Distributed stochastic approximation for adaptive frequency allocation in subway networks

We propose to build an intelligent mechanism within a computerized subway system that will adjust frequency of services according to the observed variable demand. Operating costs are generally associated with the number of one way trips per day per line, while social cost is measured as the total waiting time of all passengers per day. The proposed transit system will automatically seek optimal performance minimizing operational costs. The structure of the control variables (headways) and their relationship with other model parameters make the problem suitable for ersatz estimation where the gradient w.r.t. a control variable is estimated in terms of local gradients w.r.t. other variables.