Macroscopic traffic flow modeling with adaptive cruise control: Development and numerical solution

Computers and Mathematics with Applications

Volumn 70, Issue 8, 2015, Pages 1921-1947

  Delis, A I ^a   Nikolos, I K ^a   Papageorgiou, M ^a  

^a TECHNICAL UNIVERSITY OF CRETE   (Greece)

Author keywords

Cooperative Adaptive Cruise Control; Finite volume relaxation schemes; Hyperbolic conservation laws; Macroscopic traffic flow models; Numerical simulation; Traffic flow dynamics

Indexed keywords

COMPUTER SIMULATION; FINITE VOLUME METHOD; KINETIC THEORY OF GASES; LINEAR SYSTEMS; NONLINEAR EQUATIONS; NUMERICAL MODELS; RELAXATION TIME; STREET TRAFFIC CONTROL; VEHICLES;

ACCELERATION/DECELERATION; ADAPTIVE CRUISE CONTROL (ACC); COOPERATIVE ADAPTIVE CRUISE CONTROL; FLOW CHARAC-TERISTICS; HYPERBOLIC CONSERVATION LAWS; MACROSCOPIC TRAFFIC FLOW MODEL; SYSTEM OF PARTIAL DIFFERENTIAL EQUATIONS; TRAFFIC FLOW DYNAMICS;

ADAPTIVE CRUISE CONTROL;

EID: 84942292587     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2015.08.002     Document Type: Article

References (46)

