ECTRI FEHRL FERSI Young Researchers Seminar 2015

Transcription

1 DLR.de Chart 1 ECTRI FEHRL FERSI Young Researchers Semnar 2015 TRANSPORT USER BENEFITS MEASURE FOR TRAVEL DEMAND MODELS WITH CONSTRAINTS Chrstan Wnkler Insttute of Transport Research German Aerospace Center

2 DLR.de Chart 2 Overvew Transport nvestments are often assocated wth hgh nvestment costs for socety and cost changes for transport users Antcpaton of welfare mpacts s essental Decson makers need robust and easy decson advce Specfc gudelnes and rules are mplemented n most countres Cost beneft analyss s the standard approach The basc calculaton s: Benefts Costs Overall Economc Impact = change n transport user benefts + change n system operatng costs and revenues + change n costs of externaltes - Investment costs

3 generalzed costs g DLR.de Chart 3 Consumer surplus ntal state g O 0 g M (nverse) demand curve T 0 trps T

4 generalzed costs g DLR.de Chart 4 Consumer surplus fnal state g O 0 g M 1 (nverse) demand curve T 0 T 1 trps T

5 generalzed costs g DLR.de Chart 5 Change n Consumer surplus g O 0 g M 1 (nverse) demand curve T 0 T 1 trps T

6 generalzed costs g DLR.de Chart 6 The Rule of the Half g O 0 g M 1 (nverse) demand curve T 0 T 1 trps T

7 DLR.de Chart 7 Am of the Study combne travel demand and benefts calculaton for constraned travel demand models On the base of a trebly constraned model (EVA model) Change n consumer surplus as a beneft measure Compute a mathematcal exact ntegraton of the travel demand functon

8 DLR.de Chart 8 EVA logt model EVA model T = f g a b c jk jk j k j k k j T = O jk T = D jk T = M jk j k constrants Logt model T = P T jk jk V jk e = T V'j'k' e ' j' k' Consderaton of dfferent sets of constrants Utlty maxmzaton? Consderaton of only one set of constrants Random utlty maxmzaton

9 DLR.de Chart 9 EVA logt model Defnton of a specfc utlty functon Consderaton of shadow prces V jk = -g jk +θ + τ j +ρk, j,k The EVA logt model s then: -g jk +θ +τ j +ρk e T jk = Pjk T = T -g 'j'k' +θ ' +τ j' +ρk' e j k k j T T T jk jk jk = O = D j = M k ' j' k'

10 DLR.de Chart 10 Change n consumer surplus The change n consumer surplus s mandatory for defnng welfare mpacts The mathematcal ntegraton of the demand functon s necessary Use ether the sngle ntegraton of each alternatve or the antdervatve The antdervatve of the logt model s known ( logsum term ) The change n consumer surplus s then ( logsum dfference ): 1 0 V jk Vjk EΔCS = ln e - lne T j k j k

11 DLR.de Chart 11 Change n consumer surplus However: logsum dfference fals for constraned models Reason: shadow prces for satsfyng constrants Only the real beneft caused by changes n generalzed costs s targeted A detaled analyss of the ntegral of the demand functon s necessary Segmentaton of the ntegral accordng to sngle varables

12 DLR.de Chart 12 Change n consumer surplus Logsum dfference approach wth shadow prces can be parttoned nto: g θ τ ρ * ΔE CS = - P dg + P dθ + P dτ + P dρ r jk jk jk jk j jk k 0 j k 0 j k 0 j k 0 g θ τ ρ j k Possble smplfcatons: 1 1 * ΔE CS = ΔE CS - P dθ - P dτ θ r r j j 0 0 θ τ j In the case of nelastc constrants t s: * O D j ΔECS r = 0, P = = constant, P j = T T τ

13 DLR.de Chart 13 Change n consumer surplus It follows: O D ΔE CS = θ - θ + τ - τ T r Overall change n consumer surplus: j ΔE CS = O θ - θ + D τ - τ j T The result s vald for nelastc constrants and constant shadow prces for modes Solutons for all dfferent knds of constrants have been derved

14 DLR.de Chart 14 Example Synthetc example: fve travel zones nelastc orgn and destnaton constrants one mode travel tme and travel cost value of tme of 10 Euro/h ( Euro/mn) ntal state generalzed costs [Euro] gj ,08 3,25 6,25 5,50 3,25 2 4,08 4,08 4,78 4,58 5,00 3 6,25 4,37 4,08 4,00 4,00 4 5,50 4,58 4,42 4,08 4,08 5 4,50 6,33 4,00 3,25 3,67 fnal state generalzed costs [Euro] gj ,08 3,25 6,25 3,25 3,25 2 4,08 4,08 4,78 4,58 5,00 3 6,25 4,37 4,08 4,00 4,00 4 3,25 4,58 4,42 4,08 4,08 5 4,50 6,33 4,00 3,25 3,67

