Derivatives of the performance index for the traffic model from TRANSYT

This paper forms a starting point for the investigation of phase-based optimisation of signal timings for area traffic control. A conventional performance index, which is a weighted combination of delays, of stops, is evaluated by the traffic model from the well-known stage-based procedure TRANSYT, but is considered here as a function of phase-based control variables, start and duration of green phases. In the paper, approximate expressions for the derivatives of performance index with respect to phase-based control variables are derived. The contribution from upstream, downstream and further downstream links and platoon dispersion are taken into account. The derivatives calculated from the expressions are compared with those from numerical differentiation using a trial network from Leicestershire as an example to illustrate the effectiveness of the formulae.