Abstract
Heterogeneous traffic as observed in several south Asian countries is characterized by complex interactions of widely varying vehicle types that do not follow lanes and with smaller vehicles filling any gaps available. This paper discusses on four main components of macroscopic simulation of traffic flow in the Indian traffic context. One of the prime component, namely the traffic flow model, is discussed in detail with respect to the continuum modelling approach.
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References
Arasan VT, Dhivya G (2008) Measuring heterogeneous traffic density. In: International conference on sustainable urban transport and environment. World Academy of Science, Engineering, and Technology, pp 342–346
Arasan VT, Dhivya G (2010) Simulation of highly heterogeneous traffic flow characteristics. In: 24th European conference on modeling and simulation. Kuala Lumbur, Malasia, pp 60–86
Aw A, Rascle M (2000) Resurrection of “Second Order” models of traffic flow. SIAM J Appl Math 60:916–938
Bagnerini P, Rascle M (2003) A multi-class homogenized hyperbolic model of traffic flow. SIAM J Math Anal 35:949–973
Chanut S, Buisson C (2003) A macroscopic model and its numerical solution for a two flow mixed traffic with different speeds and lengths. Transp Res Rec 1852:209–219
Colombo RM (2002) A 2\(\times\)2 hyperbolic traffic flow model. Math Comput Modell 35:683–688
Del Castillo JM, Benitez FG (1995) On the functional form of the speed-density reationship-I: general theory. Transp Res Part B 29:373–389
Gavage SB, Colombo RM (2003) An n-populations model for traffic flow. Eur J Appl Math 14(5):587–612
Greenberg JM, Klar A, Rascle M (2003) Congestion on multilane highways. SIAM J Appl Math 63(3):813–818
Gupta A, Dhiman I (2014) Analysis of a continuum traffic flow model with non-lane based system. Int J Mod Phys C 25(10):1450045(25)
Gupta A, Katiyar V (2007) A new multi-class continuum model of traffic flow. Transportmetrica 3:73–85
Helbing D, Trieber M (1999) Numerical simulation of macroscopic traffic equations. Comput Sci Eng 1(5):89–98
Helbing D, Hennecke A, Shvetsov V, Trieber M (2001) Master: macroscopic traffic simulation based on a gas-kinetic, non-local traffic model. Transp Res Part B 35(2):183–211
Holland EN, Woods WA (1997) A continuum model for the dispersion of traffic on two-lane roads. Transp Res Part B 31(6):473–485
Hoogendoorn SP (1999) Multiclass continuum modelling of multilane traffic flow. PhD thesis, Delft University
Jiang R, Wu QS (2003) Study on propagation speed of small disturbance from a car-following approach. Transp Res Part B 37(1):85–99
Jiang R, Wu QS (2004) Extended speed gradient model for mixed traffic. Transp Res Rec 1883:78–84
Jiang R, Wu QS, Zhu ZJ (2002) A new continuum model for traffic flow and numerical tests. Transp Res Part B 36:405–419
Steven JG (2008) The Nlopt non-linear optimization package. http://ab-initio.mit.edu
Kuhne R, Michalopoulos P (2001) Continuum flow models, revised monograph on traffic flow theory: chapter 5. Technical report, FHWA
Lan WL, Chiou CY, Lin SZ, Hsu CC (2010) Cellular automaton simulations for mixed traffic with erratic motorcycles’ behaviours. Phys A 389(10):2077–2089
Leclercq L, Laval JA (2009) Traffic and Granular Flow ’07. Springer, Berlin
Leveque JR (2002) Numerical methods for conservation laws. Birkhauser, Heidelberg
Li X, Lu H (2010) An extension of LWR model considering slope and heterogeneous drivers. In: International conference on computer and information science, pp 1236–1240
Lighthill MJ, Whitham GB (1955) On kinematic waves II. A theory of traffic flow on long crowed roads. Proc R Soc A 229:281–345
Logghe S (2003) Dynamic modelling of heterogeneous vehicular traffic. PhD thesis, KULeuven, Belgium
Logghe S, Immers LH (2003) Heterogeneous traffic flow modelling with the LWR model using passenger car equivalents. In: 10th world congress on ITS, Madrid
Mallikarjuna C, Ramachadra Rao K (2009) Cellular automata model for heterogeneous traffic. J Adv Transp 43(3):321–345
Mallikarjuna C, Ramachandra Rao K (2006) Area occupancy characteristics of heterogeneous traffic. Transportmetrica 2:223–236
Mathew T, Munigety C, Bajpai A (2013) Strip-based approach for the simulation of mixed traffic conditions. J Comput Civ Eng 29(5):751–802
