Online Passenger Flow Control in Metro Lines

Crowd management during peak commuting hours is a key challenge facing oversaturated metro systems worldwide, which results in serious safety concerns and uneven service experience for commuters on different origin-destination (o-d) pairs. This paper develops realtime passenger flow control policies to manage the inflow of crowds at each station, to optimize the total load carried or revenue earned (efficiency), and to ensure that adequate service is provided to passengers on each o-d pair (fairness), as much as possible. For given train capacity, we use Blackwell's approachability theorem and Fenchel duality to characterize the attainable service level of each o-d pair. We use these insights to develop online policies for crowd control problems. Numerical experiments on a set of transit data from Beijing show that our approach performs well compared with existing benchmarks in the literature.