Pareto-improving Congestion Pricing on Multimodal Transportation Networks

Transcription

1 Pareto-improving Congestion Pricing on Mutimoda Transportation Networks Wu, Di Civi & Coasta Engineering, Univ. of Forida Yin, Yafeng Civi & Coasta Engineering, Univ. of Forida Lawphongpanich, Siriphong (Toi) Industria & System Engineering, Univ. of Forida CMS Annua Student Conference March 2009

2 Outine Background Pareto-Improving Pricing Scheme Pareto-Improving Pricing Probem on Muti-moda Network Mathematica Mode Numerica Exampes Concusion

3 Background Congestion Pricing Aeviate traffic congestion by charging tos. Current Practice: London, UK Singapore Stockhom, Sweden Can successfuy reduce congestion, but is sti facing strong objection from the genera pubic.

4 Exampe 2 10v v v v v 24 There are 3.6 traveers for OD pair (1, 3)

5 Exampe (Contd.) User Equiibrium 2 System Optima Under Margina Cost To Pareto-Improving Tota trave time: Tota trave time: Tota trave time: : : : : : : : : 69.46

6 Pareto-Improving Approach By Itaian economist Vifredo Pareto make at east one individua better off without making any other individua worse off

7 Singe Moda Pareto-Improving Scheme Studied by Lawphongpanich and Yin (2008) Pareto-improving condition may be reativey prevaent Exact Pareto-improvement may not ead to significant trave time reduction.

8 Muti-Moda Moda Pareto-Improvement Deveop a Pareto-improving mode for mutimoda networks. Aow cross-subsidy subsidy of different trave modes to encourage traveers switch to higher occupancy trave modes in order to further increase the system efficiency.

9 Muti-Moda Moda Pareto-Improvement Three trave modes: (Contd.) Singe Occupancy Vehice High Occupancy Vehice Transit (transit shares highway anes with auto modes) Three types of transportation faciities: Reguar (To) Lanes High Occupancy To (HOT) Lanes Transit services (fixed frequency and capacity)

10 Muti-Moda Moda Pareto-Improvement Assumptions (Contd.) One cass of homogenous users Tota O-D O D demand is fixed and known. Users decision on trave-mode choosing foows ogit mode based on trave cost. Traffic fow distribution foows user equiibrium condition within a chosen mode.

11 Muti-Moda Moda Pareto-Improvement Objectives (Contd.) The user utiity wi not decrease for any traveer. Remain in the same trave mode and the trave cost wi not increase. Switch to another more preferred trave mode. The tota coected to wi be enough to cover a the transit subsidy. The tota socia benefits wi increase.

12 Modeing Transit User Behavior Waiting time Transfers Strategies Boarding the first arrived vehice within a seected subset in order to achieve shortest expected trave time.

13 Network Structure Origina Network: Line a: Transit Line b: Line c:

14 Network Structure (Contd.) Modified Network: 1a 2a 3a b 2b 2c 3c Reguar ink HOT ink Transit ink Embarking ink Aighting ink (trave time, inf, 0) (trave time, inf, 0) (trave time, 0, transit capacity) (boarding time, waiting time, inf) (aighting time, 0, inf)

15 Muti-Moda Moda Pareto-Improving Mode 1 ( ) st.. Toed User Equiibrium Condition (1 10), wm, wm, m w m w, m max n exp( θ ρ j ρi β ) D τ x w θ + m m w E ρ t, w W, m M, τ τ w wm, wm, wm, UE τ m w, m = τ, L, = 0, m H S S H H τ x 0, w W, m M, L, S, τ 0, L, ( x, d, ω) Φ. L H,

16 Muti-Moda Moda Pareto-Improving Mode (Contd.) Toed User Equiibrium Condition m w, m w, m w, m ( ) τ ρ ρi = 0,,, { } T w wt, wt, w T ( ) τ μ γ ρ ρ + ( t x + ( )) x L w W m S H, L, L, (1) j i j, ( j i ) + t x ( ) x = 0, L, w W, L i, Lj, (2) 1 (n wm, m ) w wm, wm, d + β + λ E ρ = 0, w W, m M, θ (3) w fμ = 1, i I, w W, (4) + i L wt, T T γ ( x c ) = 0, L, w W w, ( wt w ) 0, T x fωi L, w W, m w, m w, m + t( x) + τ ρj ρi 0, L, w W, m { S H}, Li, Lj T w w, T w, T + t( x) τ μ γ ( ρ j ρi ) 0, L, w W, Li, Lj, (5) μ = (6) ( ), (7) (8) T γ 0, L, (9) w T μ 0, L, w W, (10)

