Optimal Presignal Control for Two-Mode Traffic at Isolated Signalized Intersections

Delay imposed on buses is witnessed at isolated signalized intersections, as part of the delay is created due to bus and car interactions at the signalized approaches. Inexpensive solutions that do not involve new infrastructure are the most desired. Toward reducing person delay, presignal lights are installed at the upstream of the intersection. Presignal is a control tool that can manage the interaction and space conflict between cars and buses at the mixed lanes, located after the presignals, approaching the intersection. This paper presents an optimal presignal control policy that determines signal settings based on minimization of total person-time spent. The developed model is comprised of a simplified signalized intersection with one approach, where two presignal lights are located: one for bus lane and one for car lane. A continuous-time model is first developed to describe the queue dynamics for the mixed lanes after the presignals and the bus and car lanes before the presignals. The optimal solutions are derived analytically via the Pontryagin maximum principle, and the optimal presignal control policy is determined and synthesized. The derived analytical solutions are verified through the use of the optimal control software, DIDO, which uses an advanced optimization method and solves complex dynamic optimization problems without prior knowledge of the analytical computations or the solution. Several examples are used to test and analyze the derived solutions. Finally, the microscopic simulation software AIMSUN is used to test, assess, and evaluate the performance of the proposed optimal control policy in a more realistic traffic condition, where stochastic arrivals are incorporated.