1. T.P. Alkim, H. Schuurman, C.M.J. Tampere, Effects of external cruise control and co-operative following on highways: an analysis with the MIXIC traffic simulation model, in: Proceedings of the IEEE Intelligent Vehicles Symposium of the Institute of Electrical and Electronics Engineers, 2000, pp. 474-479.
2. J. VanderWerf, S.E. Shladover, M.A. Miller, and N. Kourjanskaia Evaluation of the effects of adaptive cruise control systems on highway traffic flow capacity and implications for deployment of future automated systems Transp. Res. Rec. 1800 2002 78 84
3. L.C. Davis Effect of adaptive cruise control systems on traffic flow Phys. Rev. E 69 2004 066110-7
4. B. van Arem, C. van Driel, and R. Visser The impact of cooperative adaptive cruise control on traffic-flow characteristics Proc. IEEE Trans., Intell. Transp. Syst. 7 2006 429 436
5. L.C. Davis Effect of adaptive cruise control systems on mixed traffic flow near an on-ramp Physica A 379 2007 274 290
6. A. Kesting, M. Treiber, M. Schönhof, and D. Helbing Adaptive cruise control design for active congestion avoidance Transp. Res. C 16 2008 668 683
7. A. Kesting, M. Treiber, and D. Helbing Enhanced intelligent driver model to access the impact of driving strategies on traffic capacity Phil. Trans. R. Soc. A 368 2010 4584 4605
8. S.E. Shladover, X.Y. Lu, D. Cody, C. Nowakowski, Z.T. Qiu, A. Chow, J. O'Connell, J. Nienhuis, D. Su, Development and evaluations of selected mobility applications for VII: Concept of operations PATH Research Report, 2010.
9. C. Nowakowski, S.E. Shladover, D. Cody, F. Bu, J. O'Connell, J. Spring, S. Dickey, and D. Nelson Cooperative adaptive cruise control: Testing drivers' choices of following distances. Research Report. PATH 2011 University of California
10. S.E. Shladover, D. Su, and X.-Y. Lu Impacts of cooperative adaptive cruise control on freeway traffic flow Transp. Res. Rec. J. Transp. Res. Board 2324 2012 63 70
11. G.M. Arnaout, and S. Bowling A Progressive deployment strategy for Cooperative Adaptive Cruise Control to improve traffic dynamics Int. J. Autom. Comput. 11 2014 10 18
12. I.A. Ntousakis, K. Porfyri, I.K. Nikolos, M. Papageorgiou, Assessing the impact of a cooperative merging system on highway traffic using a microscopic flow simulator, in: Proceedings of the ASME International Mechanical Engineering Conference & Exposition, IMECE2014, November 14-20, Montreal, Quebec, Canada, Paper No. IMECE2014-39850, 2014.
13. I.A. Ntousakis, I.K. Nikolos, M. Papageorgiou, On microscopic modeling of adaptive cruise control systems, in: 4th International Symposium of Transport Simulation, ISTS 2014, Corsica, France, June 1-4, 2014.
14. D. Swaroop, and K.R. Rajagopal Intelligent cruise control systems and traffic flow stability Transp. Res. C 7 1999 329 352
15. J. Yi, R. Horowitz, Macroscopic traffic flow stability for adaptive cruise controlled (ACC) vehicles, in: Proceedings of the 41st IEEE Conference on Decision and Control, Las Vegas Nevada, USA, 2002.
16. H. Lenz Entwicklung nichtlinearer, diskreter Regler zum Abbau von Verkehrsflussinhomogenitaeten mithilfe makroskopischer Verhkehrsmodelle (Ph.D. dissertation) 1999 Lehrstuehl fuer Mensch-Maschine-Kommunikation, Fakultaet fuer Elektrotechnik und Informationstechnik der Technischen Universitaet Muenchen Shaker Verlag, Aachen
17. S.P. Hoogendoorn, and P.H.L. Bovy Model assessment of dynamic speed limit control WCTRS, World Conference on Transport Research 2001 WCT-Research Society Seoul, Korea 1 20
18. C. Demir, Modelling the impact of ACC-systems on the traffic flow at macroscopic modeling level, in: Traffic and Granular Flow'01, 2003, pp. 305-317.
19. D. Ngoduy, S.P. Hoogendoorn, and R. Liu Continuum modeling of cooperative traffic flow dynamics Physica A 388 2009 2705 2716
20. D. Ngoduy Application of gas-kinetic theory to modeling mixed traffic of manual and ACC vehicles Transpormetrica 8 2012 43 60
21. D. Ngoduy Platoon based macroscopic model for intelligent traffic flow Transportmetrica, Part B 1 2013 153 169
22. D. Ngoduy, and R.E. Wilson Multi-anticipative non-local macroscopic traffic model Comput.-Aided Civ. Infrastruct. Eng. 29 2014 248 263
23. D. Ngoduy Instability of cooperative adaptive cruise control traffic flow: A macroscopic approach Commun. Nonlinear Sci. Numer. Simul. 18 2013 2838 2851
24. A.I. Delis, I.K Nikolos, and M. Papageorgiou High-resolution numerical relaxation approximations to second-order macroscopic traffic flow models Transp. Res. C 44 2014 318 349
25. S. Jin, and Z. Xin The relaxing schemes of conservation laws in arbitrary space dimensions Comm. Pure Appl. Math. 48 1995 235 277
26. M. Treiber, A. Hennecke, and D. Helbing Derivation, properties, and simulation of a gas-kinetic-based, nonlocal traffic model Phys. Rev. E: Stat. Phys. Plasmas Fluids Relat. Interdisciplin. Top. 59 1 1999 239 253
27. D. Helbing, A. Hennecke, V. Shvetsov, and M. Treiber MASTER: Macroscopic traffic simulation based on a gas-kinetic, non-local traffic model Transp. Res. B 35 2 2001 183 211
28. D. Helbing, A. Hennecke, V. Shvetsov, and M. Treiber Micro- and macro-simulation of freeway traffic Math. Comput. Modelling 35 2002 517 547
29. M. Treiber, and A. Kesting Traffic Flow Dynamics: Data, Models and Simulation 2013 Springer
30. R. Borsche, M. Kimathi, and A. Klar A class of multi-phase traffic theories for microscopic, kinetic and continuum traffic models Comput. Math. Appl. 64 2012 2939 2953
31. D. Helbing, and M. Treiber Gas-kinetic-based traffic model explaining observed hysteretic phase transition Phys. Rev. Lett. 81 14 1998 3042 3048
32. M. Treiber, and D. Helbing Macroscopic simulation of widely scattered synchronized traffic states J. Phys. A: Math. Gen. 32 1999 17 23
33. D. Helbing, and M. Treiber Numerical simulation of macroscopic traffic equations Comput. Sci. Eng. 1 5 1999 89 99
34. G. Marsden, M. McDonald, and M. Braxkstone Towards an understanding of adaptive cruise control Transp. Res. C 9 2001 33 51
35. R. Natalini Convergence to equilibrium for the relaxation approximations of conservation laws Comm. Pure Appl. Math. 49 1996 795 823
36. T.P. Liu Hyperbolic conservation laws with relaxation Comm. Math. Phys. 108 1987 153 175
37. A. Chalabi, and D. Seghir Convergence of relaxation schemes for initial boundary value problems for conservation laws Comput. Math. Appl. 43 8-9 2002 1079 1093
38. M. Seaid Stable numerical methods for conservation laws with discontinuous flux function Appl. Math. Comput. 175 2006 383 400
39. R. Borges, M. Carmona, B. Costa, and W.-S. Don An improved weighted essentially non-oscillatory scheme for hyperbolic conservation laws J. Comput. Phys. 227 2008 3191 3211
40. M. Seaid Improved applications of relaxation schemes for hyperbolic systems of conservation laws and convection-diffusion problems Comput. Methods Appl. Math. 6 2 2006 56 86
41. U. Ascher, S. Ruuth, and R. Spiteri Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations Appl. Numer. Math. 25 1997 151 167
42. L. Pareschi, and G. Russo Implicit-explicit Runge-Kutta schemes and applications to hyperbolic systems with relaxation J. Sci. Comput. 25 1 2005 129 155
43. W. Shen, C. Zhang, and J. Zhang Relaxation method for unsteady convection-diffusion equations Comput. Math. Appl. 61 2011 908 920
44. D. Helbing, A. Hennecke, and M. Treiber Phase diagram of traffic states in the presence of inhomogeneities Phys. Rev. Lett. 82 21 1999 4360 4363
45. D. Helbing, M. Treiber, A. Hennecke, and Schönhof Theoretical vs. empirical classification and prediction of congested traffic states Eur. Phys. J. B 69 2009 583 598
46. M. Treiber, A. Kesting, and D. Helbing Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts Transp. Res. B 44 2010 983 1000