Observability quantification of public transportation systems with heterogeneous data sources: An information-space projection approach based on discretized space-time network flow models

Focusing on how to quantify system observability in terms of different interested states, this paper proposes a modeling framework to systemically account for the multi-source sensor information in public transportation systems. By developing a system of linear equations and inequalities, an information space is generated based on the available data from heterogeneous sensor sources. Then, a number of projection functions are introduced to match the relation between the unique information space and different system states of interest, such as, the passenger flow/density on the platform or in the vehicle at specific time intervals, the path flow of each origin-destination pair, the earning collected from the tickets to different operation companies etc., in urban rail transit systems as our study object. Their corresponding observability represented by state estimate uncertainties is further quantified by calculating its maximum feasible state range in proposed space-time network flow models. All of proposed models are solved as linear programming models by Dantzig–Wolfe decomposition, and a k-shortest-path-based approximation approach is also proposed to solve our models in large-scale networks. Finally, numerical experiments are conducted to demonstrate our proposed methodology and algorithms.