%, Treiterer [6 ] Lighthill,, PACC: 0550,0520,6470. Vol. 52,No. 9,September,2003 ν 2003 Chin. Phys. Soc. ACTA PHYSICA SINICA.

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1 Π2003Π52 (09) Π ACTA PHYSICA SINICA Vol 52 No 9 September 2003 ν 2003 Chin Phys Soc 3 1) 2) 1) 3) 1) 1) ( ) 2) ( ) 3) ( ) ( ; ) NaSch : ( SDNaSch ) NaSch ; ; NaSch : PACC: v q 1991 : q v ; 15kmΠh 4kmΠh Whitham [7 ] - [1 ] ; [ ] - [3 ] ; [4 ] ; [5 20 % ] [2 ] Treiterer [6 ] - Lighthill 3 ( )

2 [8 ] Nagel Schreck2 enberg [9 ] NaSch Fukui Ishibashi FI [10 ] [11 FI ] [12 13 ] NaSch TRANSIMS [14 ] [15 ] (Duisburg) 1 (congestion) ( start- stop wave) ( q - V) ( q max = 2500carsΠ(h lane) ) NaSch 1 6min ( q - V) [14 ] 2500carsΠ(h lane) Na2 Sch 1800carsΠ( h lane) ; NaSch 21 ( slow-tostart) NaSch NaSch v n ( t ) [ 0 (VDR) [16 ] T 2 [17 ] BJ H [18 ] v max ] L [19 ] [20 ] [21 22 ] NaSch x n ( t) n t ; v n ( t) VDR n t v max ; T 2 BJ H gap n ( t) n t gap n ( t) = x n + 1 ( t) - x n ( t) - 1 ; P NaSch [9 ] 0) ; 1) : v n min ( v n + 1 v max ) ; 2) : v n min ( v n gap n ) ; 3) P : v n max ( v n - 1 4) : x n x n + v n [2 ] VDR T 2 NaSch [ 23 ] P ; NaSch NaSch NaSch

3 9 : v i ( t) 10 4 NaSch V NaSch : 2) 3) Chowdhury [24 ] Schadschneider [25 ] 8 NaSch NaSch SDNaSch NaSch ; 1) : v n ( t + 1) min ( v n ( t) + 1 v max ) 2) P : v n ( t + 1) max( v n ( t) - 1 0) ; 3) : v n ( t + 1) min ( v n gap n ) ; 4) : x n x n + v n ( t + 1) 1) 3) L ( q2 ) L 715km m 0 v max 1000 ; v max = 5cellsΠs 135kmΠh N Na2 L v i i Sch = N L (1) V = 1 N N i = 1 v i ( t) = 1 T t = T+ t t = t 0 v i ( t) (2) q = V (3) 10 4 t 0 = 10 4 T = ( = v max = 5 L = 1000) ( ) NaSch P =

4 SDNaSch 2 < < 1 [16 ] q c = (1 - ) (1 - P) (5) > 1 [16 ] 2 [16 ] ; c SD2 NaSch NaSch 3 4 c SDNaSch NaSch 40 % 1 (2500carsΠh lane) 1 < < 2 3 NaSch ( v max = 5 L = 1000 P = 0125) < < ( 5 ) SDNaSch NaSch :NaSch ( c = 0) ; 1 < < 2 SDNaSch ( c = 1) [26 ] ( c = ; ) ( c = ) P = [26 ] ; 5 (b) SDNaSch ; q f = ( v max - P) = v f (4) v f v f = 4175 Kerner

5 9 : ( = t = 6000 ) [26 ] 41 NaSch NaSch NaSch

6 [1] Dai S Q et al 1997 Ziran Zazhi (in Chinese) [ [15] OLSIM Physics of Transport and Traffic University of Duisburg ht ] [2] Helbing D 2001 Rev Mod Phy [3] Kerner B S and Rehborn H 1997 Phy Rev Lett [4] Kerner B S and Konhguser P 1993 Phy Rev E 48 R2335 [5] Newell G F 1959 Oper Res [6] Treiterer J et al 1965 Appx IX to final Report ( Columbus : Ohio State Univ ) p202 [7] Lighthill MJ and Whitham GB 1955 Proc Roy Soc Ser A [8] Helbing D et al 2001 Trans Res Part B [9] Nagel K and Schrekenberg M 1992 J Phys I France [10] Ishibashi Y and Fukui M 1994 J Phys Soc Japan [11] Wang B H Wang L Hui P M H B 1998 The 20 th IUPAP Inter Conf on Stat Phys Topic 2 T0791 PO 02Π145 [12] Wang B H Kuang L Q and Hui P M 1998 Acta Phys Sin (in Chinese) [ ] [13] Wang L and Wang B H 1999 Acta Phys Sin (in Chinese) [ ] [14] Wagner P 1996 Traffic and granular flow (Singapore : World Scien2 tific) p193 tp :ΠΠtraffic comphys uni- duisburg de [16] Barlovic R et al 1998 Eur Phys J B [17] Takayasu M and Takayasu H 1993 Fractals [18] Benjamin S C Johnson N F and Hui P M 1996 J Phys A : Math & Gen [19] Li X B Wu Q S and Jiang R 2001 Phy Rev E [20] Dong L Y Xue Yand Dai S Q 2002 Appl Math and Mech ( En2 gl Ed ) [21] Xue Y Dong L Y and Dai S Q 2001 Acta Phys Sin (in Chinese) [ ] [22] Xue Y 2002 Shanghai University doctoral dissertation (in Chinese) [ 2002 ] [23] Tan H L Liu M R and Kong L J 2002 Acta Phys Sin (in Chinese) [ ] [24] Chowdhury D et al 2000 Physics Reports [25] Schadschneider A 2001 Traffic flow : A statistical physics point of view (Preprint submitted to Elsevier Science) [26] Kerner B S 2001 Networks and Spatial Economics 1 35 One2dimensio nal sensitive driving cellular automaton model for traffic flow 3 1) Lei Li 1) 2) Xue Yu 1) 3) Dai Shi-Qiang 1) ( Shanghai Institute of Applied Mathematics and Mechanics Shanghai University Shanghai China) 2) ( School of Energy and Power Engineering Shandong University Jinan China) 3) ( Department of Physics Guangxi University Nanning China) (Received 19 November 2002 ; revised manuscript received 8 January 2003) Abstract Based on the NaSch cellular automaton traffic model a new one- dimensional cellular automaton model ( called SDNaSch model for short) is proposed through preferentially considering the sensitive behaviour of drivers in which the randomization brake is arranged before the deterministic deceleration According to the new update rules of the evolution of vehicles numerical simulation is conducted and leads to some new results The fundamental diagram obtained by the simulation shows that the traffic capacity of a road is enhanced and closer to the observed data compared with that of the NaSch model It is found from the funda2 mental diagram that there exist two branches in some density regions which illustrates the existence of the metastable state near the critical point and the phase separation According to the evolution pattern of the vehicle speed in space and time the wide moving jams is reproduced with the phase transitions between free flow and wide moving jams With the consideration of the actu2 al traffic situation i e some drivers being sensitive and following the new rules while others being not and following the orig2 inal NaSch rules the corresponding simulation verifies the remarkable effect of the sensitive driving factor on the characteristics of traffic flows The traffic capacity rises along with the increase in the fraction of sensitive drivers Keywords : traffic flow cellular automaton model metastable state phase separation traffic phase transition PACC: Project supported by the National Natural Science Foundation of China ( Grant No )