One of the greatest problems facing transit agencies that operate high-frequency routes is maintaining stable headways and avoiding bus bunching. In this work, a real-time holding mechanism is proposed to dispatch buses on a loop-shaped route using real-time information. Holds are applied at one or several control points to minimize passenger waiting time while maintaining the highest possible frequency, i.e. using no buffer time. The bus dispatching problem is formulated as a stochastic decision process. The optimality equations are derived and the optimal holding policy is found by backward induction. A control method that requires much less information and that closely approximates the optimal dispatching policy is found. A simulation assuming stochastic operating conditions and unstable headway dynamics is performed to assess the expected average waiting time of passengers at stations. The proposed control strategy is found to provide lower passenger waiting time and better resiliency than methods used in practice and recommended in the literature.
Berrebi, Simon, Kari Watkins, and Jorge Laval. (2015) A Real-Time Bus Dispatching Policy to Minimize Headway Variance, Transportation Research Board 2015 Annual Meeting