IDEAS home Printed from https://ideas.repec.org/a/eee/transb/v147y2021icp245-257.html
   My bibliography  Save this article

The cell transmission model with free-flow speeds varying over time or space

Author

Listed:
  • Carey, Malachy

Abstract

In the cell transmission model (CTM), time is discretised into time-steps and links discretised into cells. In the original CTM, and usually thereafter, the cell lengths are chosen so that, at free-flow speeds (ffs), traffic travels exactly one cell per time-step (1 cpts), so that the ffs, denoted α, is exactly α = 1 cpts and, to avoid computational complications, the length of each cell is normally held constant over time. But the actual observed ffs's in a cell will often differ by time of day or traffic type or traffic lane, or due to speed limits that vary over time or space, or due to stochastic effects. By construction, the maximum ffs in each cell is 1 cpts (α = 1), hence when the ffs is varying within a cell, it will often be less than 1 (α < 1).

Suggested Citation

  • Carey, Malachy, 2021. "The cell transmission model with free-flow speeds varying over time or space," Transportation Research Part B: Methodological, Elsevier, vol. 147(C), pages 245-257.
    • Handle: RePEc:eee:transb:v:147:y:2021:i:c:p:245-257
    DOI: 10.1016/j.trb.2020.05.012
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S019126152030326X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.trb.2020.05.012?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Paul I. Richards, 1956. "Shock Waves on the Highway," Operations Research, INFORMS, vol. 4(1), pages 42-51, February.
    2. Yu Nie & H. Zhang, 2010. "Solving the Dynamic User Optimal Assignment Problem Considering Queue Spillback," Networks and Spatial Economics, Springer, vol. 10(1), pages 49-71, March.
    3. MERCHANT, Deepak K. & NEMHAUSER, George L., 1978. "Optimality conditions for a dynamic traffic assignment model," LIDAM Reprints CORE 345, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Daganzo, Carlos F., 1995. "The cell transmission model, part II: Network traffic," Transportation Research Part B: Methodological, Elsevier, vol. 29(2), pages 79-93, April.
    5. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    6. Malachy Carey & Y. Ge, 2012. "Comparison of Methods for Path Flow Reassignment for Dynamic User Equilibrium," Networks and Spatial Economics, Springer, vol. 12(3), pages 337-376, September.
    7. MERCHANT, Deepak K. & NEMHAUSER, George L., 1978. "A model and an algorithm for the dynamic traffic assignment problems," LIDAM Reprints CORE 346, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    8. Daganzo, Carlos F., 1994. "The cell transmission model: A dynamic representation of highway traffic consistent with the hydrodynamic theory," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 269-287, August.
    9. Deepak K. Merchant & George L. Nemhauser, 1978. "Optimality Conditions for a Dynamic Traffic Assignment Model," Transportation Science, INFORMS, vol. 12(3), pages 200-207, August.
    10. Deepak K. Merchant & George L. Nemhauser, 1978. "A Model and an Algorithm for the Dynamic Traffic Assignment Problems," Transportation Science, INFORMS, vol. 12(3), pages 183-199, August.
    11. Daganzo, Carlos F., 1995. "A finite difference approximation of the kinematic wave model of traffic flow," Transportation Research Part B: Methodological, Elsevier, vol. 29(4), pages 261-276, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Pinchao & Qian, Sean, 2020. "Path-based system optimal dynamic traffic assignment: A subgradient approach," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 41-63.
    2. Chou, Chang-Chi & Chiang, Wen-Chu & Chen, Albert Y., 2022. "Emergency medical response in mass casualty incidents considering the traffic congestions in proximity on-site and hospital delays," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 158(C).
    3. Shen, Wei & Zhang, H.M., 2009. "On the morning commute problem in a corridor network with multiple bottlenecks: Its system-optimal traffic flow patterns and the realizing tolling scheme," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 267-284, March.
