1 1 ( ) ( ) AHS Key Words: car-following, basic freeway segment, capacity bottleneck 1. ( ) ( ) ( ) 1),2) 2. (1) ( ) ( ) ( ) 3),4) 1

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1 1 1 ( ) ( ) AHS Key Words: car-following, basic freeway segment, capacity bottleneck 1. ( ) ( ) ( ) 1),2) 2. (1) ( ) ( ) ( ) 3),4) 1

2 ITS AHS(Advanced cruise-assist Highway System) AHS AHS (2) ),5) 61) (7) GM 17) (General Motors ) (Q V K ) 1. a) g) ) 69) ( ) 70) 94) ( 95) ) 3. (1) ( ) ( ) ( ) = ( ) ( ) (1) ( ) ( ) (1) t [s] x 0 (t) [m] ẋ 0 (t) =v 0 (t) [m/s] ẍ 0 (t) = v 0 (t) =a 0 (t) [m/s 2 ] x 1 (t) 1 [m] 2

3 ẋ 1 (t) =v 1 (t) 1 [m/s] ẍ 1 (t) = v 1 (t) =a 1 (t) 1 [m/s 2 ] x n, ẋ n, ẍ n n θ n (t) t n T, T 1, T 2, T 3,T 4,T 1 +,T+ 2, T 1, T 2 ( ) α, α 1, α 2, α 3, α 4, α + 1, α 1, α+ 2, α 2, β 0, β 1, β 2, β 3 l, m, n, h, l +, l, m +,m G ( ) a) Pipes 5) (ẋ 0 (t) ẋ 1 (t)) ( ) α ẍ 1 (t) ẍ 1 (t) =α (ẋ 0 (t) ẋ 1 (t)) (2) Chandler, Herman 6) (2) (responsetimelag) T (delay) T ẍ 1 (t + T )=α (ẋ 0 (t) ẋ 1 (t)) (3) (2) (3) t s 5) 13) (3) (4. ) G(s) G(s) =α e Ts s (4) (1+G(s) =0) (local stability) T α < π/2 10) 2 3 (asymptotic stability) T α < 1/2 6) Chandler, Herman 6) (3) α (α = β 0 + β 1 ẋ 1 ) ( ) Gazis, Herman 10) (3) ẍ 1 (t + T )= α x 0 (t) x 1 (t) (ẋ 0(t) ẋ 1 (t)) (5) (5) ẋ 1 (t) =c ln( ρ j ρ ) (6) c, ρ j ρ =1/(x i 1 x i ) (6) Greenberg 96) Gazis, Herman, Rothery 17) (5) May and Keller 21) {ẋ 1 (t)} m ẍ 1 (t + T )=α {x 0 (t) x 1 (t)} (ẋ 0(t) ẋ l 1 (t)) (7) (7) (2) (3) (5) 23),53),60) b) Newell 16) (8) ẍ 1 (t + T )=α 1 e α2{x0(t) x1(t) α3} (ẋ 0 (t) ẋ 1 (t)) (8) Ceder 28) (7) (9) ẍ 1 (t + T )= α 1 e (α2/{x0(t) x1(t)}) {x 0 (t) x 1 (t)} 2 (ẋ 0 (t) ẋ 1 (t)) (9) (9) (6) c) Kometani & Sasaki 7) ( ) (3) 8) ẍ 1 (t + T )=α 1 (ẋ 0 (t) ẋ 1 (t)) + α 2 ẍ 0 (t) (10) Helley 14) 3

