Real-time bus control of urban transit networks with overtaking and passenger transfers: A decomposition solution method combined with spatial branch-and-bound

Frequent disturbances and demand fluctuations can result in unreliable bus operations and transfer services. This paper investigates real-time bus control for urban transit networks under dwell and travel time disturbances. The objective is to optimize bus timetable adjustments to minimize the total bus departure deviation, headway deviation, and passenger waiting in a time horizon. We propose a mixed-integer nonlinear programming model under rolling horizon, which incorporates both traffic and passenger load dynamics while accounting for bus overtaking, passenger transfer, and bus capacity limitations. To quickly obtain high-quality solutions to satisfy real-time requirements, we develop an efficient decomposition method combined with spatial branch-and-bound. This method reduces computational complexity by breaking down the network-level problem into smaller-scale line-level problems. It iteratively updates the solution and objective function values by solving a network-level feasibility recovery problem, ensuring coordination among line-level solutions through iterations. Extensive computational experiments demonstrate that our solution algorithm exhibits superior computational efficiency compared to a state-of-the-art solver across different network scales, facilitating a real-time implementation. Furthermore, our approach outperforms conventional schedule- and headway-based control strategies, effectively reducing departure deviation, headway deviation, and passenger waiting time.