Optimization of signal-timing parameters for the intersection with hook turns

A Hook Turn (HT) traffic control scheme has been successfully implemented in urban Melbourne (Australia) ever since 1950s, for the regulation of right-turning vehicles at the intersections (in traffic system where driving is on the left). This paper addresses the optimal signal-timing of the HT scheme, which is still an open question in the literature. Under the HT scheme, right-turning vehicles should enter the intersection and stop at a waiting area. Hence, it is common to have a spillback from these vehicles if the right-turning volume is high. This paper provides an in-depth analysis of the spillback phenomenon on the traffic movements and the average delays, and proposes the models for the calculation of average delay in different cases. With the aim of minimizing the average delay of all the vehicles, a nonlinear integer-programming model is proposed for the optimal signal-timing problem of HT scheme. A Genetic Algorithm (GA) is used to solve this model, considering the complexity of its objective function. A realistic example developed based on one intersection with HT in urban Melbourne is adopted to assess the proposed methodology. Based on real survey data in morning peak and nonpeak hours, we compare the existing signal plan and optimal plan. The numerical test shows that compared with the existing plan, the optimal plan can reduce the average delay for 12.05% in peak hour and 19.96% in nonpeak hour. Sensitive analysis is also conducted to investigate the variation of right-turning ratio on the intersection operational performance.