15 DLR.de Chart 15 Example EVA logt model Calculaton of trps by the EVA logt model nttal state Tj O-resultng O-gven q 1 3,03 32,35 1,93 1,38 11,31 50,00 50,00 2, ,81 45,52 27,14 11,17 6,36 100,00 100,00 3, ,44 13,46 21,46 7,86 6,79 50,00 50,00 2, ,30 26,68 37,85 17,80 15,37 100,00 100,00 3, ,42 6,99 86,62 61,79 35,18 200,00 200,00 4, ,00 500,00 500,00 Dj-resultng 25,00 125,00 175,00 100,00 75,00 500,00 Dj-gven 25,00 125,00 175,00 100,00 75,00 500,00 tj 2,581 4,116 4,299 3,211 3,065

16 DLR.de Chart 16 Example EVA logt model Calculaton of trps by the EVA logt model nttal state Tj O-resultng O-gven q 1 3,03 32,35 1,93 1,38 11,31 50,00 50,00 2, ,81 45,52 27,14 11,17 6,36 100,00 100,00 3, ,44 13,46 21,46 7,86 6,79 50,00 50,00 2, ,30 26,68 37,85 17,80 15,37 100,00 100,00 3, ,42 6,99 86,62 61,79 35,18 200,00 200,00 4, ,00 500,00 500,00 Dj-resultng 25,00 125,00 175,00 100,00 75,00 500,00 Dj-gven 25,00 125,00 175,00 100,00 75,00 500,00 tj 2,581 4,116 4,299 3,211 3,065 T P T e -4,08 Euro+2,611Euro+2,581Euro ' j' e -g +θ +τ 'j' ' j' trps 3,03 trps

17 DLR.de Chart 17 Example EVA logt model Calculaton of trps by the EVA logt model fnal state Tj O-resultng O-gven q 1 1,45 27,93 1,57 9,62 9,43 50,00 50,00 2, ,90 49,43 27,67 10,33 6,67 100,00 100,00 3, ,26 14,29 21,39 7,10 6,96 50,00 50,00 2, ,59 25,58 34,07 14,53 14,23 100,00 100,00 3, ,80 7,77 90,30 58,41 37,72 200,00 200,00 4, ,00 500,00 500,00 Dj-resultng 25,00 125,00 175,00 100,00 75,00 500,00 Dj-gven 25,00 125,00 175,00 100,00 75,00 500,00 tj 2,068 4,194 4,313 3,128 3,107

18 DLR.de Chart 18 Example change n consumer surplus Change n consumer surplus calculated by the adjusted logsum dfference total number of trps orgnatng at zone dfference of orgn shadow prces DCS [Euro] O 1 50 q O 1-q M 1 0,224 11,22 O q O 2-q M 2-0,005-0,49 O 3 50 q O 3-q M 3 0,018 0,88 O q O 4-q M 4 0,120 11,96 O q O 5-q M 5-0,027-5,45 total number of trps attracted to zone j dfference of destnaton shadow prces S() 18,11 DCS j [Euro] 1 0 ΔE CS = O θ - θ + D τ - τ 1 0 j D 1 25 t O 1-t M 1 0,513 12,82 D t O 2-t M 2-0,078-9,69 D t O 3-t M 3-0,014-2,52 D t O 4-t M 4 0,083 8,34 D 5 75 t O 5-t M 5-0,042-3,19 S(j) 5,76 S(,j) 23,87 Euro

19 DLR.de Chart 19 Example change n consumer surplus Change n consumer surplus calculated by the Rule of a Half Dgj STj/ ,00 0,00 0,00 2,25 0,00 1 2,24 30,14 1,75 5,50 10,37 2 0,00 0,00 0,00 0,00 0,00 2 7,85 47,47 27,41 10,75 6,51 3 0,00 0,00 0,00 0,00 0,00 3 0,35 13,87 21,42 7,48 6,87 4 2,25 0,00 0,00 0,00 0,00 4 6,94 26,13 35,96 16,17 14,80 5 0,00 0,00 0,00 0,00 0,00 5 7,61 7,38 88,46 60,10 36,45 DCS ,00 0,00 0,00 12,38 0,00 2 0,00 0,00 0,00 0,00 0,00 3 0,00 0,00 0,00 0,00 0, ,62 0,00 0,00 0,00 0,00 5 0,00 0,00 0,00 0,00 0,00 28,00 Euro 1 ΔE CS = g - g T + T j j j j j Beneft s overestmated by 17%

20 DLR.de Chart 20 Concluson Multple-constraned travel demand models are expressble n terms of a logt model Dervaton of the adjusted logsum dfference as a mathematcal exact ntegral of the demand functon of constraned models Applcable for all constraned models Allows measurng benefts caused by changng costs and changng attractons The approach s easy to use and to mplement n exstng models

21 DLR.de Chart 21 ECTRI FEHRL FERSI Young Researchers Semnar 2015 TRANSPORT USER BENEFITS MEASURE FOR TRAVEL DEMAND MODELS WITH CONSTRAINTS Chrstan Wnkler Insttute of Transport Research German Aerospace Center