Synergistic sensor location for link flow inference without path enumeration: A node-based approach

Sensors are becoming increasingly critical elements in contemporary transportation systems, gathering essential (real-time) traffic information for the planning, management and control of these complex systems. In a recent paper, Hu, Peeta and Chu introduced the interesting problem of determining the smallest subset of links in a traffic network for counting sensor installation, in such a way that it becomes possible to infer the flows on all remaining links. The problem is particularly elegant because of its limited number of assumptions. Unfortunately, path enumeration was required, which – as recognized by the authors – is infeasible for large-scale networks without further simplifying assumptions (that would destroy the assumption-free nature of the problem). In this paper, we present a reformulation of this link observability problem, requiring only node enumeration. Using this node-based approach, we prove a conjecture made by Hu, Peeta and Chu by deriving an explicit relationship between the number of nodes and links in a transportation network, and the minimum number of sensors to install in order to be able to infer all link flows. In addition, we demonstrate how the proposed method can be employed for road networks that already have sensors installed on them. Numerical examples are presented throughout.