The Application of the Cell Transmission Model to the Optimisation of Signals on Signalised Roundabouts
M Maher and O Feldman, Napier University, UK
TRANSYT has been successfully used for over thirty years for the determination of the optimal signal settings (greens, offsets and cycle time) in the fixed time control of an urban network. It relies on the combination of a simple, macroscopic traffic model to calculate the value of the network Performance Index (a combination of delays and stops) for any values of the signal settings, and a hill-climbing technique to find a set of timings that minimise the Performance Index. In addition to being applied to general, signalised urban networks, TRANSYT has also been applied to signalised roundabouts. However, despite its undoubted success, one of the acknowledged weaknesses of the TRANSYT traffic model is that no account is taken of the spatial extent of queues. This is of particular concern in applications to signalised roundabouts where "blocking back" can readily occur, given the limited storage space typically to be found on the roundabout itself. Any traffic model that does not model the spatial as well as the temporal dimension of queues may produce timings that are, in reality, far from optimal. (Although the latest version, TRANSYT11, allows the user to set values of "limit queues" and adds an arbitrary penalty to the Performance Index if the limit queue is exceeded, it does not make any attempt to model the consequential traffic behaviour).
An alternative approach in such circumstances is to use a microscopic traffic simulation model, that can properly model any blocking back effects.. However, such a model is not ideally suited to the task of optimisation since it needs to be run for each of a possibly very large number of settings and, being a Monte Carlo simulation model, produces a "noisy" estimate of the Performance Index.
This paper investigates the application of the increasingly-popular "cell transmission" model to signal optimisation. The advantages of this model are (i) because it divides the roadway into short, discrete segments or cells, the spatial as well as the temporal formation and dispersion of queues is explicitly modelled, and (ii) its deterministic nature ensures that the Performance Index is smooth with respect to changes in the signal settings. It is shown that, under conditions when no blocking back occurs, the cell transmission model and TRANSYT give virtually identical results (in terms of, for example, the relationship between the Performance Index and offset along a link). However, under conditions when blocking back may readily occur, the results are very different. When the two models are applied to theoptimisation of settings on a signalised roundabout, it is found that the results from the two models are appreciably different. For example, if the optimal settings found from one model are used in the other model, the value of the Performance Index is 10-12 % higher than the minimum. The Paramics model will then be applied to assess which of the two models is closer to reality.
Association for European Transport