4 ẍ 1 (t + T )=α 1 (ẋ 0 (t) ẋ 1 (t)) + α 2 [(x 0 (t) x 1 (t)) (β 0 + β 1 ẋ(t)+β 2 ẍ(t)) ] (11) Herman & Rothery 19) (3) ẍ 2 (t + T )=α 1 (ẋ 1 (t) ẋ 2 (t)) + α 2 (ẋ 0 (t) ẋ 1 (t)) (12) d) Kometani & Sasaki 11),12) 2 1 ẍ 1 (t + T )= α 1 + α 2 ẋ 1 (t + T ) {(ẋ 0(t) ẋ 1 (t)) + α 3 ẍ 0 (t)+α 4 ẋ 0 (t)ẍ 0 (t)+α 5 ẋ 1 (t)ẍ 1 (t)} (13) Bando 50) tanh ẍ 1 (t) =α {(α 1 tanh(α 2 (x 0 (t) x 1 (t)) α 3 )+α 4 ) ẋ 1 } (14) 56),57) T 58) 47) (1) ẍ 1 (t) =α 1 1 (α 2ẋ 1 (t)+α 3 ) 2 (x 0 (t) x 1 (t)) ẋ 1 (t) (15) 2 ẋ 0 (t) 31),32) z (1) z ẍ 1 (t + T )=α 1 ẋ 1 (t)+α 2 [z(t) Z ] (16) z(t) > 1 Z > 1 {z(t)} 3 +3ẋ1(t) V f z(t) V f + (2H f + H c ) (x 0 (t) x 1 (t)) =0 H f H c {Z } 3 3Z + 2H f + H c H 0 H f H c =0 V f ( ) H f V f ( ) H c ( ) (H c <H f ) H 0 (H c <H 0 <H f ) 44) (1) 2 α 3 ẍ 1 (t + T )= {x 0 x 1 L} α 1 Y + α 2 α 4 + {ẋ 0 (t) ẋ 1 (t)} (17) α 1 Y + α 2 Y =(x 0 x 1 L)/(ẋ 0 (t) ẋ 1 (t)) L e) 2 4 2) 41) 48) α 1 f 1 (t + T 1 )= {x 0 (t) x 1 (t)} l (ẋ 0(t) ẋ 1 (t)) α 2 f 2 (t + T 2 )= {x 0 (t) x 1 (t)} (x 0(t) x n 1 (t) g(t)) f 3 (t + T 3 )=α 3 {ẋ 1 (t) V f } g(t) =β 0 + β 1 ẋ 1 (t)+β 2 {ẋ 1 (t)} 2 + β 3 {ẋ 1 (t)} 3 ẍ 1 (t) =f 1 (t)+f 2 (t)+f 3 (t) α 4 sin{θ 1 (t)} (18) 46),49) (18) f 1 (t) f 2 (t) 45) f 1 (t + T 1 + )= α+ 1 {ẋ 1(t)} m+ (ẋ 0 (t) ẋ 1 (t)) {x 0 (t) x 1 (t)} l+ f 1 (t + T1 )= α 1 {ẋ 1(t)} m (ẋ 0 (t) ẋ 1 (t)) {x 0 (t) x 1 (t)} l f 2 (t + T 2 + )= α+ 2 (x 0(t) x 1 (t) g(t)) {x 0 (t) x 1 (t)} n+ f 2 (t + T2 )= α 2 (x 0(t) x 1 (t) g(t)) {x 0 (t) x 1 (t)} n ( + ẍ 1 (t) 0 ẍ 1 (t) < 0 ) α 3 f 3 (t + T 3 )= {x 0 (t) x 1 (t)} ẍ0(t) h f 4 (t + T 4 )=G[sin{θ 1 (t + T 4 )} sin{θ 1 (t)}] g(t) =β 0 + β 1 ẋ 1 (t)+β 2 {ẋ 1 (t)} 2 + β 3 {ẋ 1 (t)} 3 4

5 ẍ 1 (t) =f 1 (t)+f 2 (t)+f 3 (t)+f 4 (t) (19) 2 (18), (19) f) Del Castillo 53) Lighthill & Whithman 97) 51),52) τ(t) ẍ 1 (t + τ(t)) = α 1 {ẋ 0 (t) ẋ 1 } + α 2 {H(t) F 1 (ẋ 1 (t))} + α 3 ẍ 0 (t) (20) H(t) τ(t) = ẋ 1 (t) F (H(t)) + H(t) df dh H(t) =x 0 (t) x 1 (t) F (t) H(t) ( ) g) 39),43) 61) a) g) ( ) (2) (5), (9), (14) Q V K (Q V K ) (Herman 10),13),17),Edie 15),May 21),33), Ceder 27),28),30), 29), 37), Bando 50) ) Q V K ( ) 98) a) g) 3 (3) Kometani & Sasaki 18), Michaels 20), Pipes 22), Weiss 25), Gipps 34) Rockwell 24), Evans and Rothery 26), and Tenny 35), 36),38),41),48),54),55), 40), 42),59) 3) 4), 62) 66) 5

