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3 FrstBest SecondBest SecondBest SecondBest EU (Q, Q 2 ) = (2500, 500) (Q, Q 2 ) = (500, 500) (Q, Q 2 ) = (500, 2500)

4 A

5 2005 =( + )/ ( :36.0% :6.6%) km 6) CHIH PENG CHU & JYH-FA TSAI(2004) )

6 GAMS 2

7 km 75500km Small 989 FHWA Johnsson & Mattson 994 ESAL:Equvarent Sngle Axle Load 4 4 3) AASHTO (962) 5) 80kN =8kp=8000pounds=8.25t=825kg kN(5t) 49kN 3

8 4 CHIH PENG CHU & JYH-FA TSAI(2004) ) 2.2 CHIH PENG CHU & JYH-FA TSAI Road prcng models wth mantenance cost n SecondBest SecondBest SecondBest SecondBest SecondBest 4

9 3 3. CHIH PENG CHU & JYH-FA TSAI, Road prcng models wth mantenance cost (2004) n ( n) : : V = Q P ɛ (3.) C t = r C (V,, V n ) (3.2) : P = τ + C t (3.3) ( ) = = dv V dp P { = dv dp P V Q ( ɛ )P ɛ P Q P ɛ } = ɛ ( ) 5

10 V : /hour P : $ C t : $ C t : {V n} (hour) Q : /hour ɛ : r : $/hour τ : $ hour BPR C t : hour t 0 : hour n= V C t = t 0 [ + α( K )β ] (3.4) K: /hour α, β: τ (3.) (3.2) (3.3) {P n} {V n} {C t n} { ˆP n}, { ˆV n}, { C ˆ t n} : or NB = P ˆP Q P ɛ dp (3.5) 6

11 NB = V ( V ) Q ˆV ɛ + V ( V ) Q ɛ dv ˆV ( ˆV ) ɛ (3.6) Q 3. V (3.6) ˆV ɛ NB = Q V ɛ Q ɛ V ɛ ɛ Q ˆV ɛ ɛ V ( ɛ = Q V ɛ + ) ɛ ˆV ɛ ɛ V ˆV ɛ ɛ = ɛ Q ɛ + (V ɛ ˆV ɛ ) (3.7) : n n B c = τ ˆV C m ( ˆV ) C m (3.8) = = C m (V ):( ) ($) C m : ($) SNB:System s Net Beneft n SNB = NB + B c = = ɛ n Q ɛ + (V = τ = ˆP C t ( ˆV,, V ˆ n ) = ( ˆV Q ) ɛ SNB = + = = {( n = = ɛ ɛ n Q ɛ + (V ɛ ˆV ɛ ) ( ˆV ) Q ɛ ɛ n Q ɛ + (V ˆV n ɛ ) + τ ˆV ) } r C t ( ˆV,, V ˆ n ) ˆV ɛ ɛ ˆV ɛ ) n = n C m ( ˆV ) C m (3.9) = r C t ( ˆV,, ˆ V n ) = 7 n C m ( ˆV ) C m = { ˆV r } C t ( ˆV,, ˆ V n ) n C m ( ˆV ) C m (3.0) =

12 SNB { ˆV n} C m = M L N V ( =, 2) (3.) N : ESAL:Equvalent Sngle Axle Load ω N = ( 80kN )4 (3.2) ω : (kn) M: 80kN km ( )($/ km) L: (km) 4 C m = k m L (3.3) k m : km ( ) $/km hour km hour km 8

13 3.2 FrstBest SNB FrstBest SNB SNB (V,, Vn ) = 0 (3.4) V ( V Q ) ɛ r C t (V,, V n ) n = V {V r } C t V (V,, Vn ) C m V (V ) = 0 n {V n} FrstBest τ τ = P C t (V,, V n ) = ( V = ) Q n = ɛ r C t (V,, V n ) {V r } C t V (V,, Vn ) + C m V (V ) (3.5) 9

