Delays at fixed-time traffic signals under time-dependent traffic conditions

Several approximate formulae have been developed in the past for the calculation of average delays at signalised intersections under time-dependent traffic conditions. However, there is a remarkable discrepancy between the results. As a new approach, the idea of Markov chains has been employed to calculate delays on a numerically exact basis. Computations enable the evaluation of average delays of drivers at fixed-time traffic signals under time-dependent input volumes and under Poisson or non-Poisson conditions. On the whole, the results show that Akcelik's estimation of average delays is not valid under real peak-period conditions as they have been observed in Germany. Catling's formula seems to provide a more realistic approximation. However, a new set of approximate formulae has been developed, which describes the exact average delays rather precisely. Moreover, the results calculated with these formulae proved to be in good agreement with empirically based data. In addition, the new approach provides a sound evaluation of the distribution of queue lengths, e.g., the.95-percentile, and their profile over time.