Stability Analysis of Stochastic Linear Car-Following Models

Published Online:https://doi.org/10.1287/trsc.2019.0932

References

  • Ahn S, Cassidy MJ (2007) Freeway traffic oscillations and vehicle lane-change maneuvers. Transportation and Traffic Theory, vol. 1 (Elsevier, Oxford, UK), 691–710.Google Scholar
  • Bando M, Hasebe K, Nakanishi K, Nakayama A (1998) Analysis of optimal velocity model with explicit delay. Physical Rev. E 58(5):5429–5435.CrossrefGoogle Scholar
  • Bertini RL, Leal MT (2005) Empirical study of traffic features at a freeway lane drop. J. Transportaion Engrg. 131(6):397–407.CrossrefGoogle Scholar
  • Cassidy MJ, Rudjanakanoknad J (2005) Increasing the capacity of an isolated merge by metering its on-ramp. Transportation Res. Part B: Methodological 39(10):896–913.CrossrefGoogle Scholar
  • Chandler RE, Herman R, Montroll EW (1958a) Traffic dynamics: Studies in car following. Oper. Res. 6(2):165–184.LinkGoogle Scholar
  • Chandler RE, Herman R, Montroll EW (1958b) Traffic dynamics: Studies in car following. Oper. Res. 6(2):165–184.Google Scholar
  • Chatfield C (1989) The Analysis of Time Series—An Introduction, 4th ed. (Chapman and Hall, London).Google Scholar
  • Eyre J, Yanakiev D, Kanellakopoulos I (1998) A simplified framework for string stability analysis of automated vehicles. Vehicle System Dynam. 30(5):375–405.CrossrefGoogle Scholar
  • Herman R, Montroll EW, Potts RB, Rothery RW (1958) Traffic dynamics: Analysis of stability in car following. Oper. Res. 7(1):86–106.Google Scholar
  • Huang YX, Guo N, Jiang R, Hu MB (2018) Instability in car-following behavior: New Nagel–Schreckenberg type cellular automata model. J. Statist. Mechanics: Theory Experiment 2018(8):083401.CrossrefGoogle Scholar
  • Jiang R, Wu Q, Zhu Z (2001) Full velocity difference model for a car-following theory. Physical Rev. E. 64(1):017101.CrossrefGoogle Scholar
  • Jiang R, Hu MB, Zhang HM, Gao ZY, Jia B, Wu QS (2015) On some experimental features of car-following behavior and how to model them. Transportation Res. Part B: Methodological 80(October):338–354.CrossrefGoogle Scholar
  • Jiang R, Hu MB, Zhang HM, Gao ZY, Jia B, Wu QS, Wang B, Yang M (2014) Traffic experiment reveals the nature of car-following. PLoS One 9(4):e94351.CrossrefGoogle Scholar
  • Jiang R, Jin CJ, Zhang HM, Huang YX, Tian JF, Wang W, Hu MB, Wang H, Jia B (2018) Experimental and empirical investigations of traffic flow instability. Transportation Res. Part C: Emerging Tech. 94(September):83–98.CrossrefGoogle Scholar
  • Jin WL, Zhang Y (2005) Paramics simulation of periodic oscillations caused by network geometry. Transportation Res. Record 1934(1):188–196.Google Scholar
  • Kim T, Zhang HM (2008) A stochastic wave propagation model. Transportation Res. Part B: Methodological 42(7–8):619–634.CrossrefGoogle Scholar
  • Koshi M, Iwasaki M, Ohkura I (1983) Some findings and an overview on vehicular flow characteristics. Proc. 8th Internat. Sympos. Transportation Traffic Flow Theory, vol. 198 (University of Toronto, Toronto), 403–426.Google Scholar
  • Kuhne R (1987) Freeway speed distribution and acceleration noise: calculations from a stochastic continuum theory and comparison with measurements. Transportation Traffic Theory 12:119–137.Google Scholar
  • Lang L, Guo N, Jiang R, Zhu K (2019) An improved inertia model to reproduce car-following instability. Physica A: Statist. Mechanics Appl. 526(July):121087.CrossrefGoogle Scholar
  • Laval J, Cassidy M, Daganzo C (2007) Impacts of lane changes at merge bottlenecks: A theory and strategies to maximize capacity. Schadschneider A, Pöschel T, Kühne R, Schreckenberg M, Wolf DE, eds. Traffic and Granular Flow ’05 (Springer, Berlin), 577–586.CrossrefGoogle Scholar
  • Laval JA, Toth CS, Zhou Y (2014) A parsimonious model for the formation of oscillations in car-following models. Transportation Res. Part B: Methodological 70(December):228–238.CrossrefGoogle Scholar
