Analysis of Traffic Properties of Commuters in a Speed-Limit Corridor with Toll Station under Microscopic Method
Publication: Journal of Transportation Engineering, Part A: Systems
Volume 146, Issue 3
Abstract
This study applies the full velocity difference (FVD) model to investigate commuters’ driving process in a speed limit corridor with a toll station and explains how some factors affect the outflow of the traffic corridor system from the microscopic perspective. First, a micromodel system is constructed to depict the commute process in a traffic corridor with a toll station considering the speed limit. Second, a metastable state is defined in the paper for deriving the properties of commute problem conveniently. Finally, numerical tests are conducted to investigate some factors’ effects on traffic properties. This study concludes that many traffic properties will be convergent when the commuter’s number increases, and that the length of the road, the speed limit, and the service time of the toll station have effects on the time headway of the origin at the equilibrium state. The results show how the outflow forms in a speed-limit corridor with a toll station from the microscopic perspective and provide insights for policymaking.
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Data Availability Statement
Some or all data, models, or code generated or used during the study are available from the corresponding author by request.
Acknowledgments
This study was supported by the National Natural Science Foundation of China (71422001 and 71890971).
References
Akamatsu, T., K. Wada, and S. Hayashi. 2015. “The corridor problem with discrete multiple bottlenecks.” Transp. Res. Part B 81 (Jan): 808–829. https://doi.org/10.1016/j.trb.2015.07.015.
Arnott, R., A. de Palma, and R. Lindsey. 1990. “Economics of a bottleneck.” J. Urban Econ. 27 (1): 111–130. https://doi.org/10.1016/0094-1190(90)90028-L.
Arnott, R., A. de Palma, and R. Lindsey. 1993. “Properties of dynamic traffic equilibrium involving bottlenecks, including a paradox and metering.” Transp. Sci. 27 (2): 148–160. https://doi.org/10.1287/trsc.27.2.148.
Bando, M., K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama. 1995. “Dynamical model of traffic congestion and numerical simulation.” Physical Rev. E 51 (2): 1035. https://doi.org/10.1103/PhysRevE.51.1035.
Ceder, A., and J. A. D. May. 1976. “Further evaluation of single and two regime traffic flow models.” Transp. Res. Rec. 567: 1–30.
Chandler, R. E., R. Herman, and E. W. Montroll. 1958. “Traffic dynamics: Studies in car following.” Oper. Res. 6 (2): 165–184. https://doi.org/10.1287/opre.6.2.165.
Correia, G. H. D. A., and A. B. Silva. 2011. “Setting speed limits in rural two-lane highways by modelling the relationship between expert judgment and measurable roadside characteristics.” J. Transp. Eng. 137 (3): 184–192. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000210.
De Palma, E., and R. Arnott. 2012. “Morning commute in a single-entry traffic corridor with no late arrivals.” Transp. Res. Part B 46 (1): 1–29.
Du, B., and D. Z. W. Wang. 2014. “Continuum modeling of park-and-ride services considering travel time reliability and heterogeneous commuters—A linear complementarity system approach.” Transp. Res. Part E 71 (Nov): 58–81. https://doi.org/10.1016/j.tre.2014.08.008.
Edie, L. C. 1961. “Car following and steady state theory for non-congested traffic.” Oper. Res. 9 (1): 66–76. https://doi.org/10.1287/opre.9.1.66.
Gazis, D. C., R. Herman, and R. W. Rothery. 1961. “Nonlinear follow-the-leader models of traffic flow.” Oper. Res. 9 (4): 545–567. https://doi.org/10.1287/opre.9.4.545.
Gipps, P. G. 1981. “A behavioural car following model for computer simulation.” Transp. Res. B 15 (2): 105–111. https://doi.org/10.1016/0191-2615(81)90037-0.
Helbing, D., and B. Tilch. 1998. “Generalized force model of traffic dynamics.” Physical Review E 58 (1): 133–138. https://doi.org/10.1103/PhysRevE.58.133.
Hendrickson, C., and G. Kocur. 1981. “Schedule delay and departure time decisions in a deterministic model.” Transp. Sci. 15 (1): 62–77. https://doi.org/10.1287/trsc.15.1.62.
Herman, R., and R. B. Potts. 1959. “Single lane traffic theory and experiment.” Theory Traffic Flow 120–146.