6 Weber-Fechner ( ) (I) (di) di/i = (Weber ) (ϕ) (I) (Fechner ) (ϕ = K 1 ln I + K 2 (K 1,K 2 )) 67) 67) 67) 2 68) 69) ( ) 4. (1) 3. 70) 71) (H(s)) µ H(s) =K P 1+ 1 T I s + T Ds e Ls (21) (21) PID PID 72) (21) ( ) L 1 74) K P ( Proportional control action) 1/(T I s)( Integral control action) T D s( Derivative control action) (PID ) K P (proportional gain) T I (integral time) T D (derivative time) 73) s t 71) (21) 74) 74) (precognitive) (pursuit) (compensatory) 3 71) (preview) 4 ( ) ( ) 6

7 2 77) 3 77) ( 71) ) 1)Weber-Fechner 67) 2) 3) 1) 2) 3) 1 74) ( ) (JARI) 78) 80) 81) ( ) ( ) 82) 84) 85) (2) 75),76) H(s) = K P 1+T I s e Ls (22) (P ) (4) 1/T I s 1/(1 + T I s) 1 77) ( 2 3 ) (3) 91) 93) 86),87) 88) 89) 90) 92),93) a) 88) T m (= / ) τ h Tm 7

8 T d Tm b) 92),93) D v (D v =30[m]) v v s 7.0[m/s] v v s ( ) e v min e v min D v D v D D s ( ) 92),93) v t [m/s] D d v t 1 D d = D s + C v v t ( D s = D c =40[m] C v =3.6[s]) c) G/ G 1. 89) 2. 89) 3. τ h ( 2 3 ) 89) 4. (jerk ) [m/s 3 ] 90) 5. 90) 6. 91) (4) 94) [km/h] [m/s 2 ] [m/s] [m/s 2 ] 5. ( = / ) 5. 48),46) (1) a) 8

9 ( ) ( ) b) ( ) (s ) (s ) (t ) c) ( ) ( ) d) ( ) ( ) e) 2),48),4) f) 4) 4) 2 66) 1 1 (18) (19) 2 9

10 (2) a) f) ( ) 2. ( 1 ) 3. ( ) AHS 2 1 AHS AHS AHS ( ) (3) a) 99) 100) 100) 101) 102) 105) b) 5.(1) a) f) c) CG(Computer Graphics) 66),106) 10

