Switch to another more preferred travel mode. Switch to another more preferred travel mode. � � The total collected toll will be enough to cover The total collected toll will be enough to cover � all the transit subsidy. all the transit subsidy. � The total social benefits will increase. The total social benefits will increase. �

Modeling Transit User Behavior Modeling Transit User Behavior � Waiting time Waiting time � � Transfers Transfers � � Strategies Strategies � � Boarding the first arrived vehicle within a Boarding the first arrived vehicle within a � selected subset in order to achieve shortest selected subset in order to achieve shortest expected travel time. expected travel time.

Network Structure Network Structure � Original Network: Original Network: � 2 1 3 Line a: Line a: Transit Transit Line b: Line b: Line c: Line c:

Network Structure (Contd.) Network Structure (Contd.) � Modified Network: Modified Network: � 1a 1a 3a 3a 2a 2a 2 2 3 3 1 1 3c 3c 2c 2c 1b 1b 2b 2b (travel time, inf, 0) (travel time, inf, 0) (travel time, inf, 0) (travel time, inf, 0) Regular link Regular link Regular link Regular link (travel time, inf, 0) (travel time, inf, 0) (travel time, inf, 0) (travel time, inf, 0) HOT link HOT link HOT link HOT link (travel time, 0, transit capacity) (travel time, 0, transit capacity) (travel time, 0, transit capacity) (travel time, 0, transit capacity) Transit link Transit link Transit link Transit link (boarding time, waiting time, inf) (boarding time, waiting time, inf) (boarding time, waiting time, inf) (boarding time, waiting time, inf) Embarking link Embarking link Embarking link Embarking link (alighting time, 0, inf) (alighting time, 0, inf) (alighting time, 0, inf) (alighting time, 0, inf) Alighting link Alighting link Alighting link Alighting link

Multi- -Modal Pareto Modal Pareto- -Improving Improving Multi Model Model ⎛ ⎞ 1 ∑ ∑ ∑∑ ∑ ⋅ − θ ρ − ρ − β ⋅ + τ w m , w m , m w m w m , ⎜ ⎟ max ln exp( ( ) ) D x θ j i l l ⎝ ⎠ w m m l w s t . . − Tolled User Equilibrium Condition (1 10), − ρ ≤ ∀ ∈ ∈ w m , w m , w m , E t , w W m , M , U E ∑∑∑ τ ≥ ∀ ∈ ∈ ∈ m w m , x 0 , w W m , M , l L , l l w m l τ = τ ∀ ∈ H S S , l L , l l τ = ∀ ∈ H H 0, l L , l τ τ ≥ ∀ ∈ H S , 0, l L , l l d ω ∈ Φ ( , , x ) .

Multi- -Modal Pareto Modal Pareto- -Improving Improving Multi Model (Contd.) Model (Contd.) � Tolled User Equilibrium Condition Tolled User Equilibrium Condition � ( ) { } + − + τ − ρ − ρ = ∀ ∈ ∈ ∈ ∪ ∈ ∈ m w m , w m , w , m ( t x ( )) x 0, l L w , W , m S H , l L l , L , (1) l l j i l i j ( ) ( ) + τ + μ + γ − ρ − ρ = ∀ ∈ ∈ ∈ + ∈ − T w w T , w T , w , T t x ( ) x 0, l L w , W l , L l , L , (2) l l l l j i l i j 1 (ln + β + λ − ρ = ∀ ∈ ∈ w m , m w w m , w m , d ) E 0 , w W m , M , (3) θ ∑ μ = ∀ ∈ ∈ w f 1 , i I w , W , (4) l l + ∀ ∈ l L i ∑ γ − = ∀ ∈ w T , T T ( ) 0 , , (5) x c l L l l l ∈ w W μ − ω = ∀ ∈ ∈ w w T , w T ( ) 0, , , (6) x f l L w W l l l i ( ) { } + − + τ − ρ − ρ ≥ ∀ ∈ ∈ ∈ ∪ ∈ ∈ m w m , w m , t x ( ) 0 , l L , w W , m S H , l L l , L , (7) l l j i i j ( ) + − + τ + μ + γ − ρ − ρ ≥ ∀ ∈ ∈ ∈ ∈ T w w T , w T , t x ( ) 0 , l L w , W l , L l , L , (8) l l l l j i i j γ ≥ ∀ ∈ T 0 , l L , (9) l μ ≥ ∀ ∈ ∈ w T 0 , l L w , W , (10) l