Optimal control to improve reliability of demand responsive transport priority at signalized intersections considering the stochastic process

Bus priority has been proposed for many years to improve traffic congestion, energy conservation, and emissions reduction. Transit signal priority is a main measure of executing bus priority. Moreover, because the time that buses arrive at an intersection should be predicted quite precisely to make a signal control scheme in advance, bus lane is an important segment in transit priority at signalized intersections to avoid disturbances from other vehicles on the road. However, in practice, the bus route of demand responsive transport is widespread, which is not inappropriate to set bus lane for each bus route because of low frequency. Therefore, in this paper, a robust optimization control method is proposed to solve the bus priority problem at signalized intersections without exclusive bus lanes and improve reliability of demand responsive transport priority at signalized intersections. First, the bus delay probability density function is formulated to describe the interaction mechanism about the bus and other vehicles at the signalized intersection. Then, the accurate bus delay expectation and variance calculation mathematical models are formulated based on the bus delay probability density function. Furthermore, a robust optimal signal control method is proposed followed by the discussions of boundary conditions. Finally, simulation test and case study were conducted to illustrate the performance of the robust optimization control method proposed in this paper. The results show that the proposed control method could significantly improve bus delay compared to considering the bus operation process as stable.