11 d) ITS ( ) 1),, Vol.10, No.1, pp.32 38, ),, No.371/IV 5, pp.1 7, ),,, No.651, pp.65 69, ),, No.524/IV 29, pp.69 78, ) Pipes, L. A.: An Operational Analysis of Traffic Dynamics, Journal of Applied Physics, Vol.24, No.3, pp , ) Chandler, R. E., Herman R. and Montroll, E. W.: Traffic Dynamics: Studies in Car Following, Oper. Res., Vol.6, pp , ) Kometani, E. and Sasaki, T.: On the Stability of Traffic Flow(Report1), J. Oper. Res. Soc. Japan, Vol.2, No.1, pp.11 26, ) Kometani, E. and Sasaki, T.: On the Stability of Traffic Flow(Report2), J. Oper. Res. Soc. Japan, Vol.2, No.2, pp.60 79, ) Herman,R.,Montroll,E.W.,Potts,R.B.andRothery, R. W.: Traffic Dynamics: Analysis of Stability in Car Follwing, Oper. Res., Vol.7, pp , ) Gazis, D. C., Herman, R. and Potts, R. B.: Car- Following Theory of Steady-State Traffic Flow,Oper. Res., Vol.7, pp , ) Kometani, E. and Sasaki, T.: A Safety Index for Traffic with Linear Spacing, Oper. Res., Vol.7, pp , ) Kometani, E. and Sasaki, T.: Dynamic Behavior of Traffic with a Nonlinear Spacing-Speed Relationship, Theory of Traffic Flow(Proc.of Sym.on TTF(GM)), pp , ) Herman, R. and Potts, R. B.: Single-Lane TrafficTheory and Experiment, Theory of Traffic Flow(Proc.of Sym. on TTF(GM)), pp , ) Helly, W.: Simulation of Bottlenecks in Single-Lane Traffic Flow,Theory of Traffic Flow(PRoc.of Sym. on TTF(GM)), pp , ) Edie, L. C.: Car-Following and Steady-State Theory for Non-Congested Traffic, Oper. Res., Vol.9, pp.66 76, ) Newll, G. F.: Nonlinear Effects in the Dynamic of Car Following, Oper. Res., Vol.9, pp , ) Gazis,D.C.,Herman,R.andRothery,R.W.:Nonlinear Follow-the Leader Models of TrafficFlow,Oper. Res., Vol.9, pp , ) Kometani, E. and Sasaki, T.: Car-Following Theory and Stability Limit of Traffic Volume,J. Oper. Res. Soc. Japan, Vol.3, pp , ) Herman, R. and Rothery, W.: Car Following and Steady State Flow, Proc. of 2nd ISTTF(London), pp.1 11, ) Michaels, R. M.: Perceptual Factors in Car-Following, Proc.of2ndISTTF(London), pp.44 59, ) May, A. D. and Keller, H. E. M.: Non-Integer Car-Following Models, Highway Res. Board, No.199, pp.19 32, ) Pipes, L. A.: Car Following Models and the Fundamental Diagram of Road Traffic, Transpn. Res., Vol.1, pp.21 29, ) Unwin, E. A. and Duckstein, L.: Stability of Reciprocal-Spacing Type Car Following Models, Transpn. Sci., Vol.1, pp , ) Rockwell,T.H.,Ernst,R.L.andHanken,A.: ASensitivity Analysis of Empirically Derived Car-Following Models, Transpn. Res., Vol.2, pp , ) Weiss, G.: On the Statistics of the Linear Car Follwing Model, Transpn. Sci., Vol.3, pp.88 89, ) Evans, L. and Rothery, R.: Experimental Measurements of Perceptual Thresholds in Car-Following, Highway Res. Recrd., No.464, pp.13 29, ) Ceder, A. and May, A. D.: Further Evaluation of Single- and Two-Regime Traffic Flow Models, Transpn. Res. Recrd., No.567, pp.1 15, ) Ceder, A.: Deterministic Traffic Flow Model for the Two-Regime Approach, Transpn. Res. Recrd., No.567, pp.16 30, ),,, No.258, pp.85 95, ) Ceder, A.: Stable Phase-Plane and Car-Following Behavior as Applied to a Macroscopic Phenomenon, Trans. Sci., Vol.13, pp.64 79, ),, No.196, pp.36-42, ),, No.198, pp.62-69, ) Easa, S. M. and May, A. D.: Generalized Procedure for Estimating Single- and Two-Regime Traffic- Flow Models, Transpn. Res. Recrd., No.772, pp.24 37, ) Gipps, P. G.: A Behavioural Car-Following Model for Computer Simulation, Transpn. Res.,Vol.15B,No.2, 11