14 3.3 SecondBest cf.c m SNB n n τ V = C m (V ) + C m = = n {( ( V ) } ) n ɛ r C t (V,, V n ) V C m (V ) C m = 0 (3.6) Q = = τ = P C t (V,, V n ) = ( V Q ) ɛ r C t (V,, V n ) SNB L(V,, V n, λ) = SNB(V,, V n ) { n {( + λ ( V ) } ) ɛ r C t (V,, V n ) V Q = } n C m (V ) C m = (3.7) SNB n} {V L V (V,, V n, λ) = 0 + λ ( V ) Q { ɛ r C t (V,, Vn ) ( )( V ɛ Q ) ɛ n = r C t (V,, Vn ) {V r } C t (V V n =,, Vn ) C m (V ) V {V r } C t (V,, Vn V ) C m V (V ) = 0 (3.8) 0 }

15 L (V,, V λ n {(( V = n, λ) = 0 Q ) ɛ r C t (V,, V n ) ) } V n = C m (V ) C m = 0 (3.9) (n + ) n} λ SecondBest {V τ = ( V Q ) ɛ r C t (V,, V n ) (3.20) (3.8) (3.20), j( n, j n, j) λ τ = τ + n = {V r } C t n = {V r } C t V (V τj + { n j= τj { n j= Vj V (V,, V n Vj r j } Ct r j } Ct V j (V,, V n ) C m V V j (V ) + Cm V (V ) (V,, V n,, V n ) Cm j V j ) ɛ ( V Q ) ɛ ) + C m j V j (V j (V j ) (3.2) ) ɛ j ( V j Q j ) ɛ j τ = n = {V r } Ct τj { n j= Vj ɛ ( V Q ) ɛ V (V,, V ) Cm n ɛ j ( V j Q j ) ɛ j r j } Ct V j (V V,, V n (V ) ) Cm j V j (V j ) (3.22) = τ r C t (V,, V ) ( V j n Q j ) ɛ j = τ j + r j C t (V,, V ) n ( V Q ) ɛ + τ n = {V r } C t τ = τ j n j= { V (V + r C t (V Vj τ j r j } Ct,, V n,, V n ) V j (V + r j C t (V ) C m V (V ) ɛ,, V ) C m j n,, V n ) V j (Vj ) ɛ j (3.23)

16 (SecondBest ) ( ) ( ) (SecondBest j ) ( j = ) ( j ) j (3.24) FrstBest SecondBest ( ) = (SecondBest ) ( ) (3.24) j = j j (3.25) = j j (3.26) (3.26) SecondBest SNB SecondBest 2

17 SNB(V,, V n ) FrstBest SNB(V,, V 2 ) ) SecondBest 3.4 SecondBest (SNB) SNB E (V ) = e L V (3.27) E : $ e : km $/ /km SNB SNB = + + n + = ɛ n Q ɛ + (V = ɛ ˆV n ɛ ) + τ ˆV = n C m ( ˆV n ) C m e L ˆV (3.28) = = (3.23) τ n = {V r } C t τ = τ j n j= { V (V + r C t (V Vj r j } Ct τ j,, V n,, V V j (V + r j C t (V ) C m V n ) (V,, V n ) C m j V j,, V n ) ) e L (V j ɛ ) e j L ɛ j (3.29) 3

18 (3.23), j e L e j L SecondBest SeconBest 4

19 4 4. SecondBest SNB SecondBest SecondBest 4.2 EU

20 00 ( 50 ) 30km 7) EU +α +α EU SecondBest FrstBest SecondBest e : $ C c : km hour 6

21 $/km/hour D: τ = ( Cm (V ) + C c L V + C m n= V + e ) D (4.) e C c km hour D n n τ V = {C m (V ) + C c L} + C m (4.2) = = (4.) (4.2) (3.) (3.2) (3.3) SecondBest EU SecondBest 7

22 4.3.2 τ = C m (V ) V + C m n= V (4.3) EU n n τ V = C m (V ) + C m (4.4) = = ( ) n n = τ V C m (V ) C m = 0 = = (4.5) (4.3) (4.5) (3.) (3.2) (3.3) 8