17 Muti-Moda Moda Pareto-Improving Mode (Contd.) 1 ( ) st.. Toed User Equiibrium Condition (1 10), wm, wm, m w m w, m max n exp( θ ρ j ρi β ) D τ x w θ + m m w E ρ t, w W, m M, τ τ w wm, wm, wm, UE τ m w, m = τ, L, = 0, m H S S H H τ x 0, w W, m M, L, S, τ 0, L, ( x, d, ω) Φ. L H,

18 Muti-Moda Moda Pareto-Improving Mode (Contd.) This probem is a mathematica programming with compementarity constraints (MPCC). Soved by adapting manifod suboptimization agorithm proposed by Lawphongpanich and Yin (2008)

19 Numerica Exampe I (5, 12) 1 5 (5, 12) (6, 18) (3, 35) (9, 20) (9, 35) 2 6 (9, 12) (2, 11) (3, 25) 7 (2, 11) (3, 12) (8, 26) (4, 26) (4, 11) 9 (7, 32) (8, 30) (6, 33) (6, 11) (2, 19) (4, 36) 8 (6, 43) (6, 11) Reguar ink HOT ink 1-3: : 30 O-D demand: 2-3: : 40 3 (8, 39) (6, 24) 4

20 Numerica Exampe I (Contd.) SO UE Pareto-improving Socia benefits System trave time Revenue Demand Trave cost Trave cost increase (%) SOV HOV Transit SOV HOV Transit SOV HOV Transit

21 Numerica Exampe I (Contd.) SO UE Pareto-improving Socia benefits System trave time Revenue Demand Trave cost Trave cost increase (%) SOV HOV Transit SOV HOV Transit SOV HOV Transit

22 Numerica Exampe I (Contd.) To SO Pareto-improving SOV HOV Transit SOV HOV Transit * * * * * * * * * *

23 Numerica Exampes II 90 inks with 14 HOT inks. 1 transit ine on each ink. 528 OD pairs Reguar ink HOT ink

24 Numerica Exampes II (Contd.) SO UE Pareto-improving Socia benefit Tota vehice trave time Tota passenger trave time Revenue SOV HOV Transit SOV HOV Transit SOV HOV Transit Max trave cost increase (%) Max trave cost decrease (%)

25 Concusion Pareto improvement can be achieved in mutimoda networks by adjusting the transit fares and charging tos on highway inks to redistribute traffic fows among trave modes and among the network. The mutimoda Pareto-improving tos can be obtained by soving an MPCC probem using a manifod suboptimization technique.

26 Thank you!

27 Mathematica Mode Feasibe Region Fow baance constraint: wm, wm, wm, Ax = E d w W m M Tota OD demand: wm, w d = D, w W, m M Transit capacity: w W x c, L, wt, T T,,,

28 Mathematica Mode (Contd.) Feasibe Region Common-ine: x f ω, i N, L, w W, wt, w + i i

29 Mathematica Mode (Contd.) Link Trave Time 4 v H S t = fft , L L. cap Transit ink trave times are the same with the auto ink trave times that they share.

30 Mathematica Mode (Contd.) Tota Link Vehice Fow v = w x w, S + w o x w, H H + ' L T f ',

31 Mathematica Mode (Contd.) User Equiibrium (UE) Condition within the Same Trave Mode C t = > p P w W m M wm, 0 if 0 wm, wm, bp,,, wm p,,. wm 0 if bp = 0 C : path trave time on path p for OD pair w by mode m, wm. p wm, t w m wm, p : the smaest trave time for OD pair by mode, b : fow on path p for OD pair w by mode m.

32 Mathematica Mode (Contd.) Moda Spit The users mode choice behavior foow ogit mode. d D w, m w, exp( θ t = exp( θ t m M w m w, m m β ) β m θ, β : parameters to be caibrated. m ) w W

33 Muti-Moda Moda User Equiibrium Theorem. The soution of the foowing variationa inequaity (VI) probem (or MUE-VI) satisfies the muti-moda moda user equiibrium conditions. w m ( wm wm ) t ( x ) x x *,, * θ ( wm, * m)( wm, wm, * n d β d d ) w m ( w w* ) i i + ω ω 0, ( xd,, ω) Φ, w i Φ: the previousy defined feasibe region.

34 Muti-Moda Moda System Optimum Objective: Maximize the tota socia benefits. w 1 w, m n θ m M exp( θ t β Muti-moda system optima (MSO) min m ) D 1 t ( x) x + d nd wm, wm, wm, w m θ w m 1 + d θ β + st.. ( x, d, ω) Φ. ω wm, m w i w m w i w