Meng Q, Weng J (2011) An improved cellular automata model for heterogeneous work zone traffic. Transp Res Part C Emerg Technol 19(6):1263–1275
Mesemmer A, Papageorgiou M (1990) Metanet: a macroscopic simulation program for motorway networks. Traffic Eng Control 31:466–470
Michalopoulos PG, Yi P, Lyrintzis AS (1993) Development of an improved high-order continuum traffic flow model. Transp Res Rec 1365:125–132
Mohan R, Ramadurai G (2013) Heterogeneous traffic flow modelling using macroscopic continuum model. In: Procedia-social and behavioral sciences
Mohan R, Ramadurai G (2017) Heterogeneous traffic flow modelling using second-order macroscopic continuum model. Phys Lett A 381:115–123
Munjal PK, Hsu YS, Lawrence RL (1971) Analysis and validation of lane drop effects on multilane freeways. Transp Res 5(4):257–266
Nair R, Mahmassani HS, Hooks EM (2011) A porous flow approach to modelling heterogeneous traffic in disordered system. Transp Res Part B 45(9):1331–1345
Ngoduy D (2006) Macroscopic discontinuity modeling for multi-class multi-lane traffic flow operations. PhD thesis, Delft University of Technology
Ngoduy D (2011) Multi-class first-order traffic model using stochastic fundamental diagrams. Transportmetrica 7(2):111–125
Ngoduy D, Liu R (2007) Multiclass frist-order simulation model to expalin non-linear traffic phenomena. Phys A 385(2):667–682
Ngoduy D, Maher MJ (2012) Calibration of second order traffic models using continuous cross-enntropy method. Transp Res Part C 24:102–121
Ngoduy D, Hoogendoorn SP, Van Zuylen HJ (2004) Cross-comparison of numerical schemes for macroscopic traffic flow models. Transp Res Rec 1876:52–61
Pares C (2008) Hyperbolic problems: theory, numerics, applications. Springer, Berlin
Payne HJ (1971) Models of freeway traffic and control. Simulation Councils Inc., La Jolla
Payne HJ (1979) FREEFLO: a macroscopic simualtion model of freeway traffic. Transp Res Rec 722:68–77
Puspita D (2007) Heterogeneous motorized traffic flow modelling using cellular automata. PhD thesis, Dublin City University
Richards PI (1956) Shockwaves on the highway. Oper Res 4(1):42–51
Ross P (1988) Traffic dynamics. Transp Res Part B 22:421–425
Tampere CMJ, van Arem B, Hoogendoorn SP (2003) Gas kinetic traffic flow modelling including continuous driver behavior models. Transp Res Rec 1852:231–238
Tang CF, Jiang R, Wu QS, Wiwathanapataphee B, Hu YH (2007a) Mixed traffic flow in anisotropic continuum model. Transp Res Rec 1999:13–22
Tang CF, Jiang R, Wu QS (2007b) Extended speed gradient model for traffic flow on two-lane freeways. Chin Phys 16:1570–1575
Tang TQ, Huang HJ, Zhao SG, Shang HY (2009) A new dynamic model for heterogeneous traffic flow. Phys Lett A 373:2461–2466
Vasik J, Ruskin JH (2012) Cellular automata simulation of traffic including cars and bicycles. Phys A 391(8):2720–2729
van Wageningen-Kessels F (2013) Multi-class continuum traffic flow models: analysis and simulation methods. PhD thesis, Delft University of Technology
Wang H, Li J, Chen Q, Ni D (2009) Speed-density relationship: from deterministic to stochastic. In: 88th annual meeting of transportation research board
Wong GCK, Wong SC (2002) A multi-class traffic flow model: an extension of LWR model with heterogeneous drivers. Transp Res Part A 36(9):763–848
Zhang HM (2002) A non-equilibrium traffic model devoid of gas-like behavior. Transp Res Part B 36:275–290
Zhang HM, Jin WL (2002) A kinematic wave traffic flow model for mixed traffic. Transp Res Rec 1802:197–204
Zhu Z, Zhang G, Wu T (2003) Numerical analysis of freeway traffic flow dynamics under multi-class drivers. Transp Res Rec 1852:201–208
Acknowledgements
The authors thank the Ministry of Urban Development, Government of India, for sponsoring the Center of Excellence in Urban Transport at Indian Institute of Technology (IIT), Madras that enabled this research work. All findings and opinions in the paper are by the authors and do not necessarily reflect the views of the funding agency.
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Mohan, R., Ramadurai, G. Numerical Study with Field Data for Macroscopic Continuum Modelling of Indian Traffic. Transp. in Dev. Econ. 5, 16 (2019). https://doi.org/10.1007/s40890-019-0081-9
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DOI: https://doi.org/10.1007/s40890-019-0081-9