Determination of a Subset of Links for Sensor Installation to Infer Network Traffic Flow Information

Information on link flows in a vehicular traffic network is critical for developing long-term planning and/or short-term operational management strategies. In the early literature, most studies to develop such strategies typically assume the availability of link traffic information on all network links, either through manual survey or advanced traffic sensor technologies. In practical applications, this assumption is generally unrealistic due to budgetary constraints. It motivates the need to estimate flows on all links of a traffic network based on the measurement of link flows on a subset of links with suitably equipped sensors. This study, addressed from a budgetary planning perspective, seeks to identify the smallest subset of links in a network on which to locate sensors that enables the accurate estimation of traffic flows on all links of the network under steady-state conditions. Here, steady-state implies that the link capacities, link flows, and the origin-destination demand rates are time invariant. A "basis link" method is proposed to determine the locations of vehicle sensors, by using the link-path incidence matrix to express the network structure and then identifying its basis in a matrix algebra context. The theoretical background and mathematical properties of the proposed method are elaborated. The conditions under which a unique solution exists for the basis are also illustrated. The approach is useful for deploying long-term planning and link-based applications in traffic networks.