12 pp , ), N.Tenny,,No.353/IV 2, pp , ),,,, No.42IV, pp.58 59, ),,, No.42IV, pp.60 61, ),,,,, No.43IV, pp , ),,,,, No.13, pp , ),, No.14(1), pp , ) J. Xing,,,, No.14(1), pp , ),,, No.10, pp.87 94, ) Kikuchi, S. and Chakroborty, P.: Car-Following Model Based on Fuzzy Inference System, Transp. Res. Recrd., No.1365, pp.82 91, ),,,, No.13, pp.25 28, ) Ozaki, H.: Reaction and Anticipation in the Car- Following Behavior, Proc. of 12th ISTTT(Berkley), pp , ), ( ), ),, No.14, pp , ) J. Xing,,, No.506/IV 26, pp.45 55, ) Ozaki, H.: Assistance of Drivers to Mitigate Highway Capacity Problem, Proc. of 2nd WC on ITS(Yokohama), pp , )Bando,M.,Hasebe,K.,Nakayama,A.,Shibata,A. and Sugiyama, Y.: Dynamical Model of Traffic Congestion and Numerical Simulation, Journal of Physical Review E, Vol.51, No.2, pp , ) DelCatillo,J.M.andBenitez,F.G.: OntheFunctional Form of the Speed-Density Relationship I: General Theory, Transp. Res., Vol.28B, No.5, pp , ) DelCatillo,J.M.andBenitez,F.G.: OntheFunctional Form of the Speed-Density Relationship II: Empirical Investigation, Transp. Res., Vol.28B, No.5, pp , ) Del Castillo, J. M.: A Car Following Model Based on the Lighthill-Whitham Theory, Proc. of 13th ISTTT(Lyon), pp , ),,,, No.17, pp.81 84, ),,, No.17, pp.85 88, ) Nakanishi, K., Itoh K., Igarashi Y. and Bando, M.: Solvable optimal velocity models and asymptotic trajectory, Journal of Physical Review E, Vol.55, No.6, pp , ) Sugiyama, Y. and Yamada, H.: Simple and exactly solvable model for queue dynamics, Journal of Physical Review E, Vol.55, No.6, pp , ) Bando, M., Hasebe, K., Nakanishi, K. and Nakayama, A.: Analysis of optimal velocity model with explicit delay, Journal of Physical Review E, Vol.58, No.5, pp , ),,,, No.15, pp , ) Holland, E. N.: A Generalised Stability Criterion for Motorway Traffic, Transpn. Res., Vol.32B, No.2, pp , ),,,, No.7, pp.73 80, ),,,,, No.47IV, pp , ),, Vol.35, No.11, pp.31 37, ) Ozaki, H.: Perception Ability of Vertical Road Alignment by Drivers, Proc. of 3rd WC on ITS(Orlando), CD-ROM only, ),,,,, No.21(2), pp , ),,,,,, No.22(2), pp , ),, - -,, ),, Vol.22, No.6, pp.21 29, ) Moon,,,, No.14(1), pp , ),,,,,, No.530/IV 30, pp , ),, Vol.3, No.4, pp.5 12, ),, ), PID,, ) - -( B. B.9. ),, ),,,, No.912 1, pp , ),, No.35, pp , ),, ( 1 ),, No.872, pp , ),,,, No.881, pp , ), 12

13 ,, No.38, pp.55 61, ),,, No.871, pp.67 72, ),,, 3,, No.936, pp , ), ( ),, Vol.22, No.2, pp.69 72, ), ( ) - 2 -,, No.902 2, pp , ), ( ),, No.901, pp , ),,,, Vol.48, No.12, pp.5 11, ),,,,, No.871, pp.73 78, ),,,,, No.38, pp.78 84, ),,,, No.41, pp.51 56, ),,, No.892, pp , ),,,, No.912 1, pp , ),,, No.921, pp.13 16, ),,,, No.936, pp , ),,,, Vol.27, No.1, pp , ),,,,, No.936, pp , ),, No.440/IV 16, pp.33 40, ) Greenberg, H.: An Analysis of TrafficFlow,Oper. Res., Vol.7, pp.79-85, ) Lighthill, M. J. and Whitham, G. B.: On Kinematic Waves: 1. Flood Movement in Long Rivers, Proc. of the Royal Society of London, Series A, Vol.229, pp , ),,, No.336, pp , ),,,, No.458/IV 18, pp.65 71, ),,,,, No.21(2), pp , ),,,, No.17, pp , ),,, No.12, pp , ),,,, Vol.32, No.1, pp.39 47, ),,,,, No.23, 2000( ). 105),,,,,. 106),,,,, No.23, 2000( ). ( ) 13

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