Traffic Oscillation using Stochastic Lagrangian Dynamics: Simulation and Mitigation via Control of Autonomous Vehicles

The phenomenon of stop-and-go waves is frequently observed in congested traffic. With the development of connected and autonomous vehicle (CAV) technologies, it is possible to reduce traffic oscillation via control of CAVs in a mixed traffic flow with both human drivers and autonomous vehicles (AVs). This paper introduces a stochastic Lagrangian model which is capable of simulating stop-and-go traffic considering the heterogeneity of drivers. The sample paths of the stochastic process are smooth without aggressive oscillation. The model is further extended to the mixed traffic flow condition, considering stochastic human driving behavior and deterministic behavior of AVs. With the proposed model, the variation of performance of AV control strategies can be quantified in addition to the average performance. A numerical example with a single lane circular road is used to investigate the impact of the AV control strategy on mitigating stop-and-go waves. Both qualitative and quantitative results show that the phenomenon of stop-and-go waves can be reduced significantly with only one AV, while the increase of AVs from 10% (two AVs) to 50% (10 AVs) offers just marginal improvement in relation to the ensemble-averaged performance and 95% confidence interval of the ensemble-averaged performance. The proposed simulation approach based on the stochastic Lagrangian model can effectively investigate the impact of AV control strategies on traffic oscillation, considering in particular the uncertainty of human driver behavior.

[1]  R. Bertini,et al.  Empirical Study of Traffic Features at a Freeway Lane Drop , 2005 .

[2]  Y. Sugiyama,et al.  Traffic jams without bottlenecks—experimental evidence for the physical mechanism of the formation of a jam , 2008 .

[3]  Jianqiang Wang,et al.  Stability and Scalability of Homogeneous Vehicular Platoon: Study on the Influence of Information Flow Topologies , 2016, IEEE Transactions on Intelligent Transportation Systems.

[4]  M J Lighthill,et al.  On kinematic waves II. A theory of traffic flow on long crowded roads , 1955, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[5]  Alexandros Sopasakis,et al.  Stochastic Modeling and Simulation of Traffic Flow: Asymmetric Single Exclusion Process with Arrhenius look-ahead dynamics , 2006, SIAM J. Appl. Math..

[6]  Carlos F. Daganzo,et al.  Lane-changing in traffic streams , 2006 .

[7]  Fangfang Zheng,et al.  Traffic state estimation using stochastic Lagrangian dynamics , 2018, Transportation Research Part B: Methodological.

[8]  G. F. Newell.  Nonlinear Effects in the Dynamics of Car Following , 1961 .

[9]  J. M. D. Castillo,et al.  On the functional form of the speed-density relationship—I: General theory , 1995 .

[10]  Soyoung Ahn,et al.  Applications of wavelet transform for analysis of freeway traffic : bottlenecks, transient traffic, and traffic oscillations , 2011 .

[11]  Robert Herman,et al.  Traffic Dynamics: Analysis of Stability in Car Following , 1959 .

[12]  C. Daganzo.  A variational formulation of kinematic waves: Solution methods , 2005 .

[13]  Michael Schreckenberg,et al.  A cellular automaton model for freeway traffic , 1992 .

[14]  Swaroop Darbha,et al.  Intelligent Cruise Control Systems And Traffic Flow Stability , 1998 .

[15]  Jorge A. Laval,et al.  A parsimonious model for the formation of oscillations in car-following models , 2014 .

[16]  Akihiro Nakayama,et al.  Metastability in the formation of an experimental traffic jam , 2009 .

[17]  E. Montroll,et al.  Traffic Dynamics: Studies in Car Following , 1958 .

[18]  Maria Laura Delle Monache,et al.  Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments , 2017, ArXiv.

[19]  C. Daganzo.  A variational formulation of kinematic waves: basic theory and complex boundary conditions , 2005 .

[20]  P. I. Richards.  Shock Waves on the Highway , 1956 .

[21]  Alireza Talebpour,et al.  Influence of connected and autonomous vehicles on traffic flow stability and throughput , 2016 .

[22]  Lili Du,et al.  Constrained optimization and distributed computation based car following control of a connected and autonomous vehicle platoon , 2016 .

[23]  Akihiro Nakayama,et al.  Phase transition in traffic jam experiment on a circuit , 2013 .