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Local stability of traffic equilibria in an isotropic network

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  • Pandey, Ayush
  • Lehe, Lewis J.
  • Gayah, Vikash V.

Abstract

For a static economic model of auto traffic in an isotropic zone, this paper classifies possible equilibria into three types, by whether traffic is hypercongested and by the relative slopes of “supply” and “demand” curves. We then conduct a local stability analysis of each type when density, demand and the unit travel time (inverse speed) evolve gradually and simultaneously according to dynamical systems of differential equations. Some hypercongested equilibria may be stable when demand adjusts quickly enough to congestion. Other hypercongested equilibria, which have counterintuitive comparative statics, are never stable. Non-hypercongested equilibria can be unstable under special circumstances. A discrete event simulation with a dynamic Poisson arrival process supports the results of the formal analysis.

Suggested Citation

  • Pandey, Ayush & Lehe, Lewis J. & Gayah, Vikash V., 2024. "Local stability of traffic equilibria in an isotropic network," Transportation Research Part B: Methodological, Elsevier, vol. 179(C).
    • Handle: RePEc:eee:transb:v:179:y:2024:i:c:s0191261523001984
    DOI: 10.1016/j.trb.2023.102873
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    as
    1. Louis Balzer & Ludovic Leclercq, 2021. "Modal equilibrium of a tradable credit scheme with a trip-based MFD and logit-based decision-making," Papers 2112.07277, arXiv.org, revised Apr 2022.
    2. Fosgerau, Mogens & Small, Kenneth A., 2013. "Hypercongestion in downtown metropolis," Journal of Urban Economics, Elsevier, vol. 76(C), pages 122-134.
    3. Terry L. Friesz & David Bernstein & Nihal J. Mehta & Roger L. Tobin & Saiid Ganjalizadeh, 1994. "Day-To-Day Dynamic Network Disequilibria and Idealized Traveler Information Systems," Operations Research, INFORMS, vol. 42(6), pages 1120-1136, December.
    4. Daganzo, Carlos F., 2005. "Improving City Mobility through Gridlock Control: an Approach and Some Ideas," Institute of Transportation Studies, Research Reports, Working Papers, Proceedings qt7w6232wq, Institute of Transportation Studies, UC Berkeley.
    5. Laval, Jorge A. & Leclercq, Ludovic & Chiabaut, Nicolas, 2018. "Minimal parameter formulations of the dynamic user equilibrium using macroscopic urban models: Freeway vs city streets revisited," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 676-686.
    6. Arnott, Richard, 2013. "A bathtub model of downtown traffic congestion," Journal of Urban Economics, Elsevier, vol. 76(C), pages 110-121.
    7. Takayama,Akira, 1985. "Mathematical Economics," Cambridge Books, Cambridge University Press, number 9780521314985, November.
    8. Gayah, Vikash V. & Daganzo, Carlos F., 2011. "Clockwise hysteresis loops in the Macroscopic Fundamental Diagram: An effect of network instability," Transportation Research Part B: Methodological, Elsevier, vol. 45(4), pages 643-655, May.
    9. Lehe, Lewis J., 2020. "Winners and losers from road pricing with heterogeneous travelers and a mixed-traffic bus alternative," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 432-446.
    10. Arnott, Richard & Inci, Eren, 2010. "The stability of downtown parking and traffic congestion," Journal of Urban Economics, Elsevier, vol. 68(3), pages 260-276, November.
    11. Richard Arnott & Moez Kilani, 2022. "Social Optimum in the Basic Bathtub Model," Transportation Science, INFORMS, vol. 56(6), pages 1505-1529, November.
    12. Arnott, Richard & Inci, Eren, 2006. "An integrated model of downtown parking and traffic congestion," Journal of Urban Economics, Elsevier, vol. 60(3), pages 418-442, November.
    13. Verhoef, Erik T., 2005. "Speed-flow relations and cost functions for congested traffic: Theory and empirical analysis," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 792-812.
    14. Verhoef, Erik T., 1999. "Time, speeds, flows and densities in static models of road traffic congestion and congestion pricing," Regional Science and Urban Economics, Elsevier, vol. 29(3), pages 341-369, May.
    15. Erik T. Verhoef, 2001. "Probing A Traffic Congestion Controversy: A Comment," Journal of Regional Science, Wiley Blackwell, vol. 41(4), pages 681-694, November.
    16. Daganzo, Carlos F., 2007. "Urban gridlock: Macroscopic modeling and mitigation approaches," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 49-62, January.
    17. Geroliminis, Nikolas & Sun, Jie, 2011. "Properties of a well-defined macroscopic fundamental diagram for urban traffic," Transportation Research Part B: Methodological, Elsevier, vol. 45(3), pages 605-617, March.
    18. Zhang, Ding & Nagurney, Anna, 1996. "On the local and global stability of a travel route choice adjustment process," Transportation Research Part B: Methodological, Elsevier, vol. 30(4), pages 245-262, August.
    19. Fosgerau, Mogens, 2015. "Congestion in the bathtub," Economics of Transportation, Elsevier, vol. 4(4), pages 241-255.
    20. Jin, Wen-Long, 2020. "Generalized bathtub model of network trip flows," Transportation Research Part B: Methodological, Elsevier, vol. 136(C), pages 138-157.
    21. Beckmann, Martin J & Ryder, Harl E, Jr, 1969. "Simultaneous Price and Quantity Adjustment in a Single Market," Econometrica, Econometric Society, vol. 37(3), pages 470-484, July.
    22. Daganzo, Carlos F. & Lehe, Lewis J., 2016. "Traffic flow on signalized streets," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 56-69.
    23. Daganzo, Carlos F. & Geroliminis, Nikolas, 2008. "An analytical approximation for the macroscopic fundamental diagram of urban traffic," Transportation Research Part B: Methodological, Elsevier, vol. 42(9), pages 771-781, November.
    24. Lehe, Lewis J. & Pandey, Ayush, 2020. "Hyperdemand: A static traffic model with backward-bending demand curves," Economics of Transportation, Elsevier, vol. 24(C).
    25. Mariotte, Guilhem & Leclercq, Ludovic & Laval, Jorge A., 2017. "Macroscopic urban dynamics: Analytical and numerical comparisons of existing models," Transportation Research Part B: Methodological, Elsevier, vol. 101(C), pages 245-267.
    26. Daganzo, Carlos F. & Lehe, Lewis J., 2015. "Distance-dependent congestion pricing for downtown zones," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 89-99.
    27. Iryo, Takamasa & Watling, David, 2019. "Properties of equilibria in transport problems with complex interactions between users," Transportation Research Part B: Methodological, Elsevier, vol. 126(C), pages 87-114.
    28. Serdar Çolak & Antonio Lima & Marta C. González, 2016. "Understanding congested travel in urban areas," Nature Communications, Nature, vol. 7(1), pages 1-8, April.
    29. Haddad, Jack & Geroliminis, Nikolas, 2012. "On the stability of traffic perimeter control in two-region urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 46(9), pages 1159-1176.
    30. Lehe, Lewis J., 2017. "Downtown tolls and the distribution of trip lengths," Economics of Transportation, Elsevier, vol. 11, pages 23-32.
    31. Li, Ye & Mohajerpoor, Reza & Ramezani, Mohsen, 2021. "Perimeter control with real-time location-varying cordon," Transportation Research Part B: Methodological, Elsevier, vol. 150(C), pages 101-120.
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