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.

在信元传输模型（CTM）中，时间被离散化为时间步长，并且链路被离散化为信元。在原始CTM中以及通常在此之后，选择信元长度，以便在自由流动速度（ffs）下，业务量每时间步长精确地传播一个信元（1 cpts），因此ffs表示为α α= 1 cpts，为避免计算复杂性，每个单元的长度通常随时间保持恒定。但是，实际观察到的ffs通常会因一天中的时间，交通类型或车道而异，或者由于速度限制随时间或空间而变化，或者由于随机效应而有所不同。通过构造，每个像元中的最大ffs为1 cpts（α= 1），因此，当一个像元在一个像元中变化时，它通常会小于1（α<1）。

我们表明，当一个小区中的流量的ffsα<1 cpts时，从标准CTM获得的流量和占用率可能会非常不准确。例如，考虑一个长度为1的单元，该单元处于自由流动状态，自由流速α<1，并且没有进一步的流动进入该单元。然后，该单元中的所有流量将在时间1 /α之前退出，然后该单元将为空。相反，对于同一场景，CTM在每个时间步中让小区中剩余业务的分数α<1退出，从而使小区外流和占用率在几何上朝着零下降，因此小区永远不会完全清空。

这个问题很严重，因为在交通网络中，可能有大量或大部分或大部分的单元和链路在要建模的全部或部分时间段内处于自由流动状态。为了克服上述问题，我们建议不要将CTM应用于ffsα<1 cpts处于自由流动状态的单元。相反，对于这些单元格和链接，我们让流量按其ffs向前移动，而不是根据CTM计算得出。这很容易实现，因为在CTM中，计算一次向前滚动一个时间步，并且在每个时间步中，信元占用率都从上一个时间步更新，因此是已知的，并且已知的占用率会立即指示该信元是否会处于自由流动状态。