Delays and Queue Lengths at Traffic Signals With Two Greens in One Cycle

Abstract

Under specific circumstances signal timing at a traffic signal allows the switching of two green times within one cycle. Practitioners expect a reduction in delays and queue length as a result of this control strategy. However, no analytical methodology is available to quantify this effect. To resolve this deficit, analytical considerations have been undertaken. They follow the principles that are also the basis for conventional signal performance analysis. The basic difference compared with a single green is that, within each cycle, the maximum length of the vehicle queue remains shorter under the two-green regime. This effect is expressed by the term uniform delay, w₁. For that parameter, a specific deterministic derivation is proposed. The second element is the incremental delay, w₂, which stands for the effects of randomness and temporary oversaturation. The analysis confirmed that this parameter could be adopted from conventional methods. Different formulas for the estimation of w₂ were investigated using simulation studies. Thus, a set of equations is given for the prediction of average delay and of percentile queue length in the case of two green times. Verification of the derived formulas was performed using Monte Carlo simulations. The results could easily be applied in practice and might be implemented into guidelines. The application demonstrated how a second green within one signal cycle reduced delays and, notably, queue lengths.