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

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 We show that when traffic in a cell has a ffs α 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