    4. Friesz, Terry L. & Kim, Taeil & Kwon, Changhyun & Rigdon, Matthew A., 2011. "Approximate network loading and dual-time-scale dynamic user equilibrium," Transportation Research Part B: Methodological, Elsevier, vol. 45(1), pages 176-207, January.
    5. Jiang, Chenming & Bhat, Chandra R. & Lam, William H.K., 2020. "A bibliometric overview of Transportation Research Part B: Methodological in the past forty years (1979–2019)," Transportation Research Part B: Methodological, Elsevier, vol. 138(C), pages 268-291.
    6. S. Waller & Athanasios Ziliaskopoulos, 2006. "A Combinatorial user optimal dynamic traffic assignment algorithm," Annals of Operations Research, Springer, vol. 144(1), pages 249-261, April.
    7. Bar-Gera, Hillel & Carey, Malachy, 2022. "Constructing a cell transmission model solution adhering fully to first-in-first-out conditions," Transportation Research Part B: Methodological, Elsevier, vol. 161(C), pages 247-267.
    8. Islam, Tarikul & Vu, Hai L. & Hoang, Nam H. & Cricenti, Antonio, 2018. "A linear bus rapid transit with transit signal priority formulation," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 114(C), pages 163-184.
    9. Satsukawa, Koki & Wada, Kentaro & Watling, David, 2022. "Dynamic system optimal traffic assignment with atomic users: Convergence and stability," Transportation Research Part B: Methodological, Elsevier, vol. 155(C), pages 188-209.
    10. Aghamohammadi, Rafegh & Laval, Jorge A., 2020. "Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models," Transportation Research Part B: Methodological, Elsevier, vol. 137(C), pages 99-118.
    11. Jin, Wen-Long, 2015. "On the existence of stationary states in general road networks," Transportation Research Part B: Methodological, Elsevier, vol. 81(P3), pages 917-929.
    12. Tong, C. O. & Wong, S. C., 2000. "A predictive dynamic traffic assignment model in congested capacity-constrained road networks," Transportation Research Part B: Methodological, Elsevier, vol. 34(8), pages 625-644, November.
    13. Wu, Chengyuan & Yang, Liangze & Du, Jie & Pei, Xin & Wong, S.C., 2024. "Continuum dynamic traffic models with novel local route-choice strategies for urban cities," Transportation Research Part B: Methodological, Elsevier, vol. 181(C).
    14. Lu, Gongyuan & Nie, Yu(Marco) & Liu, Xiaobo & Li, Denghui, 2019. "Trajectory-based traffic management inside an autonomous vehicle zone," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 76-98.
    15. Carey, Malachy & Watling, David, 2012. "Dynamic traffic assignment approximating the kinematic wave model: System optimum, marginal costs, externalities and tolls," Transportation Research Part B: Methodological, Elsevier, vol. 46(5), pages 634-648.
    16. Ma, Rui & Ban, Xuegang (Jeff) & Pang, Jong-Shi, 2014. "Continuous-time dynamic system optimum for single-destination traffic networks with queue spillbacks," Transportation Research Part B: Methodological, Elsevier, vol. 68(C), pages 98-122.
    17. Ke Han & Gabriel Eve & Terry L. Friesz, 2019. "Computing Dynamic User Equilibria on Large-Scale Networks with Software Implementation," Networks and Spatial Economics, Springer, vol. 19(3), pages 869-902, September.
    18. Wang, Yi & Szeto, W.Y. & Han, Ke & Friesz, Terry L., 2018. "Dynamic traffic assignment: A review of the methodological advances for environmentally sustainable road transportation applications," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 370-394.
    19. Ukkusuri, Satish V. & Han, Lanshan & Doan, Kien, 2012. "Dynamic user equilibrium with a path based cell transmission model for general traffic networks," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1657-1684.
    20. Aalami, Soheila & Kattan, Lina, 2022. "Proportionally fair flow markets for transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 157(C), pages 24-41.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:147:y:2021:i:c:p:245-257. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/548/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.