A real-time bus dispatching policy to minimize passenger wait on a high frequency route

• Minimizing the sum of squared headways at max frequency minimizes passenger wait.
• We derived structural properties of an optimal policy by backward induction.
• We found a simple near-optimal dispatching policy to send buses at a constant rate.
• It outperformed methods used in practice and in the literature under simulation.

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.

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