Heyes, M. P., and R. Ashworth. 1972. “Further research on car-following models.” Transp. Res. 6 (3): 287–291. https://doi.org/10.1016/0041-1647(72)90020-2.
Huang, H. J., and W. X. Wu. 2014. “Equilibrium and modal split in a competitive highway/transit system under different road-use pricing strategies.” J. Transp. Econ. Policy 48 (1): 153–169.
Jiang, R., Q. Wu, and Z. Zhu. 2001. “Full velocity difference model for a car-following theory.” Physical Rev. E 64 (1): 017101. https://doi.org/10.1103/PhysRevE.64.017101.
Khoury, J. E., and F. J. Srour. 2015. “The value of dynamic, revenue maximizing congestion pricing in a highly congested corridor.” J. Transp. Eng. 141 (12): 04015029 https://doi.org/10.1061/(ASCE)TE.1943-5436.0000798.
Kometani, E., and T. Sasaki. 1959. “Dynamic behaviour of traffic with a nonlinear spacing-speed relationship.” In Proc., Symp. on Theory of Traffic Flow 1959, 105–119. New York: Elsevier.
Kuwahara, M. 1990. “Equilibrium queuing patterns at a two-tandem bottleneck during the morning peak.” Transp. Sci. 24 (3): 217–229. https://doi.org/10.1287/trsc.24.3.217.
Lago, A., and C. F. Daganzo. 2007. “Spillovers, merging traffic and the morning commute.” Transp. Res. Part B 41 (6): 670–683. https://doi.org/10.1016/j.trb.2006.10.002.
Lam, W. H. K., L. T. Mei, X. Q. Cao, and X. M. Li. 2013. “Modeling the effects of rainfall intensity on traffic speed, flow, and density relationships for urban roads.” J. Transp. Eng. 139 (7): 758–770. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000544.
Li, C. Y., and H. J. Huang. 2017. “Morning commute in a single-entry traffic corridor with early and late arrivals.” Transp. Res. Part B 97 (Mar): 23–49.
Li, C. Y., and H. J. Huang. 2018. “User equilibrium of a single-entry traffic corridor with continuous scheduling preference.” Transp. Res. Part B 108 (Feb): 21–38.
Li, C. Y., H. J. Huang, and T. Q. Tang. 2017. “Analysis of social optimum for staggered shifts in a single-entry traffic corridor with no late arrivals.” Physica A 474 (Mar): 8–18. https://doi.org/10.1016/j.physa.2017.01.062.
Li, C. Y., G. M. Xu, and T. Q. Tang. 2018. “Social optimum for evening commute in a single-entry traffic corridor with no early departures.” Physica A 502 (Jul): 236–247. https://doi.org/10.1016/j.physa.2018.02.098.
Li, Y. F., L. Zhang, H. Zheng, S. Peeta, X. Z. He, T. X. Zheng, and Y. G. Li. 2016. “A car-following model considering the effect of electronic throttle opening angle under connected environment.” Nonlinear Dyn. 85 (4): 2115–2125. https://doi.org/10.1007/s11071-016-2817-y.
Li, Z. C., W. H. K. Lam, and S. C. Wong. 2014. “Bottleneck model revisited: An activity-based perspective.” Transp. Res. Part B 68 (Oct): 262–287. https://doi.org/10.1016/j.trb.2014.06.013.
Lighthill, M. H., and G. B. Whitham. 1955. “On kinematic waves II: A theory of traffic flow on long crowed roads.” Proc. Royal Soc. A 229 (1178): 317–345. https://doi.org/10.1098/rspa.1955.0089.
May, J. A. D., and H. E. M. Keller. 1967. “Non integer car following models.” Highway Res. Rec. 199 (1): 19–32.
Newell, G. F. 1988. “Traffic flow for the morning commute.” Transp. Sci. 22 (1): 47–58. https://doi.org/10.1287/trsc.22.1.47.
Pipes, L. A. 1953. “An operational analysis of traffic dynamics.” J. Appl. Phys. 24 (3): 274. https://doi.org/10.1063/1.1721265.
Ravishankar, K. V. R., and T. V. Mathew. 2011. “Vehicle-type dependent car-following model for heterogeneous traffic conditions.” J. Transp. Eng. 4 (6): 775–781. https://doi.org/10.1061/(ASCE)TE.1943-5436.0000273.
Richards, P. I. 1956. “Shock waves on the high way.” Oper. Res. 4 (1): 42–51. https://doi.org/10.1287/opre.4.1.42.
