Evidence of convective instability in congested traffic flow: A systematic empirical and theoretical investigation

Transportation Research Part B: Methodological

Volumn 45 `, Issue 9, 2011, Pages 1362-1377

  Treiber, Martin ^a   Kesting, Arne ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Analytical results; Convective instability; Growth rate; Spatiotemporal dynamics; Traffic database; Traffic flow oscillations

Indexed keywords

DATA FLOW ANALYSIS; GROWTH RATE; OPEN SYSTEMS; TRAFFIC CONGESTION;

ANALYTICAL RESULTS; CONVECTIVE INSTABILITIES; MACROSCOPIC TRAFFIC MODELS; PROPAGATION VELOCITIES; SPATIO-TEMPORAL DYNAMICS; SPATIOTEMPORAL PATTERNS; THEORETICAL INVESTIGATIONS; TRAFFIC FLOW;

STABILITY;

DATABASE; EMPIRICAL ANALYSIS; FLOW STABILITY; GROWTH RATE; NUMERICAL MODEL; SPATIOTEMPORAL ANALYSIS; THEORETICAL STUDY; TRAFFIC MANAGEMENT;

EID: 83555177368     PISSN: 01912615     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trb.2011.05.011     Document Type: Article

References (41)

1. Ahn S., Cassidy M.J. Freeway traffic oscillations and vehicle lane-change maneuvers. Transportation and Traffic Theory 2007 2007, 691-710. Elsevier, Chapter 29. R.E. Allsop, M.G.H. Bell, B.G. Heydecker (Eds.).
2. Aw A., Rascle M. Ressurection of "second order" models of traffic flow. SIAM Journal on Applied Mathematics 2000, 60(3):916-938.
3. Bertini R.L., Leal M.T. Empirical study of traffic features at a freeway lane drop. Journal of Transportation Engineering 2005, 131(6):397-407.
4. Coifman B.A., Wang Y. Average velocity of waves propagating through congested freeway traffic. Transportation and Traffic Theory: Flow, Dynamics and Human Interaction 2005, 165-179. Elsevier. H.S. Mahmassani (Ed.).
5. Daganzo C.F. A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections. Transportation Research Part B 2002, 36(2):131-158.
6. Daganzo C.F. A behavioral theory of multi-lane traffic flow. Part II: Merges and the onset of congestion. Transportation Research Part B 2002, 36(2):159-169.
7. Helbing D. Traffic and related self-driven many-particle systems. Reviews of Modern Physics 2001, 73(4):1067-1141.
8. Helbing D., Hennecke A., Treiber M. Phase diagram of traffic states in the presence of inhomogeneities. Physical Review Letters 1999, 82(21):4360-4363.
9. Helbing D., Treiber M., Kesting A., Schönhof M. Theoretical vs. empirical classification and prediction of congested traffic states. The European Physical Journal B 2009, 69(4):583-598.
10. Hoogendoorn S., Bovy P. State-of-the-art of vehicular traffic flow modelling. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering 2001, 215(4):283-303.
11. Huerre P., Monkewitz P. Local and global instabilities in spatially developing flows. Annual Review of Fluid Mechanics 1990, 22(1):473-537.
12. Kerner B. Empirical macroscopic features of spatio-temporal traffic patterns at highway bottlenecks. Physical Review E 2002, 65(4). 046138(1-30).
13. Kerner B., Rehborn H. Experimental properties of complexity in traffic flow. Physical Review E 1996, 53(5):R4275-R4278.
14. Kesting A., Treiber M. How reaction time, update time and adaptation time influence the stability of traffic flow. Computer-Aided Civil and Infrastructure Engineering 2008, 23(2):125-137.
15. Li X., Peng F., Ouyang Y. Measurement and estimation of traffic oscillation properties. Transportation Research Part B 2010, 44(1):1-14.
16. Lighthill M., Whitham G. On kinematic waves: II. A theory of traffic on long crowded roads. Proceedings of The Royal Society of London Series A 1955, 229:317-345.
17. Mauch M., Cassidy M.J. Freeway traffic oscillations: observations and predictions. Transportation and Traffic Theory in the 21st Century: Proceedings of the Symposium of Traffic and Transportation Theory 2002, 653-672. Elsevier. M.A. Taylor (Ed.).
