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

Malachy Carey

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)
78 Downloads (Pure)


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). We show that when traffic in a cell has a ffs α < 1 cpts then the flows and occupancies obtained from the standard CTM can be very inaccurate. For example, consider a cell of length 1 that is in a free flow state with free-flow speed α < 1 and no further flow into the cell. Then all traffic in the cell will have exited by time 1/α and the cell will then be empty. In contrast, for the same scenario, the CTM lets a fraction α < 1 of the remaining traffic in the cell exit in each time step, so that the cell outflow and occupancy decline geometrically toward zero, so that the cell never fully empties. The problem is serious since in traffic networks there may be large numbers, or a large proportion, or a majority, of cells and links that are in a free-flow state for all or part of the time span being modelled. To overcome the above problem, we propose that the CTM not be applied to cells that are in a free-flow state with ffs α < 1 cpts. Instead, for those cells and links, we let traffic move forward at its ffs rather than as computed from the CTM. This is easily accomplished since, in the CTM the computations roll forward one time step at a time and, in each time step, the cell occupancy is updated from the previous time step, hence is known and the known occupancy immediately indicates whether the cell will be in a free-flow state.

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalTransportation Research Part B: Methodological
Issue numbern/a
Early online date26 Jun 2020
Publication statusPublished online - 26 Jun 2020


  • Cell transmission model
  • Free flow
  • Free flow speed less than 1
  • Uncongested traffic
  • Approximation error
  • Corrected outflows
  • Corrected travel times


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