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

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  • 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
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    References listed on IDEAS

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    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)

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