A New Macro Model for Traffic Flow on a Highway with Ramps and Numerical Tests

In this paper, we present a new macro model for traffic flow on a highway with ramps based on the existing models. We use the new model to study the effects of on-off-ramp on the main road traffic during the morning rush period and the evening rush period. Numerical tests show that, during the two rush periods, these effects are often different and related to the status of the main road traffic. If the main road traffic flow is uniform, then ramps always produce stop-and-go traffic when the main road density is between two critical values, and ramps have little effect on the main road traffic when the main road density is less than the smaller critical value or greater than the larger critical value. If a small perturbation appears on the main road, ramp may lead to stop-and-go traffic, or relieve or even eliminate the stop-and-go traffic, under different circumstances. These results are consistent with real traffic, which shows that the new model is reasonable.

[1]  Kerner,et al.  Cluster effect in initially homogeneous traffic flow. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  D. Helbing.  Traffic and related self-driven many-particle systems , 2000, cond-mat/0012229.

[3]  Michael J. Cassidy,et al.  Increasing Capacity of an Isolated Merge by Metering its On-Ramp , 2004 .

[4]  Ding-wei Huang,et al.  Analytical results of asymmetric exclusion processes with ramps. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Rui Jiang,et al.  Spatiotemporal congested traffic patterns in macroscopic version of the Kerner–Klenov speed adaptation model , 2007 .

[6]  A. Lyrintzis,et al.  Modelling of freeway merging and diverging flow dynamics , 1996 .

[7]  Rui Jiang,et al.  Cellular automata model simulating traffic interactions between on-ramp and main road. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Boris S. Kerner,et al.  Deterministic microscopic three-phase traffic flow models , 2006 .

[9]  R. Jiang,et al.  Phase diagram of speed gradient model with an on-ramp , 2007 .

[10]  Mao-Bin Hu,et al.  ENHANCING HIGHWAY CAPACITY BY HOMOGENIZING TRAFFIC FLOW , 2008 .

[11]  R. Jiang,et al.  A new continuum model for traffic flow and numerical tests , 2002 .

[12]  R. Jiang,et al.  Spatial–temporal patterns at an isolated on-ramp in a new cellular automata model based on three-phase traffic theory , 2004 .

[13]  Boris S. Kerner,et al.  Cellular automata approach to three-phase traffic theory , 2002, cond-mat/0206370.

[14]  V. K. Katiyar,et al.  Phase transition of traffic states with on-ramp , 2006 .

[15]  S. Wong,et al.  Essence of conservation forms in the traveling wave solutions of higher-order traffic flow models. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Dong Ngoduy,et al.  DERIVATION OF CONTINUUM TRAFFIC MODEL FOR WEAVING SECTIONS ON FREEWAYS , 2006 .

[17]  Rui Jiang,et al.  A new dynamics model for traffic flow , 2001 .

[18]  Arvind Kumar Gupta,et al.  A NEW MULTI-CLASS CONTINUUM MODEL FOR TRAFFIC FLOW , 2007 .

[19]  Hyun-Woo Lee,et al.  Traffic states of a model highway with on-ramp , 2000 .

[20]  Peng Zhang,et al.  High-resolution numerical approximation of traffic flow problems with variable lanes and free-flow velocities. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[21]  Boris S. Kerner,et al.  Probabilistic breakdown phenomenon at on-ramp bottlenecks in three-phase traffic theory: Congestion nucleation in spatially non-homogeneous traffic , 2006 .

[22]  L. C. Davis.  Effect of adaptive cruise control systems on mixed traffic flow near an on-ramp , 2005 .

[23]  A. Schadschneider,et al.  Statistical physics of vehicular traffic and some related systems , 2000, cond-mat/0007053.

[24]  B. Kerner,et al.  A microscopic model for phase transitions in traffic flow , 2002 .

[25]  Ding-wei Huang,et al.  Ramp-induced transitions in traffic dynamics. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  H. Lee,et al.  ORIGIN OF SYNCHRONIZED TRAFFIC FLOW ON HIGHWAYS AND ITS DYNAMIC PHASE TRANSITIONS , 1998, cond-mat/9805097.

[27]  Rui Jiang,et al.  Phase transition at an on-ramp in the Nagel–Schreckenberg traffic flow model , 2006 .

[28]  Markos Papageorgiou,et al.  Freeway ramp metering: an overview , 2002, IEEE Trans. Intell. Transp. Syst..

[29]  Boris S. Kerner,et al.  Local cluster effect in different traffic flow models , 1998 .

[30]  Avishai Ceder,et al.  Observing freeway ramp merging phenomena in congested traffic , 2007 .

[31]  Ziyou Gao,et al.  The effect of restricted velocity in the two-lane on-ramp system , 2007 .