Traffic Behavior and Jams Induced by Slow-down Sections

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1 55 * * * Trff Behvor nd Jms Indued y Slow-down Setons Shuh MASUKURA, Fulty of Engneerng, Shzuok Unversty Hrotosh HANAURA, Fulty of Engneerng, Shzuok Unversty Tksh NAGATANI, Fulty of Engneerng, Shzuok Unversty (Reeved 1 July 8; n revsed form 6 Deemer 8) We study the jmmng trnstons ndued y slow-down setons. We present the extended verson of the optml veloty model to tke nto ount the lne hngng. We show tht the fundmentl (flow-densty) dgrm hnges onsderly y ntrodung slow-down setons. It s shown tht the trff flow s dvded nto the three dstnt trff sttes.e. the free trff, the sturted trff, nd the homogeneous ongested trff. Also, the two-lne trff flow s dvded nto sx trff sttes. We lrfy tht dsontnuous fronts our efore slowdown seton n the sturted trff. We derve the reltonshp etween denstes efore nd fter the dsontnuous front. (KEY WORDS): Trff flow, Jmmng trnston, Phse dgrm, Two-lne hghwy, Trff stte 1 1) IT -8) * E-ml: gonnonn@yhoo.o.jp 9) Ssk-Kometn 1) Ssk-Kometn Stop-nd go-wve 11) 1) 13)

2 56 14,15) 16,17,18) 3 4 N x L=N x L S L N 1() 1() L= L S +L N L= L S1 + L S +L N1 + L N d x dx = α V ( x ) (1) dt dt V( x )x x (=x +1 - x ) α ρ x ρ=1/ x ρ ρ L U xˆ x, vˆ v =, U t = ˆt, L α = αˆ L U L U dx 1 dxˆ =, d x 1 d xˆ = dt U dtˆ ˆ dt U dt () xˆ, vˆ, tˆ, αˆ () (1)(1) x V( x ) α V( x )τ α=. ().5 [1/s] [s]. α. α. 7) x [ tnh ( x x ) + tnh ( x )] v f,mx V ( x ) = f, f, (3) v s1,mx V ( x ) [ ( ) ( )] (4) = tnh x x s, + tnh x s, v s,mx V ( x ) = s, s, [ tnh ( x x ) + tnh ( x )] (5)

3 57 v f,mx v s1,mx v s,mx v s1,mx < v f,mx v s,mx < v f,mx x f, x s, (3)-(5)(1) 4 RungeKutt t=1/18 N=5 t=5 v f,mx =. x f, = x s, =3. α=.5 L=1[m] U=45[km/h] x =3. 3[m]. 9[km/h] 1km [km/h] ρ=5 Q=5 v=1.9 5 Q=4 v=. x ρ ρ =1~ 1 L S =L N =L/ v s1,mx =1. 1() L N1 L N v f,mx (3)L S1 v s1,mx (4) L S v s,mx (5) L S1 = L S =L N1 = L N =L/4 v s1,mx = v s,mx =1. v f,mx =. v s,mx =1. t=3 t=3~5 =.5 V f,mx =. V s,mx =1. urrent (L N1 =L N =L S1 =L S =5L) urrent(l N =L S =L) x= +1 x=l x L N L S () x= x=l (1) dx/dt= V( x) Q th ( ) = ρ V (6) ρ L N1 L S1 L N L S () 1 1() L N v f,mx (3)L S v s1,mx (4) v s,mx =1. 3 ρ =5t=5

4 58 N1N S1S 4 v f,mx =. v s,mx =1. v s,mx = Hedwy N1 l J1 L 5 S1 1 Poston N l J L 15 S 3 (v s1,mx = v s,mx =1.) (V f,mx =.) (V s,mx =1.) Mxml vlue of the urrent of slowdown seton v f,mx =. v s,mx =1.5 v s,mx =1. v s1,mx =1.5 v s,mx =1. v s1,mx = v s,mx =1. 6 v s1,mx =1.5v s,mx =1. ρ =5t=5 N1N S1 S S S1 S1 S1, S1 N1 7 v f,mx =. v s1,mx =1.5 v s,mx =1. v f,mx =. v s1,mx =1.5 v s,mx =1. 6 ~e 7 ~e 1 8 =.5 V s,mx =1. urrent (v s1,mx =1.5, v s,mx =1.) urrent (v s1,mx =v s,mx =1.) V f,mx =. V s,mx =1.5 5 N1 S1 N S Hedwy 6 4 d l J L 4 e 1() v s1,mx =1.5 v s,mx =1. 5 v s1,mx = v s,mx =1. v s1,mx =1.5 v s,mx = Poston 6 (v s1,mx =1.5, v s,mx =1.)

5 59 d e (V f,mx =.) (V s1,mx =1.5) (V s,mx =1.) Mxml vlue of the urrent of slowdown seton 7 3 () () 8 x <.x (7) xf > x nd x >x (8) xf x x x (7)(8) 4 9[km/h] 1[m] 9[m] 9[km/h] 65[m] x =6[m] 8() L S =L/ v s1,mx =1. 8() L S =L/ v s1,mx =1. 8() L S1 = L S =L/4 v s1,mx = v s,mx =1. 8() 9 () 8

6 6 Lne 9 8() v f,mx =. v s,mx =1. Lne () Lne 8() 1 v f,mx =. v s,mx = () Frton 11 8()

7 61 The numer of lne hnge/unt tme From lne1 to lne From lne to lne1 Trff jm length rto on lne () 14 8() 13 ρ = Hedwy Poston 3 Lne 4 13 () 8() 8() 8() () 17 1 Lne Veloty Lne 1 Poston () 13 () 8()

8 6 Frton The numer of lne hnge/unt tme () Lne Lne 17 8() 18 Trff jm length rto Jm1 Jm Totl () 4 1) ) Ngtn, T.: The physs of trff jm, Rep. Prog. Phys. 65 () ) Helng, D.: Trff nd relted self-drven mny-prtle systems, Rev. Mod. Phys. 73 (1) ) Kerner, B. S.: The Physs of Trff (Sprnger, 4). 5) Helng, D., Herrmnn, H. J., Shrekenerg, M., Wolf, D. E. (Eds.) Trff nd Grnulr Flow 99, Sprnger, Hedelerg,. 6) Chowdhury, D., Snten, L., Shdshneder, A.: Sttstl physs of vehulr trff nd some relted systems, Phys. Rep. 39 () ) (3) ) ) Grtner, N. H., Wlson, N. H. M. (Eds.): Trnsportton nd Trff Theory (Elsever 1987).

9 63 1) Kometn, E. nd Ssk, T.: On the Stlty of Trff Flow, J. Opns. Res. Jpn, (1958) ) 371 / ) 66 / ) Nshnr, K., Fuku M., nd Shdshneder A.: A stohst ellulr utomton model for trff flow wth multple metstle sttes, J. Phys. A, ) (B ) ) ) Ssoh, A. & Ohr, T.: Shok wve relton ontnng lne hnge soure term for two-lne trff flow, J. Phys. So. Jpn, ) Kurt, S., Ngtn, T.: Spto-temporl dynms of jms n two-lne trff flow wth lokge, Phys. A, 381 (3) )