18. Mika H.S., Kreer J.B., Yuan L.S. Dual mode behavior of freeway traffic. Highway Research Record 1969, 279:1-12.
19. Orosz G., Stépán G. Subcritical Hopf bifurcations in a car-following model with reaction-time delay. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science 2006, 462(2073):2643-2670.
20. Orosz G., Wilson R.E., Stépán G. Traffic jams: dynamics and control. Philosophical Transactions of the Royal Society A 2010, 368:4455-4479.
21. Payne H. A macroscopic simulation model of freeway traffic. Transportation Research Record 1979, 772:68-77.
22. Pipes L. An operational analysis of traffic dynamics. Journal of Applied Physics 1953, 24(3):274.
23. Reuschel A. Fahrzeugbewegungen in der Kolonne. österreichisches Ingenieur-Archiv 1950, 4:193-215.
24. Richards P. Shock waves on the highway. Operations Research 1956, 4(1):42-51.
25. Schönhof M., Helbing D. Empirical features of congested traffic states and their implications for traffic modeling. Transportation Science 2007, 41(2):1-32.
26. Schönhof M., Helbing D. Criticism of three-phase traffic theory. Transportation Research Part B 2009, 43(7):784-797.
27. Sugiyama Y., Fukui M., Kikuchi M., Hasebe K., Nakayama A., Nishinari K., Tadaki S., Yukawa S. Traffic jams without bottlenecks - experimental evidence for the physical mechanism of the formation of a jam. New Journal of Physics 2008, 10(3). 033001(1-7).
28. Treiber M., Hennecke A., Helbing D. Derivation, properties, and simulation of a gas-kinetic-based, non-local traffic model. Physical Review E 1999, 59(1):239-253.
29. Treiber M., Hennecke A., Helbing D. Congested traffic states in empirical observations and microscopic simulations. Physical Review E 2000, 62(2):1805-1824.
30. Treiber, M., Kesting, A., submitted for publication. Validation of traffic flow models with respect to the spatiotemporal evolution of congested traffic patterns. arXiv:1008.1639.
31. Treiber, M., Kesting, A., 2010b. Verkehrsdynamik und Simulation - Daten, Modelle und Anwendungen der Verkehrsflussdynamik. Springer (in German), ISBN:978-3-642-05227-9. http://www.verkehrsdynamik.de.
32. Treiber M., Kesting A., Helbing D. Delays, inaccuracies and anticipation in microscopic traffic models. Physica A 2006, 360(1):71-88.
33. Treiber M., Kesting A., Helbing D. Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts. Transportation Research Part B 2010, 44(8-9):983-1000.
34. Treiber, M., Kesting, A., Wilson, R.E., in press. Reconstructing the traffic state by fusion of heterogenous data. Computer-Aided Civil and Infrastructure Engineering. arxiv.org/abs/0909.4467.
35. Treiterer J., Myers J. The hysteresis phenomenon in traffic flow. Proc. 6th Int. Symp. on Transportation and Traffic Theory 1974, 13. Elsevier, New York. D. Buckley (Ed.).
36. Wagner P., Nagel K. Comparing traffic flow models with different number of 'phases'. The European Physical Journal B 2008, 63(3):315-320.
37. Ward, J.A., Wilson, R.E., in press. Criteria for convective versus absolute string instability in car-following models. Proceedings of the Royal Society A. doi:10.1098/rspa.2010.0437.
38. Wilson R. Mechanisms for spatio-temporal pattern formation in highway traffic models. Philosophical Transactions of the Royal Society A 2008, 366(1872):2017-2032.
39. Wilson R.E., Ward J.A. Car-following models: fifty years of linear stability analysis - a mathematical perspective. Transportation Planning and Technology 2011, 34(1):3-18.
40. Windover J., Cassidy M. Some observed details of freeway traffic evolution. Transportation Research Part A 2001, 35(10):881-894.
41. Zielke B., Bertini R., Treiber M. Empirical measurement of freeway oscillation characteristics: an international comparison. Transportation Research Record 2008, 2088:57-67.