  • Li X, Ouyang Y (2011) Characterization of traffic oscillation propagation under nonlinear car-following laws. Transportation Res. Part B: Methodological 45(9):1346–1361.CrossrefGoogle Scholar
  • Li X, Peng F, Ouyang Y (2010) Measurement and estimation of traffic oscillation properties. Transportation Res. Part B: Methodological 44(1):1–14.CrossrefGoogle Scholar
  • Li X, Wang X, Ouyang Y (2012) Prediction and field validation of traffic oscillation propagation under nonlinear car-following laws. Transportation Res. Part B: Methodological 46(3):409–423.CrossrefGoogle Scholar
  • Li X, Cui J, An S, Parsafard M (2014) Stop-and-go traffic analysis: Theoretical properties, environmental impacts and oscillation mitigation. Transportation Res. Part B: Methodological 70(December):319–339.CrossrefGoogle Scholar
  • Lighthill MJ, Whitham GB (1955) On kinematic waves II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. A: Math. Physical Engrg. Sci. 229(1178):317–345.Google Scholar
  • Mauch M, Cassidy MJ (2002) Freeway traffic oscillations: observations and predictions. Taylor M, ed. Transportation Traffic Theory in the 21st Century (Emerald Group Publishing Limited, Bingley, UK), 653–673.Google Scholar
  • Newell GF (1961) Nonlinear effects in the dynamics of car following. Oper. Res. 9(2):209–229.LinkGoogle Scholar
  • Newell GF (2002) A simplified car-following theory: a lower order model. Transportation Res. Part B: Methodological 36(3):195–205.CrossrefGoogle Scholar
  • Richards PI (1956) Shock waves on the highway. Oper. Res. 4(1):42–51.LinkGoogle Scholar
  • Talebpour A, Mahmassani HS (2016) Influence of connected and autonomous vehicles on traffic flow stability and throughput. Transportation Res. Part C: Emerging Tech. 71(October):143–163.CrossrefGoogle Scholar
  • Tian J, Jiang R, Jia B, Gao Z, Ma S (2016a) Empirical analysis and simulation of the concave growth pattern of traffic oscillations. Transportation Res. Part B: Methodological 93(November):338–354.CrossrefGoogle Scholar
  • Tian J, Zhang HM, Treiber M, Jiang R, Gao ZY, Jia B (2016b) On the role of speed adaptation and spacing indifference in traffic instability: Evidence from car-following experiments and its stochastic modeling. Working paper, Tianjin University, Tianjin, China.Google Scholar
  • Treiber M, Kesting A (2013) Traffic Flow Dynamics: Data, Models and Simulation (Springer-Verlag, Berlin).Google Scholar
  • Treiber M, Kesting A (2017) The intelligent driver model with stochasticity-new insights into traffic flow oscillations. Transportation Res. Procedia 23:174–187.CrossrefGoogle Scholar
  • Treiber M, Hennecke A, Helbing D (2000) Congested traffic states in empirical observations and microscopic simulations. Physical Rev. E 62(2):1805–1824.CrossrefGoogle Scholar
  • Treiber M, Kesting A, Helbing D (2006) Delays, inaccuracies and anticipation in microscopic traffic models. Physica A: Statist. Mechanics Appl. 360(1):71–88.CrossrefGoogle Scholar
  • Van Arem B, van Driel CJG, Visser R (2006) The impact of cooperative adaptive cruise control on traffic-flow characteristics. IEEE Trans. Intelligent Transportation Systems 7(4):429–436.CrossrefGoogle Scholar
  • Wagner P (2012) Analyzing fluctuations in car-following. Transportation Res. Part B: Methodological 46(10):1384–1392.CrossrefGoogle Scholar
  • Xu T, Laval JA (2019) Analysis of a two-regime stochastic car-following model: Explaining capacity drop and oscillation instabilities. Transportation Res. Rec., ePub ahead of print June 2, https://journals.sagepub.com/doi/full/10.1177/0361198119850464.CrossrefGoogle Scholar
  • Zheng Z, Ahn S, Chen D, Laval J (2011) Applications of wavelet transform for analysis of freeway traffic: Bottlenecks, transient traffic, and traffic oscillations. Transportation Res. Part B: Methodological 45(2):372–384.CrossrefGoogle Scholar
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