Optimal holding time calculation algorithm to improve the reliability of high frequency bus route considering the bus capacity constraint

The self-equalizing bus headway control method, as a type of headway-based control method, has been proved to resist bus bunching effectively. This control method is suitable for use in real-time transit operations owing to its simplicity in the formulation and solution. However, previous studies paid more attention on the demonstration that the bus headways can converge under variable conditions, without considering the bus capacity constraint. In addition, when the bus capacity constraint is considered, the optimal holding time calculation becomes a nonlinear problem instead of a simple linear problem. Therefore, in this study, a more precise and comprehensive model is proposed to describe the bus operation process. An optimal holding time calculation algorithm is proposed to solve the nonlinear optimization problem by transforming it into an one-dimensional line search problem. The proposed model was validated through numerical tests. In the traditional analyses, bus bunching will worsen if no additional control method is applied to the bus system. However, the present study indicates that bus bunching will be mitigated to some extent by the public transit system itself without external control at relatively high traffic demand level.

Automated summary

The self-equalizing bus headway control method has been shown to effectively resist bus bunching and is suitable for real-time transit operations. This study proposes a more precise and comprehensive model to describe the bus operation process and validates an optimal holding time calculation algorithm through numerical tests.