23 5 5. FrstBest SecondBest EU CHIH PENG CHU & JYH-FA TSAI, Road prcng models wth mantenance cost (2004) NEXCO NEXCO NEXCO 5. 8kN 80kN, 2 : 2: (Q, Q 2 ) = (2500, 500), (500, 500), (500, 2500) - (ɛ, ɛ 2 ) = (0.65, 0, 85) $/hour (r, r 2 ) = (20, 20) (V, V 2 ) = (, ) 9

24 kn :(ω, ω 2 ) = (8, 80) hour t 0 = 0. BPR - (α, β) = (0.5, 4) K = 3000 $/hour/km k m = 207 $/km/ M = 0. km L = 6 - EU k m $ :(e, e 2 ) = (0, 00) $/km/hour :(C c, C c2 ) = (0, 0) $/hour/km k m = 87 6(km) 60(km/hour) 0.(hour) km 50 km hour 6) km 840 4) 00 = $ GAMS (General Algebrac Modelng System) (Q, Q 2 ) = (2500, 500) 5. 20

25 5.2.2 (Q, Q 2 ) = (500, 500) (Q, Q 2 ) = (500, 2500) = FrstBest FB FB FB SNB FB 3 SecondBest SB EU EU ED 2

26 SB FB FB FB SB SB EU SNB ED SB SB SNB SB SB EU ED SB SB SNB 5.4 8) 7) 22

27 equty of no-envy farness 5.5 FB FB SNB SNB SB 23

28 SNB EU EU SB SB SB ED SB ED SB SNB SB 24

29 6 FrstBest FB SNB FB SNB SecondBest SB SNB SNB SNB SB SB SB ED SNB SB SB EU 25

30 FB FB FB 26

31 ) CHIH-PENG CHU & JYH-FA TSAI.:Road prcng models wth mantenance cost, Transportaton, Vol.3, pp , ) Xaole Guo, Ha Yang.: Pareto-mprovng congeston prcng and revenue refundng wth multple user classes, Transportaton Reseach Part B, Vol.44, pp , 200 3) Davd M. Newbery.: Road Damage Externaltes and Road User Charges, Econometrca, Vol.56, No.2, pp , Mar.988 4) Vrgna Transportaton Research Councl.: Development of Truck Equvalent Sngle-Axle Load (ESAL) Factors Based on Wegh-n-Moton Data for Pavement Desgn n Vrgna, Fnal Report VTRC, 09-R8, ) Shab B. Anan, Samer M. Madanat.: Hghway Mantenance Margnal Cost. What f the fourth power assumpton s not vald?, Transport Polcy, Vol.7, pp , 200 6) Martn S. Feldsten.: Equty and Effcency n Publc Sector Prcng: the Optmal Two-Part Tarff, the QUARTERLY JOURNAL OF ECONOMICS, Vol.LXXXVI, No.2, pp.75-87, May.972 7).: I,,., 985 8).: II,,.2, 988 9).: [ ],, ).: - - ).: 2005, pp.5-54, )

32 3) ).: 22, ).: -3, ).: - - 2,, ).:, Vol.5, No.4, 2003 Wnter, pp , 2 28

33 A 3.

34 5. 2

35 表 5. 計算結果 (Q, Q2 ) = (2500, 500) 付 3

36 表 5.2 計算結果 (Q, Q2 ) = (500, 500) 付 4

37 表 5.3 計算結果 (Q, Q2 ) = (500, 2500) 付 5

38 5.2 (Q, Q 2 ) = (2500, 500) 6

39 5.3 (Q, Q 2 ) = (500, 500) 7

40 5.4 (Q, Q 2 ) = (500, 2500) 8

8 8 0

8 8 0 ,07,,08, 8 8 0 7 8 7 8 0 0 km 7 80. 78. 00 0 8 70 8 0 8 0 8 7 8 0 0 7 0 0 7 8 0 00 0 0 7 8 7 0 0 8 0 8 7 7 7 0 j 8 80 j 7 8 8 0 0 0 8 8 8 7 0 7 7 0 8 7 7 8 7 7 80 77 7 0 0 0 7 7 0 0 0 7 0 7 8 0 8 8 7