Silvano, A. P., and K. L. Bang. 2016. “Impact of speed limits and road characteristics on free-flow speed in urban areas.” J. Transp. Eng. 142 (2): 04015039 https://doi.org/10.1061/(ASCE)TE.1943-5436.0000800.
Tan, W., Z. C. Li, and Z. J. Tan. 2017. “Modeling the effects of speed limit, acceleration, and deceleration on overall delay and traffic emission at a signalized intersection.” J. Transp. Eng. 143 (12): 04017063 https://doi.org/10.1061/JTEPBS.0000101.
Tang, T. Q., H. J. Huang, and H. Y. Shang. 2015. “Influences of the driver’s bounded rationality on micro driving behavior, fuel consumption and emissions.” Transp. Res. Part D 41 (Dec): 423–432. https://doi.org/10.1016/j.trd.2015.10.016.
Tang, T. Q., H. J. Huang, and H. Y. Shang. 2016. “An extended macro traffic flow model accounting for the driver’s bounded rationality and numerical tests.” Physica A 468 (Feb): 322–333. https://doi.org/10.1016/j.physa.2016.10.092.
Tang, T. Q., T. Wang, L. Chen, and H. Y. Shang. 2017. “Impacts of energy consumption and emissions on the trip cost without late arrival at the equilibrium state.” Physica A 479 (Aug): 341–349. https://doi.org/10.1016/j.physa.2017.03.019.
Vickrey, W. S. 1969. “Congestion theory and transport investment.” Am. Econ. Rev. 59 (2): 251–260.
Vincent, A. C., V. D. Berg, and E. T. Verhoef. 2016. “Autonomous cars and dynamic bottleneck congestion: The effects on capacity, value of time and preference heterogeneity.” Transp. Res. Part B 94 (Dec): 43–60. https://doi.org/10.1016/j.trb.2016.08.018.
Wang, D. Z. W., and B. Du. 2016. “Continuum modelling of spatial and dynamic equilibrium in a travel corridor with heterogeneous commuters—A partial differential complementarity system approach.” Transp. Res. Part B 85 (Mar): 1–18. https://doi.org/10.1016/j.trb.2015.12.014.
Wardrop, J. G. 1952. “Road paper. Some theoretical aspects of road traffic research.” Proc. Inst. Civ. Eng. Civ. Eng. 1 (3): 325–362.
Wu, W. X., and H. J. Huang. 2015. “An ordinary differential equation formulation of the bottleneck model with user heterogeneity.” Transp. Res. Part B 81 (Nov): 34–58. https://doi.org/10.1016/j.trb.2015.08.007.
Xiao, F., Z. Qian, and H. M. Zhang. 2013. “Managing bottleneck congestion with tradable credits.” Transp. Res. Part B 56 (Oct): 1–14. https://doi.org/10.1016/j.trb.2013.06.016.
Xiao, L. L., H. J. Huang, and R. H. Liu. 2015a. “Congestion behavior and tolls in a bottleneck model with stochastic capacity.” Transp. Sci. 49 (1): 46–65. https://doi.org/10.1287/trsc.2013.0483.
Xiao, L. L., H. J. Huang, and R. H. Liu. 2015b. “Tradable credit scheme for rush hour travel choice with heterogeneous commuters.” Adv. Mech. Eng. 7 (10): 1–12. https://doi.org/10.1177/1687814015612430.
Xiao, L. L., R. H. Liu, and H. J. Huang. 2014. “Stochastic bottleneck capacity, merging traffic and morning commute.” Transp. Res. Part E 64 (1): 48–70.
Yang, H., and H. J. Huang. 1997. “Analysis of the time-varying pricing of a bottleneck with elastic demand using optimal control theory.” Transp. Res. Part B 31 (6): 425–440.
Zhao, Z., W. H. Chen, X. M. Wu, and Z. Liu. 2016. “Vehicle-following model using virtual piecewise spline tow bar.” J. Transp. Eng. 142 (11): 04016051 https://doi.org/10.1061/(ASCE)TE.1943-5436.0000886.
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Published In
Journal of Transportation Engineering, Part A: Systems
Volume 146 • Issue 3 • March 2020
Copyright
©2020 American Society of Civil Engineers.
History
Received: Sep 26, 2018
Accepted: Aug 12, 2019
Published online: Jan 13, 2020
Published in print: Mar 1, 2020
Discussion open until: Jun 13, 2020
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