A new extended lattice model of traffic flow is presented by taking into account both multianticipative behavior and the reaction-time delay of drivers. The linear stability theory and the nonlinear analysis method are applied to the model. The linear stability condition is obtained. The Korteweg–de Vries (KdV) equation near the neutral stability line and the modified Korteweg–de Vries (mKdV) equation near the critical point are derived. The numerical results show that the stability of traffic flow will be enhanced by multianticipative consideration and will be weakened with the increase of the reaction-time delay. The unfavorable effect induced by driver reaction delays can be partly compensated by considering multianticipative behavior.

References

References
1.
Nagatani
,
T.
,
1998
, “
Modified KdV Equation for Jamming Transition in the Continuum Models of Traffic
,”
Physica A
,
261
(
3–4
), pp.
599
607
.10.1016/S0378-4371(98)00347-1
2.
Nagatani
,
T.
,
1999
, “
TDGL and MKdV Equations for Jamming Transition in the Lattice Models of Traffic
,”
Physica A
,
264
(
3–4
), pp.
581
592
.10.1016/S0378-4371(98)00466-X
3.
Li
,
Z. P.
,
Li
,
X. L.
, and
Liu
,
F. Q.
,
2008
, “
Stabilization Analysis and Modified KdV Equation of Lattice Models With Consideration of Relative Current
,”
Int. J. Mod. Phys. C
,
19
(
8
), pp.
1163
1173
.10.1142/S0129183108012868
4.
Tian
,
J. F.
,
Jia
,
B.
,
Li
,
X. G.
, and
Gao
,
Z. Y.
,
2010
, “
Flow Difference Effect in the Lattice Hydrodynamic Model
,”
Chin. Phys. B
,
19
(
4
), p.
040303
.10.1088/1674-1056/19/4/040303
5.
Peng
,
G. H.
,
2013
, “
A New Lattice Model of Two-Lane Traffic Flow With the Consideration of Optimal Current Difference
,”
Commun. Nonlinear Sci. Numer. Simul.
,
18
(
3
), pp.
559
566
.10.1016/j.cnsns.2012.07.015
6.
Xue
,
Y.
,
2004
, “
Lattice Models of the Optimal Traffic Current
,”
Acta Phys. Sin.
,
53
(
1
), pp.
25
30
.
7.
Ge
,
H. X.
,
Dai
,
S. Q.
,
Xue
,
Y.
, and
Dong
,
L. Y.
,
2005
, “
Stabilization Analysis and Modified Korteweg-de Vries Equation in a Cooperative Driving System
,”
Phys. Rev. E
,
71
(
6
), p.
066119
.10.1103/PhysRevE.71.066119
8.
Wang
,
T.
,
Gao
,
Z. Y.
, and
Zhao
,
X. M.
,
2012
, “
Multiple Flux Difference Effect in the Lattice Hydrodynamic Model
,”
Chin. Phys. B
,
21
(
2
), p.
020512
.10.1088/1674-1056/21/2/020512
9.
Sun
,
D. H.
,
Tian
,
C.
, and
Liu
,
W. N.
,
2010
, “
A Traffic Flow Lattice Model Considering Relative Current Influence and Its Numerical Simulation
,”
Chin. Phys. B
,
19
(
8
), p.
080514
.10.1088/1674-1056/19/8/080514
10.
Li
,
Z. P.
,
Liu
,
F. Q.
, and
Sun
,
J.
,
2011
, “
A Lattice Traffic Model With Consideration of Preceding Mixture Traffic Information
,”
Chin. Phys. B
,
20
(
8
), p.
088901
.10.1088/1674-1056/20/8/088901
11.
Xie
,
D. F.
,
Gao
,
Z. Y.
, and
Zhao
,
X. M.
,
2008
, “
Stabilization of Traffic Flow Based on the Multiple Information of Preceding Cars
,”
Comm. Comp. Phys.
,
3
(
4
), pp.
899
912
.
12.
Peng
,
G. H.
, and
Sun
,
D. H.
,
2010
, “
A Dynamical Model of Car-Following With the Consideration of the Multiple Information of Preceding Cars
,”
Phys. Lett. A
,
374
(
15–16
), pp.
1694
1698
.10.1016/j.physleta.2010.02.020
13.
Jin
,
Y. F.
,
Xu
,
M.
, and
Gao
,
Z. Y.
,
2011
, “
KdV and Kink-Antikink Solitons in an Extended Car-Following Model
,”
ASME J. Comput. Nonlinear Dyn.
,
6
(
1
), p.
011018
.10.1115/1.4002336
14.
Yang
,
S. H.
,
Liu
,
W. N.
,
Sun
,
D. H.
, and
Li
,
C. G.
,
2013
, “
A New Extended Multiple Car-Following Model Considering the Backward-Looking Effect on Traffic Flow
,”
ASME J. Comput. Nonlinear Dyn.
,
8
(
1
), p.
011016
.10.1115/1.4007310
15.
Lenz
,
H.
,
Wagner
,
C. K.
, and
Sollacher
,
R.
,
1999
, “
Multi-Anticipative Car-Following Model
,”
Eur. Phys. J. B
,
7
(
2
), pp.
331
335
.10.1007/s100510050618
16.
Treiber
,
M.
,
Kesting
,
A.
, and
Helbing
,
D.
,
2006
, “
Delays, Inaccuracies and Anticipation in Microscopic Traffic Models
,”
Physica A
,
360
(
1
), pp.
71
88
.10.1016/j.physa.2005.05.001
17.
Ossen
,
S.
