A real-time bus dispatching policy to minimize headway variance
Berrebi, Simon Jonas Youna
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Transit agencies include buffer time in their schedules to maintain stable headways and avoid bus bunching. In this work, a real-time holding mechanism is proposed to dispatch buses on a loop-shaped route, solely based on operating conditions in real-time. Holds are applied at the terminal station to minimize the expected variance of bus headways at departure. The bus-dispatching problem is formulated as a stochastic decision process. The optimality equations are derived and structural properties of the optimal policy are inferred by backward induction. The exact optimal holding policy is then found in closed form, as a function of the expected travel time of buses currently running. 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 recommended in the literature and used in practice.