, and
Hoogendoorn
,
S. P.
,
2006
, “
Multi-Anticipation and Heterogeneity in Car-Following: Empirics and a First Exploration of Their Implications
,”
IEEE Intelligent Transportation Systems Conference
, Toronto, Canada, 17–20 September, pp.
1615
1620
.
18.
Mo
,
Y. L.
,
He
,
H. D.
,
Xue
,
Y.
,
Shi
,
W.
, and
Lu
,
W. Z.
,
2008
, “
Effect of Multi-Velocity-Difference in Traffic Flow
,”
Chin. Phys. B
,
17
(
12
), pp.
4446
4450
.10.1088/1674-1056/17/12/019
19.
Bando
,
M.
,
Hasebe
,
K.
,
Shibata
,
A.
, and
Sugiyama
,
Y.
,
1995
, “
Dynamical Model of Traffic Congestion and Numerical Simulation
,”
Phys. Rev. E
,
51
(
2
), pp.
1035
1042
.10.1103/PhysRevE.51.1035
20.
Treiber
,
M.
,
Hennecke
,
A.
, and
Helbing
,
D.
,
2000
, “
Congested Traffic States in Empirical Observations and Microscopic Simulation
,”
Phys. Rev. E
,
62
(
2
), pp.
1805
1824
.10.1103/PhysRevE.62.1805
21.
Helly
,
W.
,
1959
, “
Simulation of Bottlenecks in Single Lane Traffic Flow
,”
International Symposium on the Theory of Traffic Flow
, pp.
207
238
.
22.
Bando
,
M.
,
Hasebe
,
K.
,
Nakanishi
,
K.
, and
Nakayama
,
A.
,
1998
, “
Analysis of Optimal Velocity Model With Explicit Delay
,”
Phys. Rev. E
,
58
(
5
), pp.
5429
5435
.10.1103/PhysRevE.58.5429
23.
Orosz
,
G.
,
Wilson
,
R. E.
, and
Krauskopf
,
B.
,
2004
, “
Global Bifurcation Investigation of an Optimal Velocity Traffic Model With Driver Reaction Time
,”
Phys. Rev. E
,
70
(
2
), p.
026207
.10.1103/PhysRevE.70.026207
24.
Davis
,
L. C.
,
2003
, “
Modifications of the Optimal Velocity Traffic Model to Include Delay Due to Driver Reaction Time
,”
Physica A
,
319
, pp.
557
567
.10.1016/S0378-4371(02)01457-7
25.
Yu
,
L.
,
Li
,
T.
, and
Shi
,
Z. K.
,
2010
, “
Density Waves in a Traffic Flow Model With Reaction-Time Delay
,”
Physica A
,
389
(
13
), pp.
2607
2616
.10.1016/j.physa.2010.03.009
26.
Zhu
,
H. B.
, and
Dai
,
S. Q.
,
2008
, “
Analysis of Car-Following Model Considering Driver's Physical Delay in Sensing Headway
,”
Physica A
,
387
(
13
), pp.
3290
3298
.10.1016/j.physa.2008.01.103
27.
Ge
,
H. X.
,
Meng
,
X. P.
,
Cheng
,
R. J.
, and
Lo
,
S. M.
,
2011
, “
Time-Dependent Ginzburg-Landau Equation in a Car-Following Model Considering the Driver's Physical Delay
,”
Physica A
,
390
(
1
), pp.
3348
3353
.10.1016/j.physa.2011.04.033
28.
Chen
,
J. Z.
,
Shi
,
Z. K.
, and
Hu
,
Y. M.
,
2012
. “
Stabilization Analysis of a Multiple Look-Ahead Model With Driver Reaction Delays
,”
Int. J. Mod. Phys. C
,
23
(
6
), p.
1250048
.10.1142/S0129183112500489
29.
Tordeux
,
A.
,
Lassarre
,
S.
, and
Roussignol
,
M.
,
2010
, “
An Adaptive Time Gap Car-Following Model
,”
Transp. Res. B
,
44
(
8–9
), pp.
1115
1131
.10.1016/j.trb.2009.12.018
30.
Lassarre
,
S.
,
Roussignol
,
M.
, and
Tordeux
,
A.
,
2012
, “
Linear Stability Analysis of First-Order Delayed Car-Following Models on a Ring
,”
Phys. Rev. E
,
86
(
3
), p.
036207
.10.1103/PhysRevE.86.036207
31.
Kang
,
Y. R.
, and
Sun
,
D. H.
,
2013
, “
Lattice Hydrodynamic Traffic Flow Model With Explicit Drivers' Physical Delay
,”
Nonlinear Dyn.
,
71
(
3
), pp.
531
537
.10.1007/s11071-012-0679-5
32.
Wilson
,
R. E.
,
Berg
,
P.
,
Hooper
,
S.
, and
Lunt
,
G.
,
2004
, “
Many-Neighbour Interaction and Non-Locality in Traffic Models
,”
Eur. Phys. J. B
,
39
(
3
), pp.
397
408
.10.1140/epjb/e2004-00205-y
33.
Ge
,
H. X.
,
2009
, “
The Korteweg-de Vries Soliton in the Lattice Hydrodynamic Model
,”
Physica A
,
388
(
8
), pp.
1682
1686
.10.1016/j.physa.2008.11.026
34.
Ge
,
H. X.
,
Cheng
,
R. J.
, and
Dai
,
S. Q.
,
2005
, “
KdV and Kink-Antikink Solitons in Car-Following Models
,”
Physica A
,
357
(
3–4
), pp.
466
476
.10.1016/j.physa.2005.03.059
You do not currently have access to this content.